## CryptoDB

### Papers from CRYPTO 2024

**Year**

**Venue**

**Title**

2024

CRYPTO

$k$-SUM in the Sparse Regime: Complexity and Applications
Abstract

In the average-case k-SUM problem, given r integers chosen uniformly at random from {0,\dots,M-1}, the objective is to find a ``solution'' set of k numbers that sum to 0 modulo M. In the dense regime of M <= r^k, where solutions exist with high probability, the complexity of these problems is well understood. Much less is known in the sparse regime of M >> r^k, where solutions are unlikely to exist.
Motivated by applications to cryptography, we initiate the study of the sparse regime for k-SUM and its variant k-XOR, especially their planted versions, where a random solution is planted in a randomly generated instance and has to be recovered. We provide evidence for the hardness of these problems and show applications to constructing public-key encryption schemes. Our contributions are summarized below.
Complexity: We study the complexity of these problems in the sparse regime and show:
- Conditional Lower Bounds: Assuming established conjectures about the hardness of average-case (non-planted) k-SUM/k-XOR when M = r^k, we provide non-trivial lower bounds on the running time of algorithms for planted k-SUM when r^k <= M <= r^{2k}.
- Hardness Amplification: We show that for any M \geq r^k, if an algorithm running in time T solves planted k-SUM/k-XOR with success probability Omega(1/polylog(r)), then there is an algorithm running in time Otilde(T) that solves it with probability (1-o(1)).
This enables us to use even relatively mild hardness of k-SUM/k-XOR in our cryptographic constructions. Our primary technical contribution is the proof of this result, which departs significantly from existing approaches to hardness amplification.
- New Reductions and Algorithms: We provide reductions for k-SUM/k-XOR from search to decision, as well as worst-case and average-case reductions to the Subset Sum problem from k-SUM. Additionally, we present a new algorithm for average-case k-XOR that is faster than known worst-case algorithms at low densities.
Applications: We show that by additionally assuming mild hardness of k-XOR, we can construct Public Key Encryption (PKE) from a weaker variant of the Learning Parity with Noise (LPN) problem than was known before. In particular, such LPN hardness does not appear to imply PKE on its own -- this suggests that k-XOR/k-SUM can be used to bridge ``minicrypt'' and ``cryptomania'' in some cases. We are optimistic that this technique will find other applications in cryptography

2024

CRYPTO

10-Party Sublinear Secure Computation from Standard Assumptions
Abstract

Secure computation enables mutually distrusting parties to jointly compute a function on their secret inputs, while revealing nothing beyond the function output. A long-running challenge is understanding the required communication complexity of such protocols, in particular, when communication can be sublinear in the circuit representation size of the desired function. While several techniques have demonstrated the viability of sublinear secure computation in the two-party setting, known methods for the corresponding multi-party setting rely either on fully homomorphic encryption, non-standard hardness assumptions, or are limited to a small number of parties. In this work, we expand the study of multi-party sublinear secure computation by demonstrating sublinear-communication 10-party computation from various combinations of standard hardness assumptions. In particular, our contributions show:
- 8-party homomorphic secret sharing under the hardness of (DDH or DCR), the superpolynomial hardness of LPN, and the existence of constant-depth pseudorandom generators;
- A general framework for achieving (N+2)-party sublinear secure computation assuming N-party homomorphic secret sharing.
Together, our constructions imply the existence of a 10-party MPC protocol with sublinear computation. At the core of our techniques lies a novel series of computational approaches based homomorphic secret sharing.

2024

CRYPTO

A Formal Treatment of End-to-End Encrypted Cloud Storage
Abstract

Users increasingly store their data in the cloud, thereby benefiting from easy access, sharing, and redundancy. To additionally guarantee security of the outsourced data even against a server compromise, some service providers have started to offer end-to-end encrypted (E2EE) cloud storage. With this cryptographic protection, only legitimate owners can read or modify the data. However, recent attacks on the largest E2EE providers have highlighted the lack of solid foundations for this emerging type of service.
In this paper, we address this shortcoming by initiating the formal study of E2EE cloud storage. We give a formal syntax to capture the core functionality of a cloud storage system, capturing the real-world complexity of such a system’s constituent interactive protocols. We then define game-based security notions for confidentiality and integrity of a cloud storage system against a fully malicious server. We treat both selective and fully adaptive client compromises. Our notions are informed by recent attacks on E2EE cloud storage providers. In particular we show that our syntax is rich enough to capture the core functionality of MEGA and that recent attacks on it arise as violations of our security notions. Finally, we present an E2EE cloud storage system that provides all core functionalities and that is both efficient and provably secure with respect to our selective security notions. Along the way, we discuss challenges on the path towards bringing the security of cloud storage up to par with other end-to-end primitives, such as secure messaging and TLS.

2024

CRYPTO

A Modular Approach to Registered ABE for Unbounded Predicates
Abstract

Registered attribute-based encryption (Reg-ABE), introduced by Hohenberger et.al. (Eurocrypt'23), emerges as a pivotal extension of attribute-based encryption (ABE), aimed at mitigating the key-escrow problem. Although several Reg-ABE schemes with black-box use of cryptography have been proposed so far, there remains a significant gap in the class of achievable predicates between vanilla ABE and Reg-ABE. To narrow this gap, we propose a modular framework for constructing Reg-ABE schemes for a broader class of predicates. Our framework is a Reg-ABE analog of the predicate transformation framework for ABE introduced by Attrapadung (Eurocrypt'19) and later refined by Attrapadung and Tomida (Asiacrypt'20) to function under the standard MDDH assumption.
As immediate applications, our framework implies the following new Reg-ABE schemes under the standard MDDH assumption:
\begin{itemize}
\item the first Reg-ABE scheme for (non-)monotone span programs with the traditional completely unbounded property.
\item the first Reg-ABE scheme for general non-monotone span programs (also with the completely unbounded property) as defined in the case of vanilla ABE by Attrapadung and Tomida (Asiacrypt'20).
\end{itemize}
Here, the term ``completely unbounded'' signifies the absence of restrictions on attribute sets for users and policies associated with ciphertexts.
From a technical standpoint, we first substantially modify pair encoding schemes (PES), originally devised for vanilla ABE by Attrapadung (Eurocrypt'14), to make them compatible with Reg-ABE. Subsequently, we present a series of predicate transformations through which we can construct complex predicates, particularly those with an ``unbounded'' characteristic, starting from simple ones. Finally, we define new properties of PES necessary for constructing Reg-ABE schemes and prove that these properties are preserved through the transformations. This immediately implies that we can obtain Reg-ABE schemes for any predicates derived via predicate transformations.

2024

CRYPTO

A Modular Approach to Unclonable Cryptography
Abstract

We explore a new pathway to designing unclonable cryptographic primitives. We propose a new notion called unclonable puncturable obfuscation (UPO) and study its implications for unclonable cryptography. Using UPO, we present modular (and in some cases, arguably, simple) constructions of many primitives in unclonable cryptography, including, public-key quantum money, quantum copy-protection for many classes of functionalities, unclonable encryption, and single-decryption encryption.
Notably, we obtain the following new results assuming the existence of UPO:
1. We show that any cryptographic functionality can be copy-protected as long as this functionality satisfies a notion of security, which we term puncturable security. Prior feasibility results focused on copy-protecting specific cryptographic functionalities.
2. We show that copy-protection exists for any class of evasive functions as long as the associated distribution satisfies a preimage-sampleability condition. Prior works demonstrated copy-protection for point functions, which follows as a special case of our result.
We put forward a candidate construction of UPO and prove two notions of security, each based on the existence of (post-quantum) sub-exponentially secure indistinguishability obfuscation and one-way functions, the quantum hardness of learning with errors, and a new conjecture called simultaneous inner product conjecture.

2024

CRYPTO

A Systematic Study of Sparse LWE
Abstract

In this work, we introduce the sparse LWE assumption, an assumption that draws inspiration from both Learning with Errors (Regev JACM 10) and Sparse Learning Parity with Noise (Alekhnovich FOCS 02). Exactly like LWE, this assumption posits indistinguishability of $(\mathbf{A}, \mathbf{s}\mathbf{A}+\mathbf{e} \mod p)$ from $(\mathbf{A}, \mathbf{u})$ for a random $\mathbf{u}$ where the secret $\mathbf{s}$, and the error vector $\mathbf{e}$ is generated exactly as in LWE. However, exactly like sparse LPN the coefficient matrix $\mathbf{A}$ is chosen randomly from $\mathbb{Z}^{n\times m}_{p}$ so that each column has Hamming weight exactly $k$ for some small $k$. We study the problem in the regime where $k$ is a constant or polylogarithmic. The primary motivation for proposing this assumption is efficiency. Compared to LWE, the samples can be computed and stored with roughly $O(n/k)$ factor improvement in efficiency. Our results can be summarized as:
\begin{itemize}
\item {\bf Foundations:} We show several properties of sparse LWE samples, including: 1) The hardness of LWE/LPN with dimension $k$ implies the hardness of sparse LWE/LPN with sparsity $k$ and arbitrary dimension $n \geq k$. 2) When the number of samples $m=\Omega(n \log p)$, length of the shortest vector of a lattice spanned by rows of a random sparse matrix is large, close to that of a random dense matrix of the same dimension (up to a small constant factor). 3) Trapdoors with small polynomial norm exist for random sparse matrices with dimension $n \times m = O(n \log p)$. 4) Efficient algorithms for sampling such matrices together with trapdoors when the dimension is $n \times m = \tilde{O}(n^2)$.
\item {\bf Cryptanalysis:} We examine the suite of algorithms that have been used to break LWE and sparse LPN. While naively many of the attacks that apply to LWE do not exploit sparsity, we consider natural extensions that make use of sparsity. We propose a model to capture all these attacks. Using this model we suggest heuristics on how to identify concrete parameters. Our initial cryptanalysis suggests that concretely sparse LWE with a modest $k$ and slightly bigger dimension than LWE will satisfy similar level of security as LWE with similar parameters.
\item {\bf Applications:} We show that the hardness of sparse LWE implies very efficient homomorphic encryption schemes for low degree computations. We obtain the first secret key Linearly Homomorphic Encryption (LHE) schemes with {\em slightly super-constant}, or even {\em constant}, overhead, which further has applications to private information retrieval, private set intersection, etc. We also obtain secret key homomorphic encryption for arbitrary constant-degree polynomials with slightly super-constant, or constant, overhead.
\end{itemize}
We stress that our results are preliminary. However, our results make a strong case for further investigation of sparse LWE.

2024

CRYPTO

Accelerating SLH-DSA by Two Orders of Magnitude with a Single Hash Unit
Abstract

We report on efficient and secure hardware implementation techniques for the FIPS 205 SLH-DSA Hash-Based Signature Standard. We demonstrate that very significant overall performance gains can be obtained from hardware that optimizes the padding formats and iterative hashing processes specific to SLH-DSA. A prototype implementation, SLotH, contains Keccak/SHAKE, SHA2-256, and SHA2-512 cores and supports all 12 parameter sets of SLH-DSA. SLotH also supports side-channel secure PRF computation and Winternitz chains. SLotH drivers run on a small RISC-V control core, as is common in current Root-of-Trust (RoT) systems.
The new features make SLH-DSA on SLotH many times faster compared to similarly-sized general-purpose hash accelerators. Compared to unaccelerated microcontroller implementations, the performance of SLotH's SHAKE variants is up to 300× faster; signature generation with 128f parameter set is is 4,903,978 cycles, while signature verification with 128s parameter set is only 179,603 cycles. The SHA2 parameter sets have approximately half of the speed of SHAKE parameter sets. We observe that the signature verification performance of SLH-DSA's ``s'' parameter sets is generally better than that of accelerated ECDSA or Dilithium on similarly-sized RoT targets. The area of the full SLotH system is small, from 63 kGE (SHA2, Cat 1 only) to 155 kGe (all parameter sets). Keccak Threshold Implementation adds another 130 kGE.
We provide sensitivity analysis of SLH-DSA in relation to side-channel leakage. We show experimentally that an SLH-DSA implementation with CPU hashing will rapidly leak the SK.seed master key. We perform a 100,000-trace TVLA leakage assessment with a protected SLotH unit.

2024

CRYPTO

Accountability in Threshold Decryption via Threshold Traitor Tracing
Abstract

A $t$-out-of-$n$ threshold decryption system assigns key shares to $n$ parties so that any $t$ of them can decrypt a well-formed ciphertext.
Existing threshold decryption systems are not secure when these parties are rational actors:
an adversary can offer to pay the parties for their key shares.
The problem is that a quorum of $t$~parties, working together, can sell the adversary a decryption key that reveals nothing about the identity of the traitor parties.
This provides a risk-free profit for the parties since there is no accountability for their misbehavior --- the information they sell to the adversary reveals nothing about their identity.
This behavior can result in a complete break in many applications of threshold decryption,
such as encrypted mempools, private voting, and sealed-bid auctions.
In this work we propose a solution to this problem.
Suppose a quorum of~$t$ or more parties construct a decoder algorithm~$D(\cdot)$ that takes as input a ciphertext and outputs the corresponding plaintext or $\bot$. They sell~$D$ to the adversary.
Our threshold decryption systems are equipped with a tracing algorithm that can trace~$D$ to members of the quorum that created it.
The tracing algorithm is only given blackbox access to~$D$ and will identify some members of the misbehaving quorum.
The parties can then be held accountable, which may discourage them from selling the decoder~$D$ in the first place.
Our starting point is standard (non-threshold) traitor tracing, where $n$ parties each holds a secret key.
Every party can decrypt a well-formed ciphertext on its own.
However, if a subset of parties ${\cal J} \subseteq [n]$ collude to create a pirate decoder $D(\cdot)$ that can decrypt well-formed ciphertexts, then it is possible to trace $D$ to at least one member of ${\cal J}$ using only blackbox access to the decoder~$D$.
In this work we develop the theory of traitor tracing for threshold decryption, where now only a subset ${\cal J} \subseteq [n]$ of~$t$ or more parties can collude to create a pirate decoder $D(\cdot)$.
This problem has recently become quite important due to the real-world deployment of threshold decryption in encrypted mempools, as we explain in the paper.
While there are several non-threshold traitor tracing schemes that we can leverage, adapting these constructions to the threshold decryption settings requires new cryptographic techniques.
A $t$-out-of-$n$ threshold decryption system assigns key shares to $n$ parties
so that any $t$ of them can decrypt a well-formed ciphertext.
Existing threshold decryption systems are {\em not secure}
when these parties are rational actors:
an adversary can offer to pay the parties for their key shares.
The problem is that a quorum of $t$~parties, working together,
can sell the adversary a decryption key
that reveals nothing about the identity of the traitor parties.
This provides a risk-free profit for the parties
since there is no accountability for their misbehavior ---
the information they sell to the adversary
reveals nothing about their identity.
This behavior can result in a complete break
in many applications of threshold decryption,
such as encrypted mempools, private voting, and sealed-bid auctions.
In this work we propose a solution to this problem.
Suppose a quorum of~$t$ or more parties construct a
decoder algorithm~$D(\cdot)$ that takes as input a ciphertext
and outputs the corresponding plaintext or $\bot$.
They sell~$D$ to the adversary.
Our threshold decryption systems are equipped with a tracing algorithm
that can trace~$D$ to members of the quorum that created it.
The tracing algorithm is only given blackbox access to~$D$ and will
identify some members of the misbehaving quorum.
The parties can then be held accountable,
which may discourage them from selling the decoder~$D$ in the first place.
Our starting point is standard (non-threshold) traitor tracing,
where $n$ parties each holds a secret key.
Every party can decrypt a well-formed ciphertext on its own.
However, if a subset of parties ${\cal J} \subseteq [n]$ collude to create a
pirate decoder $D(\cdot)$ that can decrypt well-formed ciphertexts,
then it is possible to trace $D$ to at least one member of ${\cal J}$
using only blackbox access to the decoder~$D$.
In this work we develop the theory of traitor tracing
for threshold decryption,
where now only a subset ${\cal J} \subseteq [n]$ of~$t$ or more parties
can collude to create a pirate decoder $D(\cdot)$.
This problem has recently become quite important
due to the real-world deployment of threshold decryption in encrypted mempools,
as we explain in the paper.
While there are several non-threshold traitor tracing schemes
that we can leverage,
adapting these constructions to the threshold decryption settings requires new cryptographic techniques.
We present a number of constructions for traitor tracing for threshold decryption,
and note that much work remains to explore the large design space.

2024

CRYPTO

Adaptive Security in SNARGs via iO and Lossy Functions
Abstract

We construct an adaptively sound SNARGs in the plain model with CRS
relying on the assumptions of (subexponential) indistinguishability obfuscation (iO),
subexponential one-way functions and a notion of lossy functions we call
length parameterized lossy functions. Length parameterized lossy functions take
in separate security and input length parameters and have the property that the
function image size in lossy mode depends only on the security parameter.
We then show a novel way of constructing such functions from the Learning with
Errors (LWE) assumption.
Our work provides an alternative path towards achieving adaptively secure
SNARGs from the recent work of Waters and Wu. Their work required
the use of (essentially) perfectly re-randomizable one way functions (in addition to
obfuscation). Such functions are only currently known to be realizable from
assumptions such as discrete log or factoring that are known to not hold
in a quantum setting.

2024

CRYPTO

Adaptively Secure 5 Round Threshold Signatures from MLWE/MSIS and DL with Rewinding
Abstract

T-out-of-N threshold signatures have recently seen a renewed interest, with various types now available, each offering different tradeoffs. However, one property that has remained elusive is \emph{adaptive} security. When we target thresholdizing existing efficient signatures schemes based on the Fiat-Shamir paradigm such as Schnorr, the elusive nature becomes clear. This class of signature schemes typically rely on the forking lemma to prove unforgeability. That is, an adversary is \emph{rewound and run twice} within the security game. Such a proof is at odds with adaptive security, as the reduction must be ready to answer $2(T - 1)$ secret key shares in total, implying that it can reconstruct the full secret key. Indeed, prior works either assumed strong idealized models such as the algebraic group model (AGM) or modified the underlying signature scheme so as not to rely on rewinding based proofs.
In this work, we propose a new proof technique to construct adaptively secure threshold signatures for existing rewinding-based Fiat-Shamir signatures. As a result, we obtain the following:
1. The first adaptively secure 5 round lattice-based threshold signature under the MLWE and MSIS assumptions in the ROM. The resulting signature is a standard signature of Raccoon, a lattice-based signature scheme by del Pino et al., submitted to the additional NIST call for proposals.
2. The first adaptively secure 5 round threshold signature under the DL assumption in the ROM. The resulting signature is a standard Schnorr signature. To the best of our knowledge, this is the first adaptively secure threshold signature based on DL even assuming stronger models like AGM.
Our work is inspired by the recent statically secure lattice-based 3 round threshold signature by del Pino et al. (Eurocrypt~2024) based on Raccoon. While they relied on so-called one-time additive masks to solve lattice specific issues, we notice that these masks can also be a useful tool to achieve adaptive security. At a very high level, we use these masks throughout the signing protocol to carefully control the information the adversary can learn from the signing transcripts. Intuitively, this allows the reduction to return a total of $2(T-1)$ \emph{randomly sampled} secret key shares to the adversary consistently and without being detected, resolving the above paradoxical situation. Lastly, by allowing the parties to maintain a simple state, we can compress our 5 round schemes into 4 rounds.

2024

CRYPTO

Adaptively Secure BLS Threshold Signatures from DDH and co-CDH
Abstract

Threshold signature is one of the most important cryptographic primitives in distributed systems. A popular choice of threshold signature scheme is the BLS threshold signature introduced by Boldyreva (PKC'03). Some attractive properties of Boldyreva's threshold signature are that the signatures are unique and short, the signing process is non-interactive, and the verification process is identical to that of non-threshold BLS. These properties have resulted in its practical adoption in several decentralized systems. However, despite its popularity and wide adoption, up until recently, the Boldyreva scheme has been proven secure only against a static adversary. Very recently, Bacho and Loss (CCS'22) presented the first proof of adaptive security for the Boldyreva scheme, but they have to rely on strong and non-standard assumptions such as the hardness of one-more discrete log (OMDL) and the Algebraic Group Model~(AGM). In this paper, we present the first adaptively secure threshold BLS signature scheme that relies on the hardness of DDH and co-CDH in asymmetric pairing groups in the Random Oracle Model~(ROM). Our signature scheme also has non-interactive signing, compatibility with non-threshold BLS verification, and practical efficiency like Boldyreva's scheme. These properties make our protocol a suitable candidate for practical adoption with the added benefit of provable adaptive security.

2024

CRYPTO

Adaptively Sound Zero Knowledge SNARKs for UP
Abstract

We study succinct non-interactive arguments (SNARGs) and succinct non-interactive arguments of knowledge (SNARKs) for the class $\mathsf{UP}$ in the reusable designated verifier model. $\mathsf{UP}$ is an expressive subclass of $\mathsf{NP}$ consisting of all $\mathsf{NP}$ languages where each instance has at most one witness; a designated verifier SNARG (dvSNARG) is one where verification of the SNARG proof requires a private verification key; and such a dvSNARG is reusable if soundness holds even against a malicious prover with oracle access to the (private) verification algorithm.
Our main results are as follows.
(1) A reusably and adaptively sound zero-knowledge (zk) dvSNARG for $\mathsf{UP}$, from subexponential LWE and evasive LWE (a relatively new but popular variant of LWE). Our SNARGs achieve very short proofs of length $(1 + o(1)) \cdot \lambda$ bits for $2^{-\lambda}$ soundness error.
(2) A generic transformation that lifts any ``Sahai-Waters-like'' (zk) SNARG to an adaptively sound (zk) SNARG, in the \emph{designated-verifier} setting. In particular, this shows that the Sahai-Waters SNARG for $\mathsf{NP}$ is adaptively sound in the designated verifier setting, assuming subexponential hardness of the underlying assumptions. The resulting SNARG proofs have length $(1 + o(1)) \cdot \lambda$ bits for $2^{-\lambda}$ soundness error. Our result sidesteps the Gentry-Wichs barrier for adaptive soundness by employing an exponential-time security reduction.
(3) A generic transformation that lifts any adaptively sound (zk) SNARG for $\mathsf{UP}$ to an adaptively sound (zk) SNARK for $\mathsf{UP}$, while preserving zero-knowledge. The resulting SNARK achieves the strong notion of black-box extraction. There are barriers to achieving such SNARKs for all of $\mathsf{NP}$ from falsifiable assumptions, so our restriction to $\mathsf{UP}$ is, in a sense, necessary.
Applying (3) to our SNARG for $\mathsf{UP}$ from evasive LWE (1), we obtain a reusably and adaptively sound designated-verifier zero-knowledge SNARK for $\mathsf{UP}$ from subexponential LWE and evasive LWE. Moreover, applying both (2) and (3) to the Sahai-Waters SNARG, we obtain the same result from LWE, subexponentially secure one-way functions, and subexponentially secure indistinguishability obfuscation. Both constructions have succinct proofs of size $\mathsf{poly}(\secp).$ These are the first SNARK constructions (even in the designated-verifier setting) for a non-trivial subset of $\mathsf{NP}$ from (sub-exponentially) falsifiable assumptions.

2024

CRYPTO

Advancing Scalability in Decentralized Storage: A Novel Approach to Proof-of-Replication via Polynomial Evaluation
Abstract

Proof-of-Replication (PoRep) plays a pivotal role in decentralized storage networks, serving as a mechanism to verify that provers consistently store retrievable copies of specific data. While PoRep’s utility is unquestionable, its implementation in large-scale systems, such as Filecoin, has been hindered by scalability challenges. Most existing PoRep schemes, such as Fisch’s (Eurocrypt 2019), face an escalating number of challenges and growing computational overhead as the number of stored files increases.
This paper introduces a novel PoRep scheme distinctively tailored for expansive decentralized storage networks. At its core, our approach hinges on polynomial evaluation, diverging from the probabilistic checking prevalent in prior works. Remarkably, our design requires only a single challenge, irrespective of the number of files, ensuring both prover’s and verifier’s run-times remain manageable even as file counts soar.
Our approach introduces a paradigm shift in PoRep designs, offering a blueprint for highly scalable and efficient decentralized storage solutions.

2024

CRYPTO

Aggregating Falcon Signatures With LaBRADOR
Abstract

Several prior works have suggested to use non-interactive arguments of knowledge with short proofs to aggregate signatures of Falcon, which is part of the first post-quantum signatures selected for standardization by NIST. Especially LaBRADOR, based on standard structured lattice assumptions and published at CRYPTO'23, seems promising to realize this task. However, no prior work has tackled this idea in a rigorous way. In this paper, we thoroughly prove how to aggregate Falcon signatures using LaBRADOR. We start by providing the first complete knowledge soundness analysis for the non-interactive version of LaBRADOR. Here, the multi-round and recursive nature of LaBRADOR requires a complex and thorough analysis. For this purpose, we introduce the notion of predicate special soundness (PSS). This is a general framework for evaluating the knowledge error of complex Fiat-Shamir arguments of knowledge protocols in a modular fashion, which we believe to be of independent interest. We then explain the exact steps to take in order to adapt the non-interactive LaBRADOR proof system for aggregating Falcon signatures and provide concrete proof size estimates. Additionally, we formalize the folklore approach of obtaining aggregate signatures from the class of hash-then-sign signatures through arguments of knowledge.

2024

CRYPTO

Algebraic Structure of the Iterates of $\chi$
Abstract

We consider the map $\chi:\F_2^n\to\F_2^n$ for $n$ odd given by $y=\chi(x)$ with $y_i=x_i+x_{i+2}(1+x_{i+1})$, where the indices are computed modulo $n$. We suggest a generalization of the map $\chi$ which we call generalized $\chi$-maps. We show that these maps form an abelian group which is isomorphic to the group of units in $\F_2[X]/(X^{(n+1)/2})$. Using this isomorphism we easily obtain closed-form expressions for iterates of $\chi$ and explain their properties.

2024

CRYPTO

Amplification of Non-Interactive Zero Knowledge, Revisited
Abstract

In an (α,β)-weak non-interactive zero knowledge (NIZK), the soundness error is at most α and the zero-knowledge error is at most β. Goyal, Jain, and Sahai (CRYPTO 2019) stated that if α+β<1 for some constants α,β, then (α,β)-weak NIZK can be turned into fully-secure NIZK, assuming sub-exponentially-secure public-key encryption. Later, however, they have discovered a gap in their proof.
We revisit the problem of NIZK amplification:
– We amplify NIZK arguments assuming only polynomially-secure public-key encryption, for any constants α+β<1.
– We amplify NIZK proofs assuming only one-way functions, for any constants α+β<1.
– When the soundness error α is negligible to begin with, we can also amplify NIZK arguments assuming only one-way functions.
Our results take a different route than that of Goyal, Jain, and Sahai. They are based on the hidden-bits paradigm, and can be viewed as a reduction from NIZK amplification to the better understood problem of pseudorandomness amplification.

2024

CRYPTO

Attribute Based Encryption for Turing Machines from Lattices
Abstract

We provide the first attribute based encryption (ABE) scheme for Turing machines supporting unbounded collusions from lattice assumptions. In more detail, the encryptor encodes an attribute x together with a bound t on the machine running time and a message m into the ciphertext, the key generator embeds a Turing machine M into the secret key and decryption returns m if and only if M (x) = 1. Crucially, the input x and machine M can be of unbounded size, the time bound t can be chosen dynamically for each input and decryption runs in input specific time.
Previously the best known ABE for uniform computation supported only non-deterministic log space Turing machines (NL from pairings (Lin and Luo, Eurocrypt 2020). In the post-quantum regime, the state of the art supports non-deterministic finite automata from LWE in the symmetric key setting (Agrawal, Maitra and Yamada, Crypto 2019).
In more detail, our results are:
1. We construct the first ABE for NL from the LWE and evasive LWE assumptions. This yields the first (conjectured) post-quantum ABE for NL.
2. Relying on new and arguably natural assumptions which we call path LWE, evasive path LWE and circular tensor LWE, in addition to standard LWE, we construct ABE for all Turing machines.
Towards our ABE for Turing machines, we obtain the first CP-ABE for circuits of unbounded depth and size from the same assumptions – this may be of independent interest. At a high level, our path LWE assumption states that the joint distribution of specially constructed FHE and ABE encodings are pseudorandom. The evasive path LWE assumption incorporates path LWE into the celebrated evasive LWE assumption (Wee, Eurocrypt 2022 and Tsabary, Crypto 2022), while the circular tensor LWE assumption incorporates circularity into the tensor LWE (Wee, Eurocrypt 2022) assumption. We believe these assumptions provide an important new tool for encrypted computation and are likely to find other applications.

2024

CRYPTO

Bare PAKE: Universally Composable Key Exchange from just Passwords
Abstract

In the past three decades, an impressive body of knowledge has been built around secure and private password authentication. In particular, secure password-authenticated key exchange (PAKE) protocols require only minimal overhead over a classical Diffie-Hellman key exchange. PAKEs are also known to fulfill strong composable security guarantees that capture many password-specific concerns such as password correlations or password mistyping, to name only a few. However, to enjoy both round-optimality and strong security, applications of PAKE protocols must provide \emph{unique} session and participant identifiers. If such identifiers are not readily available, they must be agreed upon at the cost of additional communication flows, a fact which has been met with incomprehension among practitioners, and which hindered the adoption of provably secure password authentication in practice.
In this work, we resolve this issue by proposing a new paradigm for truly \emph{password-only} yet securely composable PAKE, called \emph{bare} PAKE. We formally prove that two prominent PAKE protocols, namely CPace and EKE, can be cast as bare PAKEs and hence do not require pre-agreement of anything else than a password. Our bare PAKE modeling further allows us to investigate a novel ``reusability'' property of PAKEs, i.e., whether $n^2$ pairwise keys can be exchanged from only $n$ messages, just as the Diffie-Hellman non-interactive key exchange can do in a public-key setting. As a side contribution, this add-on property of bare PAKEs leads us to observe that some previous PAKE constructions relied on unnecessarily strong, ``reusable'' building blocks. By showing that ``non-reusable'' tools suffice for standard PAKE, we open a new path towards round-optimal post-quantum secure password-authenticated key exchange.

2024

CRYPTO

BaseFold: Efficient Field-Agnostic Polynomial Commitment Schemes from Foldable Codes
Abstract

This works introduces BaseFold, a new field-agnostic Polynomial Commitment Scheme (PCS) for multilinear polynomials that has O(log^{2}(n)) verifier costs and O(n log n) prover time. An important application of a multilinear PCS is constructing Succinct Non-interactive Arguments (SNARKs) from multilinear polynomial interactive oracle proofs (PIOPs). Furthermore, field-agnosticism is a major boon to SNARK efficiency in applications that require (or benefit from) a certain field choice.
Our inspiration for BaseFold is the Fast Reed-Solomon Interactive-Oracle Proof of Proximity (FRI IOPP), which leverages two properties of Reed-Solomon (RS) codes defined over FFT-Friendly fields: O(n log n) encoding time, and a second property that we call foldability. We first introduce a generalization of the FRI IOPP that works over any foldable linear code in linear time. Second, we construct a new family of linear codes which we call random foldable codes, that are a special type of punctured Reed-Muller codes, and prove tight bounds on their minimum distance. Unlike
RS codes, our new codes are foldable and have O(n log n) encoding time over any sufficiently large field. Finally, we construct a new multilinear PCS by carefully interleaving our IOPP with the classical sumcheck protocol, which also gives a new multilinear PCS from FRI.
BaseFold is 2-3 times faster than prior multilinear PCS constructions from FRI when defined over the same finite field. More significantly, using Hyperplonk (Eurocrypt, 2022) as a multilinear PIOP backend for apples-to-apples comparison, we show that BaseFold results in a SNARK that has better concrete efficiency across a range of field choices than with any prior multilinear PCS in the literature. Hyperplonk with Basefold has a proof size that is more than 10 times smaller than Hyperplonk with Brakedown and its verifier is over 30 times faster for circuits with more than 2^{20} gates. Compared to FRI, Hyperplonk with Basefold retains efficiency over any sufficiently large field. For illustration, with BaseFold we can prove ECDSA signature verification over the secp256k1 curve more than 20 times faster than Hyperplonk with FRI and the verifier is also twice as fast. Proofs of signature verification have many useful applications, including offloading blockchain transactions and enabling anonymous credentials over the web.

2024

CRYPTO

Black-Box (and Fast) Non-Malleable Zero Knowledge
Abstract

Non-malleable zero-knowledge (NMZK), originally introduced in the seminal work of Dolev, Dwork, and Naor (STOC 91), is a fundamental concept for modeling the security of proof systems against man-in-the-middle attacks.
After 30 years of active research, Kim, Liang, and Pandey (CRYPTO 2022) presented the first efficient constant-round NMZK argument system based solely on symmetric-key cryptography. Their construction relies on a non-black-box use of the involved cryptographic primitives and on multiple executions of Ligero (CCS 2017) that affect both the round complexity and the computational efficiency of their protocol. Their work left open the natural important challenge of achieving NMZK using the underlying primitives only in a black-box fashion (regardless of the number of rounds and actual efficiency).
In this paper, we solve the aforementioned open problem by presenting the first NMZK argument system based on the black-box use of cryptographic primitives. Our work is optimal in the use of primitives since we only need one-way functions, and asymptotically optimal in the number of rounds since we only require a constant number of rounds. Our argument system is non-malleable with respect to the strong ``simulation-extractability'' flavor of non-malleability.
Furthermore, we also show that our construction can be efficiently instantiated in Minicrypt, significantly improving upon the work of Kim et al., both in terms of round complexity and computational efficiency.

2024

CRYPTO

CDS Composition of Multi-Round Protocols
Abstract

We revisit the Cramer, Damg{\aa}rd, Schoenmakers (CDS) approach for composing sigma protocols, and adapt it to a setting in which the underlying protocols have multiple rounds of interaction. The goal of CDS composition is to prove compound NP-relations by combining multiple ``atomic'' proof systems. Its key feature is that it interacts with the atomic proofs in a generic fashion, enabling simpler and more efficient implementation.
Recent developments in multi-round protocols call for the adaptation of CDS composition beyond its original scope, which not only was restricted to three-move protocols but in fact fails in the multi-round case, as well as in the composition of so-called $k$-special sound proofs.
We propose a new method for multi-round composition in the plain model, in a soundness preserving way and with an ``offline'' zero-knowledge simulation property. The need for handling arbitrary monotone access structures in $\mathsf{mNC}^1$, which is all Boolean function families represented by polynomial-size formulas over some fixed complete basis, leads us to identify a complexity theoretic problem of independent interest.
Prior to our work, multi-round composition was either restricted to the random oracle model, or worked only for argument systems, and moreover required heavy ``online'' zero-knowledge simulation.

2024

CRYPTO

Certifying Private Probabilistic Mechanisms
Abstract

In past years,
entire research communities have arisen to address concerns of privacy and fairness in data analysis.
At present, however, the public must trust that institutions will re-implement algorithms voluntarily to account for these social concerns.
Due to additional cost, widespread adoption is unlikely without effective legal enforcement.
A technical challenge for enforcement is that the methods proposed are often \emph{probabilistic mechanisms}, whose output must be drawn according to precise, and sometimes secret, distributions.
The Differential Privacy (DP) case is illustrative: if a cheating curator answers queries according to an overly-accurate mechanism, privacy violations could go undetected.
This raises our central question:
\textit{Can we efficiently certify the output of a probabilistic mechanism enacted by an untrusted party?}
To this end:
\begin{enumerate}
\item
We introduce two new notions: {\it Certified Probabilistic Mechanisms} (CPM) and \emph{Random Variable Commitment Schemes} (RVCS).
A CPM is an interactive protocol that forces a prover to enact a given probabilistic mechanism or be caught; importantly, the interaction does not reveal the mechanism's secret parameters.
An RVCS---a key primitive for constructing CPMs---is a commitment scheme where the verifier is convinced that the commitment is to an RV sampled according to an agreed-upon distribution, but learns nothing else.
\item
We instantiate the general notion of CPM for the special case of Certifying DP.
We build a lightweight, doubly-efficent interactive proof system to certify arbitrary-predicate counting queries released via the DP Binomial mechanism.
The construction relies on a commitment scheme with perfect hiding and additive homomorphic properties that can be used to release a broad class of queries about a committed database, constructed on top of Pedersen commitments.
\item
Finally, we demonstrate the immediate feasibility of Certified DP via a highly-efficient and scalable
prototype
implementation to answer counting queries of arbitrary predicates.
The mechanism is composed of an offline and online stage, where
the online phase allows for non-interactive certification of queries. For example, we show that CDP queries over a US Census Public Use Microdata Sample (PUMS)~\cite{census-pums} ($n=7000$) can be completed in only 1.6~ms and verified in just \emph{38~$\mu$s}. Our implementation is available in open source at \url{https://github.com/jlwatson/certified-dp}.

2024

CRYPTO

Cheater Identification on a Budget: MPC with Identifiable Abort from Pairwise MACs
Abstract

Cheater identification in secure multi-party computation (MPC) allows the honest parties to agree upon the identity of a cheating party, in case the protocol aborts. In the context of a dishonest majority, this becomes especially critical, as it serves to thwart denial-of-service attacks and mitigate known impossibility results on ensuring fairness and guaranteed output delivery.
In this work, we present a new, lightweight approach to achieving identifiable abort in dishonest majority MPC. We avoid all of the heavy machinery used in previous works, instead relying on a careful combination of lightweight detection mechanisms and techniques from state-of-the-art protocols secure with (non-identifiable) abort.
At the core of our construction is a homomorphic, multi-receiver commitment scheme secure with identifiable abort. This commitment scheme can be constructed from cheap vector oblivious linear evaluation protocols based on learning parity with noise. To support cheater identification, we design a general compilation technique, similar to a compiler of Ishai et al. (Crypto 2014), but avoid its requirement for adaptive security of the underlying protocol. Instead, we rely on a different (and seemingly easier to achieve) property we call online extractability, which may be of independent interest. Our MPC protocol can be viewed as a version of the BDOZ MPC scheme (Bendlin et al., Eurocrypt 2011) based on pairwise information-theoretic MACs, enhanced to support cheater identification and a highly efficient preprocessing phase, essentially as efficient as the non-identifiable protocol of Le Mans (Rachuri \& Scholl, Crypto 2022).

2024

CRYPTO

Circuit ABE with poly(depth, λ)-sized Ciphertexts and Keys from Lattices
Abstract

We present new lattice-based attribute-based encryption (ABE) and
laconic function evaluation (LFE) schemes for circuits with *sublinear*
ciphertext overhead. For depth $d$ circuits over $\ell$-bit inputs, we obtain
* an ABE with ciphertext and secret key size $O(1)$;
* a LFE with ciphertext size $\ell + O(1)$ and digest size $O(1)$;
* an ABE with public key and ciphertext size $O(\ell^{2/3})$ and
secret key size $O(1)$,
where $O(\cdot)$ hides $\poly(d,\lambda)$ factors. The first two
results achieve almost optimal ciphertext and secret key / digest
sizes, up to the $\poly(d)$ dependencies. The security of our schemes
relies on $\ell$-succinct LWE, a falsifiable assumption which is
implied by evasive LWE. At the core of our results is a new technique
for compressing LWE samples $s(A-x \otimes G)$ as well
as the matrix $A$.

2024

CRYPTO

Collision Resistance from Multi-Collision Resistance for all Constant Parameters
Abstract

A {\em $t$-multi-collision-resistant hash function} ($t$-MCRH) is a family of shrinking functions for which it is computationally hard to find~$t$ distinct inputs mapped to the same output by a function sampled from this family. Several works have shown that $t$-MCRHs are sufficient for many of the applications of collision-resistant hash functions (CRHs), which correspond to the special case of~$t = 2$.
An important question is hence whether $t$-MCRHs for $t > 2$ are fundamentally weaker objects than CRHs. As a first step towards resolving this question, Rothblum and Vasudevan (CRYPTO '22) recently gave non-black-box constructions of infinitely-often secure CRHs from $t$-MCRHs for $t \in \{3,4\}$ assuming the MCRH is sufficiently shrinking. Earlier on, Komargodski and Yogev (CRYPTO '18) also showed that $t$-MCRHs for any constant~$t$ imply the weaker notion of a {\em distributional} CRH.
In this paper, we remove the limitations of prior works, and completely resolve the question of the power of $t$-MCRHs for constant $t$ in the infinitely-often regime, showing that the existence of such a function family always implies the existence of an infinitely-often secure CRH. As in the works mentioned above, our proof is non-black-box and non-constructive. We further give a new domain extension result for MCRHs that enables us to show that the underlying MCRH need only have arbitrarily small linear shrinkage (mapping $(1 + \epsilon)n$ bits to $n$ bits for any fixed $\epsilon > 0$) to imply the existence of CRHs.

2024

CRYPTO

Compact Key Storage: A Modern Approach to Key Backup and Delegation
Abstract

End-to-End (E2E) encrypted messaging, which prevents even the service provider from learning communication contents, is gaining popularity. Since users care about maintaining access to their data even if their devices are lost or broken or just replaced, these systems are often paired with cloud backup solutions: typically, the user will encrypt its messages with a fixed key, and upload the ciphertexts to the server. Unfortunately, this naive solution has many drawbacks. First, it often undermines the fancy security guarantees of the core application, such as forward-secrecy (FS) and post-compromise security (PCS), in case the single backup key is compromised. Second, they are wasteful for backing up conversations in large groups, where many users are interested in backing up the same sequence of messages.
Instead, we formalize a new primitive called Compact Key Storage (CKS) as the "right" solution to this problem. Such CKS scheme allows a mutable set of parties to delegate to a server storage of an increasing set of keys, while each client maintains only a small state. Clients update their state as they learn new keys (maintaining PCS), or whenever they want to forget keys (achieving FS), often without the need to interact with the server. Moreover, access to the keys (or some subset of them) can be efficiently delegated to new group members, who all efficiently share the same server's storage.
We carefully define syntax, correctness, privacy, and integrity of CKS schemes, and build two efficient schemes provably satisfying these notions. Our line scheme covers the most basic "all-or-nothing" flavor of CKS, where one wishes to compactly store and delegate the entire history of past secrets. Thus, new users enjoy the efficiency and compactness properties of the CKS only after being granted access to the entire history of keys. In contrast, our interval scheme is only slightly less efficient but allows for finer-grained access, delegation, and deletion of past keys.

2024

CRYPTO

Compressing Unit-Vector Correlations via Sparse Pseudorandom Generators
Abstract

A unit-vector (UV) correlation is an additive secret-sharing of a vector of length B that contains 1 in a secret random position and 0's elsewhere. UV correlations are a useful resource for many cryptographic applications, including low-communication secure multiparty computation and multi-server private information retrieval. However, current practical methods for securely generating UV correlations involve a significant communication cost per instance, and become even more expensive when requiring security against malicious parties.
In this work, we present a new approach for constructing a pseudorandom correlation generator (PCG) for securely generating n independent instances of UV correlations of any polynomial length B. Such a PCG compresses the n UV instances into correlated seeds whose length is sublinear in the description size n log B. Our new PCGs apply in both the honest-majority and dishonest-majority settings, and are based on a variety of assumptions. In particular, in the honest-majority case they only require "unstructured" assumptions. Our PCGs give rise to secure end-to-end protocols for generating n instances of UV correlations with o(n) bits of communication. This applies even to an authenticated variant of UV correlations, which is useful for security against malicious parties. Unlike previous theoretical solutions, some instances of our PCGs offer good concrete efficiency.
Our technical approach is based on combining a low-degree sparse pseudorandom generator, mapping a sparse seed to a pseudorandom sparse output, with homomorphic secret sharing for low-degree polynomials. We then reduce such sparse PRGs to local PRGs over large alphabets, and explore old and new approaches for maximizing the stretch of such PRGs while minimizing their locality.
Finally, towards further compressing the PCG seeds, we present a new PRG-based construction of a multiparty distributed point function (DPF), whose outputs are degree-1 Shamir-shares of a secret point function. This result is independently motivated by other DPF applications.

2024

CRYPTO

Computation Efficient Structure-Aware PSI From Incremental Function Secret Sharing
Abstract

Structure-Aware Private Set Intersection (sa-PSI), recently introduced by Garimella et al. (Crypto'22), is a PSI variant where Alice's input set $S_A$ has a publicly known structure (for example, interval, ball or union of balls) and Bob's input $S_B$ is an unstructured set of elements. Prior work achieves sa-PSI where the communication cost only scales with the description size of $S_A$ instead of the set cardinality. However, the computation cost remains linear in the cardinality of $S_A$, which could be prohibitively large.
In this work, we present a new semi-honest sa-PSI framework where both computation and communication costs only scale with the description size of $S_A$. Our main building block is a new primitive that we introduce called Incremental Boolean Function Secret Sharing (ibFSS), which is a generalization of FSS that additionally allows for evaluation on input prefixes. We formalize definitions and construct a weak ibFSS for a $d$-dimensional ball with $\ell_\infty$ norm, which may be of independent interest. Independently, we improve spatial hashing techniques (from prior work) when $S_A$ has structure union of $d$-dimensional balls in $(\{0,1\}^u)^d$, each of diameter $\delta$, from $O(u \cdot d \cdot (\log \delta)^d)$ to $O(\log \delta \cdot d)$ in terms of both computation and communication. Finally, we resolve the following open questions from prior work with communication and computation scaling with the description size of the structured set.
- Our PSI framework can handle a union of overlapping structures, while prior work strictly requires a disjoint union.
- We have a new construction that enables Bob with unstructured input $S_B$ to learn the intersection.
- We extend to a richer class of functionalities like structure-aware PSI Cardinality and PSI-Sum of associated values.

2024

CRYPTO

Concretely Efficient Lattice-based Polynomial Commitment from Standard Assumptions
Abstract

Polynomial commitment is a crucial cryptographic primitive in constructing zkSNARKs. Most practical constructions to date are either vulnerable against quantum adversaries or lack homomorphic properties, which are essential for recursive proof composition and proof batching. Recently, lattice-based constructions have drawn attention for their potential to achieve all the desirable properties, though they often suffer from concrete inefficiency or rely on newly introduced assumptions requiring further cryptanalysis.
In this paper, we propose a novel construction of a polynomial commitment scheme based on standard lattice-based assumptions. Our scheme achieves a square-root proof size and verification complexity, ensuring concrete efficiency in proof size, proof generation, and verification. Additionally, it features a transparent setup and publicly verifiability.
When compared with Brakedown (CRYPTO 2023), a recent code-based construction, our scheme offers comparable performance across all metrics. Furthermore, its proof size is approximately 4.1 times smaller than SLAP (EUROCRYPT 2024), a recent lattice-based construction.

2024

CRYPTO

Constant-Round Arguments for Batch-Verification and Bounded-Space Computations from One-Way Functions
Abstract

What are the minimal cryptographic assumptions that suffice for constructing efficient argument systems, and for which tasks? Recently, Amit and Rothblum [STOC 2023] showed that one-way functions suffice for constructing constant-round arguments for bounded-depth computations. In this work we ask: what other tasks have efficient argument systems based only on one-way functions? We show two positive results:
First, we construct a new argument system for batch-verification of $k$ $UP$ statements ($NP$ statements with a unique witness) for witness relations that are verifiable in depth $D$.
Taking $M$ to be the length of a single witness, the communication complexity is $O(\log k) \cdot (M + k \cdot D \cdot n^{\sigma})$, where $\sigma > 0$ is an arbitrarily small constant. In particular, the communication is quasi-linear in the length of a single witness, so long as $k < M / (D \cdot n^{\sigma})$.
The number of rounds is constant and the honest prover runs in polynomial time given witnesses for all $k$ inputs' membership in the language.
Our second result is a constant-round doubly-efficient argument system for languages in P that are computable by bounded-space Turing machines. For this class of computations, we obtain an exponential improvement in the trade-off between the number of rounds and the (exponent of the) communication complexity, compared to known unconditionally sound protocols [Reingold, Rothblum and Rothblum, STOC 2016].

2024

CRYPTO

Cryptanalysis of Algebraic Verifiable Delay Functions
Abstract

Verifiable Delay Functions (VDF) are a class of cryptographic primitives aiming to guarantee a minimum computation time, even for an adversary with massive parallel computational power. They are useful in blockchain protocols, and several practical candidates have been proposed based on exponentiation in a large finite field: Sloth++, Veedo, MinRoot. The underlying assumption of these constructions is that computing an exponentiation x^e requires at least log2(e) sequential multiplications.
In this work, we analyze the security of these algebraic VDF candidates. In particular, we show that the latency of exponentiation can be reduced using parallel computation, against the preliminary assumptions.

2024

CRYPTO

Cryptanalysis of Lattice-Based Sequentiality Assumptions and Proofs of Sequential Work
Abstract

This work \emph{completely breaks} the sequentiality assumption (and broad generalizations thereof) underlying the candidate lattice-based proof of sequential work (PoSW) recently proposed by Lai and Malavolta at CRYPTO 2023.
In addition, it breaks an essentially identical variant of the PoSW, which differs from the original in only an arbitrary choice that is immaterial to the design and security proof (under the falsified assumption).
This suggests that whatever security the original PoSW may have is fragile, and further motivates the search for a construction based on a sound lattice-based assumption.
Specifically, for sequentiality parameter~$T$ and SIS parameters $n,q,m = n \log q$, the attack on the sequentiality assumption finds a solution of quasipolynomial norm $m^{\lceil{\log T}\rceil}$ (or norm $O(\sqrt{m})^{\lceil{\log T}\rceil}$ with high probability) in only \emph{logarithmic} $\tilde{O}_{n,q}(\log T)$ depth; this strongly falsifies the assumption that finding such a solution requires depth \emph{linear} in~$T$.
(The $\tilde{O}$ notation hides polylogarithmic factors in the variables appearing in its subscript.)
Alternatively, the attack finds a solution of polynomial norm $m^{1/\varepsilon}$ in depth $\tilde{O}_{n,q}(T^{\varepsilon})$, for any constant $\varepsilon > 0$.
Similarly, the attack on the (slightly modified) PoSW constructs a valid proof in \emph{polylogarithmic} $\tilde{O}_{n,q}(\log^2 T)$ depth, thus strongly falsifying the expectation that doing so requires linear sequential work.

2024

CRYPTO

CryptAttackTester: high-assurance attack analysis
Abstract

Quantitative analyses of the costs of cryptographic attack algorithms play a central role in comparing cryptosystems, guiding the search for improved attacks, and deciding which cryptosystems to standardize. Unfortunately, these analyses often turn out to be wrong. Sometimes errors are not caught until years later.
This paper introduces CryptAttackTester (CAT), a software framework for high-assurance quantification of attack effectiveness. CAT enforces complete definitions of attack algorithms all the way down through the model of computation, enforces complete definitions of probability predictions and cost predictions all the way down through the cost metric, and systematically tests the predictions on small-scale inputs.
For example, CAT gives a fully defined meaning to the statement "the median cost of brute-force search for an AES-128 key is under 2^141.89 bit operations", and provides clear, auditable reasons to believe that the statement is correct. This does not rule out all possible analysis errors, but with CAT it is no longer possible for bugs to hide inside ambiguous or untested security-level claims. The paper gives various examples of errors in the literature that survived typical informal testing practices and that would have been caught if CAT-enforced links had been in place.
As an important case study, the bulk of the current CAT release consists of full definitions of a broad spectrum of algorithms for information-set decoding (ISD), along with cost/probability predictions for each algorithm. ISD is the top attack strategy against the McEliece cryptosystem. The predictions cover interactions between (1) high-level search strategies from Prange, Lee–Brickell, Leon, Stern, Dumer, May–Meurer–Thomae, and Becker–Joux–May–Meurer; (2) random walks from Omura, Canteaut–Chabaud, Canteaut–Sendrier, and Bernstein–Lange–Peters; and (3) speedups in core subroutines such as linear algebra and sorting. The predictions also account for various attack overheads that were omitted from previous analyses. These gaps add up to roughly 10 bits, depending on parameters. CAT's tests catch much smaller errors than this.
The cost metric selected in CAT has a very simple definition, is a lower bound for the price-performance ratio of non-quantum special-purpose hardware (although the bound is loose for attacks bottlenecked by long-distance communication), and allows many optimization efforts to be shared with the design of cryptographic circuits.

2024

CRYPTO

Doubly Efficient Cryptography: Commitments, Arguments and RAM MPC
Abstract

Can a sender commit to a long input without even reading all of it? Can a prover convince a verifier that an NP statement holds without even reading the entire witness? Can a set of parties run a multiparty computation (MPC) protocol in the RAM model, without necessarily even reading their entire inputs? We show how to construct such ``doubly efficient'' schemes in a setting where parties can preprocess their input offline, but subsequently they can engage in many different protocol executions over this input in sublinear online time. We do so in the plain model, without any common setup. Our constructions rely on doubly efficient private information retrieval (DEPIR) as a building block and can be instantiated based on Ring LWE.
In more detail, we begin by constructing doubly efficient (interactive) commitments, where the sender preprocesses the input offline, and can later commit to this input to arbitrary receivers in sublinear online time. Moreover, the sender can open individual bits of the committed input in sublinear time. We then use these commitments to implement doubly succinct (interactive) arguments, where the prover preprocesses the statement/witness offline, and can subsequently run many proof protocols to convince arbitrary verifiers of the statement's validity in sublinear online time. Furthermore, we augment these to get a doubly efficient ``commit, prove and locally open'' protocol, where the prover can commit to a long preprocessed input, prove that it satisfies some global property, and locally open individual bits, all in sublinear time. Finally, we leverage these tools to construct a RAM-MPC with malicious security in the plain model. Each party individually preprocesses its input offline, and can then run arbitrary MPC executions over this input with arbitrary other parties. The online run-time of each MPC execution is only proportional to the RAM run-time of the underlying program, that can be sublinear in the input size.

2024

CRYPTO

Exploring the Advantages and Challenges of Fermat NTT in FHE Acceleration
Abstract

Recognizing the importance of a fast and resource-efficient polynomial multiplication in homomorphic encryption, in this paper, we design a \emph{multiplier-less} number theoretic transform using a Fermat number as an auxiliary modulus. To make this algorithm scalable with the degree of polynomial, we apply a univariate to multivariate polynomial ring transformation.
We develop an accelerator architecture for fully homomorphic encryption using these algorithmic techniques for efficient multivariate polynomial multiplication. For practical homomorphic encryption application benchmarks, the hardware accelerator achieves a 1,200$\times$ speed-up compared to software implementations. Finally, we conclude the paper by discussing the advantages and limitations of the proposed polynomial multiplication method.

2024

CRYPTO

Feistel-like Structures Revisited: Classification and Cryptanalysis
Abstract

In 2022, Liu et al. summarized the Feistel-like structures which use a single round function, and proposed the unified form of these structures which is named the unified structure. This paper focuses on the unified structures which satisfy the following two conditions: (1) the round function is a permutation and (2) the size of the round function is the same as that of the branch. The main results are as follows:
First of all, we give the definition of Affine Equivalence of different structures, present a condition for two structures being affine equivalent, and give two normalized forms of a unified structure.
Surprisingly, we find that a target-heavy generalised Feistel structure is always affine equivalent to a source-heavy generalised Feistel structure, which shows these two structures always have almost the same cryptographic properties.
Secondly, we give the definition of a self-equivalent structure, whose dual structure is affine equivalent to the structure itself. We prove that there is a large portion of the unified structures such as the SM4 structure and the Mars structure that are among the self-equivalent ones. For these structures, there is a one-to-one correspondence beween the impossible differentials and the zero correlation linear hulls, which shows that the longest integrals of a self-equivalent structure cover at least the rounds of the longest zero correlation linear hulls/impossible differentials.
At last, we give the refined full-diffusion round of unified structures, and exploit the $\epsilon-\delta$ technique to compute this value, which can be further used to give a provable security evaluation of unified structures against the impossible differential and zero correlation linear cryptanalysis. For example, we prove that both the longest impossible differential and zero correlation linear hull of the $d$-branch SM4-like structures cover exactly $3d-1$ rounds.

2024

CRYPTO

Field-Agnostic SNARKs from Expand-Accumulate Codes
Abstract

Efficient realizations of succinct non-interactive arguments of knowledge (SNARK) have gained popularity due to their practical applications in various domains. Among existing schemes, those based on error-correcting codes are of particular interest because of their good concrete efficiency, transparent setup, and plausible post-quantum security. However, many existing code-based SNARKs suffer from the disadvantage that they only work over specific finite fields.
In this work, we construct a code-based SNARK that does not rely on any specific underlying field; i.e., it is \emph{field-agnostic}. Our construction follows the framework of Brakedown and builds a polynomial commitment scheme (and hence a SNARK) based on recently introduced \emph{expand-accumulate codes}. Our work generalizes these codes to arbitrary finite fields; our main technical contribution is showing that, with high probability, these codes have constant rate and constant relative distance (crucial properties for building efficient SNARKs), solving an open problem from prior work.
As a result of our work we obtain a SNARK where,
for a statement of size $M$, the prover time is $O(M\log M)$ and the proof size is $O(\sqrt{M})$. We demonstrate the concrete efficiency of our scheme empirically via experiments. Proving ECDSA verification on the secp256k1 curve requires only 0.23s for proof generation, 2~orders of magnitude faster than SNARKs that are not field-agnostic. Compared to the original Brakedown result (which is also field-agnostic), we obtain proofs that are 1.9--2.8$\times$ smaller due to the good concrete distance of our underlying error-correcting code, while introducing only a small overhead of 1.2$\times$ in the prover time.

2024

CRYPTO

Fine-Grained Non-Interactive Key Exchange, Revisited
Abstract

We revisit the construction of multiparty non-interactive key-exchange protocols with fine-grained security, which was recently studied in (Afshar et al., Eurocrypt 2023). Their work introduced a 4-party non-interactive key exchange with quadratic hardness, and proved it secure in Shoup's generic group model. This positive result was complemented with a proof that n-party non-interactive key exchange with superquadratic security cannot exist in Maurer's generic group model, for any n > 2. Because Shoup's model is stronger than Maurer's model, this leaves a gap between the positive and the negative result, and their work left as an open question the goal of closing this gap, and of obtaining fine-grained non-interactive key exchange without relying on idealized models.
In this work, we make significant progress on both questions. We obtain two main results:
- A 4-party non-interactive key exchange protocol, assuming the existence of exponentially secure injective pseudorandom generators, and the subexponential hardness of the computational Diffie-Hellman assumption. In addition, our scheme is conceptually simpler, and can be generalized to other settings (with more parties or from other assumptions).
- Assuming the existence of non-uniformly secure injective pseudorandom generators with exponential hardness, we further show that our protocol is secure in Maurer's model, albeit with a smaller hardness gap (up to N^1.6), making progress on filling the gap between the positive and the negative result of (Afshar et al., Eurocrypt 2023). Somewhat intriguingly, proving the security of our scheme in Maurer's idealized model turns out to be significantly harder than proving its security in the standard model.

2024

CRYPTO

Fine-Grained Non-Interactive Key-Exchange without Idealized Assumptions
Abstract

In this paper, we study multi-party non-interactive key ex-change (NIKE) in the fine-grained setting. More precisely, we propose three multi-party NIKE schemes in three computation models, namely, the bounded parallel-time, bounded time, and bounded storage models. Their security is based on a very mild assumption (e.g. NC1 \subsetneq \oplus L/poly) or even without any complexity assumption. This improves the recent work of Afshar, Couteau, Mahmoody, and Sadeghi (EUROCRYPT 2023) that requires idealized assumptions, such as random oracles or generic groups.
Additionally, we show that all our constructions satisfy a natural desirable property that we refer to as extendability, and we give generic transformations from extendable multi-party NIKE to multi-party identity-based NIKEs in the fine-grained settings.

2024

CRYPTO

Flood and Submerse: Distributed Key Generation and Robust Threshold Signature from Lattices
Abstract

We propose a new framework based on random submersions — that is projection over a random subspace blinded by a small Gaussian noise — for constructing verifiable short secret sharing and showcase it to construct efficient threshold lattice-based signatures in the hash-and-sign paradigm, when based on noise flooding. This is, to our knowledge, the first hash-and-sign lattice-based threshold signature. Our threshold signature enjoys the very desirable property of robustness, including at key generation. In practice, we are able to construct a robust hash-and-sign threshold signature for threshold and provide a typical parameter set for threshold T = 16 and signature size 13kB. Our constructions are provably secure under standard MLWE assumption in the ROM and only require basic primitives as building blocks. In particular, we do not rely on FHE-type schemes.

2024

CRYPTO

Formal Security Proofs via Doeblin Coefficients: Optimal Side-channel Factorization from Noisy Leakage to Random Probing
Abstract

Masking is one of the most popular countermeasures to side-
channel attacks, because it can offer provable security. However, depend-
ing on the adversary’s model, useful security guarantees can be hard
to provide. At first, masking has been shown secure against t-threshold
probing adversaries by Ishai et al. at Crypto’03. It has then been shown
secure in the more generic random probing model by Duc et al. at Euro-
crypt’14. Prouff and Rivain have introduced the noisy leakage model to
capture more realistic leakage at Eurocrypt’13. Reduction from noisy
leakage to random probing has been introduced by Duc et al. at Eu-
rocrypt’14, and security guarantees were improved for both models by
Prest et al. at Crypto’19, Duc et al. in Eurocrypt’15/J. Cryptol’19,
and Masure and Standaert at Crypto’23. Unfortunately, as it turns out,
we found that previous proofs in either random probing or noisy leakage
models are flawed, and such flaws do not appear easy to fix.
In this work, we show that the Doeblin coefficient allows one to overcome
these flaws. In fact, it yields optimal reductions from noisy leakage to
random probing, thereby providing a correct and usable metric to prop-
erly ground security proofs. This shows the inherent inevitable cost of
a reduction from the noisy leakages to the random probing model. We
show that it can also be used to derive direct formal security proofs using
the subsequence decomposition of Prouff and Rivain.

2024

CRYPTO

Formally Verifying Kyber Episode V: Machine-checked IND-CCA security and correctness of ML-KEM in EasyCrypt
Abstract

We present a formally verified proof of the correctness and IND-CCA security of ML-KEM, the Kyber-based Key Encapsulation Mechanism (KEM) undergoing standardization by NIST.
The proof is machine-checked in EasyCrypt and it includes:
1) A formalization of the correctness (decryption failure probability) and IND-CPA security of the Kyber base public-key encryption scheme, following Bos et al. at Euro S&P 2018;
2) A formalization of the relevant variant of the Fujisaki-Okamoto transform in the Random Oracle Model (ROM), which follows closely (but not exactly) Hofheinz, Hovelmanns and Kiltz at TCC 2017;
3) A proof that the IND-CCA security of the ML-KEM specification and its correctness as a KEM follows from the previous results;
4) Two formally verified implementations of ML-KEM written in Jasmin that are provably constant-time, functionally equivalent to the ML-KEM specification and, for this reason, inherit the provable security guarantees established in the previous points.
The top-level theorems give self-contained concrete bounds for the correctness and security of ML-KEM down to (a variant of) Module-LWE.
We discuss how they are built modularly by leveraging various EasyCrypt features.

2024

CRYPTO

FRIDA: Data Availability Sampling from FRI
Abstract

As blockchains like Ethereum continue to grow, clients with limited resources can no longer store the entire chain.
Light nodes that want to use the blockchain, without verifying that it is in a good state overall, can just download the block headers without the corresponding block contents.
As those light nodes may eventually need some of the block contents, they would like to ensure that they are in principle available.
Data availability sampling, introduced by Bassam et al., is a process that allows light nodes to check the availability of data without download it.
In a recent effort, Hall-Andersen, Simkin, and Wagner have introduced formal definitions and analyzed several constructions.
While their work thoroughly lays the formal foundations for data availability sampling, the constructions are either prohibitively expensive, use a trusted setup, or have a download complexity for light clients scales with a square root of the data size.
In this work, we make a significant step forward by proposing an efficient data availability sampling scheme without a trusted setup and only polylogarithmic overhead.
To this end, we find a novel connection with interactive oracle proofs of proximity (IOPPs).
Specifically, we prove that any IOPP meeting an additional consistency criterion can be turned into an erasure code commitment, and then, leveraging a compiler due to Hall-Andersen, Simkin, and Wagner, into a data availability sampling scheme.
This new connection enables data availability to benefit from future results on IOPPs.
We then show that the widely used FRI IOPP satisfies our consistency criterion and demonstrate that the resulting data availability sampling scheme outperforms the state-of-the-art asymptotically and concretely in multiple parameters.

2024

CRYPTO

FuLeakage: Breaking FuLeeca by Learning Attacks
Abstract

FuLeeca is a signature scheme submitted to the recent NIST call for additional signatures. It is an efficient hash-and-sign scheme based on quasi-cyclic codes in the Lee metric and resembles the lattice-based signature Falcon.
FuLeeca proposes a so-called concentration step within the signing procedure to avoid leakage of secret-key information from the signatures. However, FuLeeca is still vulnerable to learning attacks, which were first observed for lattice-based schemes. We present three full key-recovery attacks by exploiting the proximity of the code-based FuLeeca scheme to lattice-based primitives.
More precisely, we use a few signatures to extract an n/2-dimensional circulant sublattice from the given length-n code, that still contains the exceptionally short secret-key vector. This significantly reduces the classical attack cost and, in addition, leads to a full key recovery in quantum-polynomial time. Furthermore, we exploit a bias in the concentration procedure to classically recover the full key for any security level with at most 175.000 signatures in less than an hour.

2024

CRYPTO

Fully Malicious Authenticated PIR
Abstract

Authenticated PIR enables a server to initially commit to a database of $N$ items, for which a client can later privately obtain individual items with complexity sublinear in $N$, with the added guarantee that the retrieved item is consistent with the committed database. A crucial requirement is {\em privacy with abort}, i.e., the server should not learn anything about a query {\em even} if it learns whether the client aborts.
This problem was recently considered by Colombo et al. (USENIX '23), who proposed solutions secure under the assumption that the database is committed to {\em honestly}. Here, we close this gap for their DDH-based scheme, and present a solution that tolerates fully malicious servers that provide potentially malformed commitments. Our scheme has communication and client computational complexity $\mathcal{O}_{\lambda}(\sqrt{N})$, does not require any additional assumptions, and does not introduce heavy machinery (e.g., generic succinct proofs). We do so by introducing \emph{validation queries}, which, from the server's perspective, are computationally indistinguishable from regular PIR queries. Provided that the server succeeds in correctly answering $\kappa$ such validation queries, the client is convinced with probability $1-\frac{1}{2^\kappa}$ that the server is unable to break privacy with abort.

2024

CRYPTO

Fully Secure MPC and zk-FLIOP Over Rings: New Constructions, Improvements and Extensions
Abstract

We revisit the question of the overhead to achieve full security (i.e., guaranteed output delivery) in secure multiparty computation (MPC). Recent works have closed the gap between full security and semi-honest security, by introducing protocols where the parties first compute the circuit using a semi-honest protocol and then run a verification step with sublinear communication in the circuit size. However, the number of interaction rounds in the verification step is also sublinear in the circuit's size. Unlike communication, the round complexity typically grows with the circuit's \textit{depth} and not its size. Hence, for large but shallow circuits, this may yield a significant overhead. Motivated by this gap, we make the following contributions:
(1) We present a new MPC framework to obtain full security, compatible with effectively \emph{any} ring, that has an additive communication overhead of only $O(\log |C|)$, where $|C|$ is the number of multiplication gates in the circuit, and a \textit{constant} number of additional rounds beyond the underlying semi-honest protocol. Our framework works with any linear secret sharing scheme and relies on a new to utilize the machinery of \textit{zero-knowledge fully linear interactive oracle proofs} (zk-FLIOP) in a black-box way. We present several instantiations to the building blocks of our compiler, from which we derive concretely efficient protocols in different settings.
(2) We present extensions to the zk-FLIOP primitive for very general settings: one for proving statements over potentially non-commutative rings that only require certain commutative properties of its largest exceptional set; and one for proving statements over Galois Rings. For Galois rings, we present concrete improvements on the current state-of-the-art for the case of constant-round proofs, by making use of \emph{Reverse Multiplication Friendly Embeddings} (RMFEs).

2024

CRYPTO

Fully-Succinct Multi-Key Homomorphic Signatures from Standard Assumptions
Abstract

Multi-Key Homomorphic Signatures (MKHS) allow one to evaluate a function on data signed by distinct users while producing a succinct and publicly-verifiable certificate of the correctness of the result. All the constructions of MKHS in the state of the art achieve a weak level of succinctness where signatures are succinct in the total number of inputs but grow linearly with the number of users involved in the computation. The only exception is a SNARK-based construction which relies on a strong notion of knowledge soundness in the presence of signing oracles that not only requires non-falsifiable assumptions but also encounters some impossibility results.
In this work, we present the first construction of MKHS that are fully succinct (also with respect to the number of users) while achieving adaptive security under standard falsifiable assumptions. Our result is achieved through a novel combination of batch arguments for NP (BARGs) and functional commitments (FC), and yields diverse MKHS instantiations for circuits of unbounded depth based on either pairing or lattice assumptions. Additionally, our schemes support efficient verification with pre-processing, and they can easily be extended to achieve multi-hop evaluation and context-hiding.

2024

CRYPTO

Game-Theoretically Fair Distributed Sampling
Abstract

Cleve's celebrated result (STOC'86) showed that a strongly fair multi-party coin-toss is impossible in the presence of majority-sized coalitions. Recently, however, a fascinating line of work studied a relaxed fairness notion called \emph{game-theoretic fairness}, which guarantees that no coalition should be incentivized to deviate from the prescribed protocol. A sequence of works has explored the feasibility of game-theoretic fairness for \emph{two-sided} coin-toss, and indeed demonstrated feasibility in the dishonest majority setting under standard cryptographic assumptions. In fact, the recent work of Wu, Asharov, and Shi (EUROCRYPT'22) completely characterized the regime where game-theoretic fairness is feasible. However, this line of work is largely restricted to two-sided coin-toss, and more precisely on a \emph{uniform} coin-toss (i.e., Bernoulli with parameter $1/2$). The only exceptions are the works on game-theoretically fair leader election, which can be viewed as a special case of uniform $n$-sided coin-toss where $n$ is the number of parties.
In this work, we \emph{initiate} the comprehensive study of game-theoretic fairness for multi-party \emph{sampling from general distributions}. In particular, for the case of $m$-sided \emph{uniform} coin-toss we give a nearly complete characterization of the regime in which game-theoretic fairness is feasible. Interestingly, contrary to standard fairness notions in cryptography, the composition of game-theoretically fair two-sided coin-toss protocols does not necessarily yield game-theoretically fair multi-sided coins. To circumvent this, we introduce new techniques compatible with game-theoretic fairness.
In particular, we give the following results:
- We give a protocol from standard cryptographic assumptions that achieves game-theoretic fairness for uniform $m$-sided coin-toss against half- or more-sized adversarial coalitions.
- To complement our protocol, we give a general impossibility result that establishes the optimality of our protocol for a broad range of parameters modulo an additive constant. Even in the worst-case, the gap between our protocol and our impossibility result is only a small constant multiplicative factor.
- We also present a game-theoretically fair protocol for \emph{any} efficiently sampleable $m$-outcome distribution in the dishonest majority setting. For instance, even for the case of $m=2$ (i.e., two-sided coin-toss), our result implies a game-theoretically fair protocol for an \emph{arbitrary} Bernoulli coin. In contrast, the work of Wu, Asharov, and Shi only focussed on a Bernoulli coin with parameter $1/2$.

2024

CRYPTO

Generic and Algebraic Computation Models: When AGM Proofs Transfer to the GGM
Abstract

The Fuchsbauer, Kiltz, and Loss (Crypto 2018) claim that (some) hardness results in the algebraic group model imply the same hardness results in the generic group model was recently called into question by Katz, Zhang, and Zhou (Asiacrypt 2022). The latter gave an interpretation of the claim under which it is incorrect. We give an alternate interpretation under which it is correct, using natural frameworks for capturing generic and algebraic models for arbitrary algebraic structures. Most algebraic analyses in the literature can be captured by our frameworks, making the claim correct for them.

2024

CRYPTO

Generic MitM Attack Frameworks on Sponge Constructions
Abstract

This paper proposes general meet-in-the-middle (MitM) attack frameworks for preimage and collision attacks on hash functions based on (generalized) sponge construction.
As the first contribution, our MitM preimage attack framework covers a wide range of sponge-based hash functions, especially those with lower claimed security level for preimage compared to their output size. Those hash functions have been very widely standardized (e.g., {\tt Ascon-Hash}, {\tt PHOTON}, etc.), but are rarely studied against preimage attacks. Even the recent MitM attack framework on sponge construction by Qin et al. (EUROCRYPT 2023) cannot attack those hash functions. As the second contribution, our MitM collision attack framework shows a different tool for the collision cryptanalysis on sponge construction, while previous collision attacks on sponge construction are mainly based on differential attacks.
Most of the results in this paper are the first third-party cryptanalysis results. If cryptanalysis previously existed, our new results significantly improve the previous results, such as improving the previous 2-round collision attack on {\tt Ascon-Hash} to the current 4 rounds, improving the previous 3.5-round quantum preimage attack on SPHINCS$^+$-{\tt Haraka} to our 4-round classical preimage attack, etc.

2024

CRYPTO

Greyhound: Fast Polynomial Commitments from Lattices
Abstract

In this paper, we propose Greyhound, the first concretely efficient polynomial commitment scheme from standard lattice assumptions. At the core of our construction lies a simple three-round protocol for proving evaluations for polynomials of bounded degree N with verifier time complexity O(\sqrt{N}). By composing it with the LaBRADOR proof system (CRYPTO 2023), we obtain a succinct proof of polynomial evaluation (i.e. polylogarithmic in N) that admits a sublinear verifier runtime.
To highlight practicality of Greyhound, we provide implementation details including concrete sizes and runtimes. Notably, for large polynomials of degree at most N=2^{30}, the scheme produces evaluation proofs of size 53KB, which is more than 10^4 times smaller than the recent lattice-based framework, called SLAP (EUROCRYPT 2024), and around three orders of magnitude smaller than Ligero (CCS 2017) and Brakedown (CRYPTO 2023).

2024

CRYPTO

HAWKEYE – Recovering Symmetric Cryptography From Hardware Circuits
Abstract

We present the first comprehensive approach for detecting and analyzing symmetric cryptographic primitives in gate-level descriptions of hardware. To capture both ASICs and FPGAs, we model the hardware as a directed graph, where gates become nodes and wires become edges. For modern chips, those graphs can easily consist of hundreds of thousands of nodes. More abstractly, we find subgraphs corresponding to cryptographic primitives in a potentially huge graph, the sea-of-gates, describing an entire chip. As we are particularly interested in unknown cryptographic algorithms, we cannot rely on searching for known parts such as S-boxes or round constants.
Instead, we are looking for parts of the chip that perform highly local computations. A major result of our work is that many symmetric algorithms can be reliably located and sometimes even identified by our approach, which we call HAWKEYE. Our findings are verified by extensive experimental results, which involve SPN, ARX, Feistel, and LFSR-based ciphers implemented for both FPGAs and ASICs. We demonstrate the real-world applicability of HAWKEYE by evaluating it on OpenTitan's Earl Grey chip, an open-source secure micro-controller design. HAWKEYE locates all major cryptographic primitives present in the netlist comprising 424341 gates in 44.3 seconds.

2024

CRYPTO

Hintless Single-Server Private Information Retrieval
Abstract

We present two new constructions for private information retrieval (PIR) in the classical setting where the clients do not need to do any preprocessing or store any database dependent information, and the server does not need to store any client-dependent information.
Our first construction (HintlessPIR) eliminates the client preprocessing step from the recent LWE-based SimplePIR (Henzinger et. al., USENIX Security 2023) by outsourcing the ``hint'' related computation to the server, leveraging a new concept of \emph{homomorphic encryption with composable preprocessing}.
We realize this concept with RLWE encryption schemes, and by leveraging the composibility of this technique we are able to preprocess almost all the expensive parts of the homomorphic computation and reuse them across multiple protocol executions.
As a concrete application, we propose highly efficient matrix vector multiplication that allows us to build HintlessPIR. For a database of size 8GB, HintlessPIR achieves throughput about 6.37GB/s without requiring transmission of any client or server state.
We additionally formalize the matrix vector multiplication protocol as a novel primitive that we call LinPIR, which may be of independent interest.
In our second construction (TensorPIR) we reduce the communication of HintlessPIR from square root to cubic root in the database size.
We show how to use RLWE encryption with preprocessing to outsource LWE decryption for ciphertexts generated by homomorphic multiplications.
This allows the server to do more complex processing using a more compact query under LWE.
We implement and benchmark HintlessPIR which achieves better concrete costs than TensorPIR for a large set of databases of interest.
We show that it improves the communication of recent preprocessing constructions when clients do not have large numbers of queries or the database updates frequently.
The computation cost for removing the hint is small and decreases as the database becomes larger, and it is always more efficient than other constructions with client hints such as Spiral PIR (Menon and Wu, S&P 2022).
In the setting of anonymous queries we also improve on Spiral's communication.

2024

CRYPTO

How (not) to Build Quantum PKE in Minicrypt
Abstract

The seminal work by Impagliazzo and Rudich (STOC'89) demonstrated the impossibility of constructing classical public key encryption (PKE) from one-way functions (OWF) in a black-box manner. However, the question remains: can quantum PKE (QPKE) be constructed from quantumly secure OWF?
A recent line of work has shown that it is indeed possible to build QPKE from OWF, but with one caveat --- they rely on quantum public keys, which cannot be authenticated and reused. In this work, we re-examine the possibility of perfect complete QPKE in the quantum random oracle model (QROM), where OWF exists.
Our first main result: QPKE with classical public keys, secret keys and ciphertext, does not exist in the QROM, if the key generation only makes classical queries.
Therefore, a necessary condition for constructing such QPKE from OWF is to have the key generation classically ``un-simulatable’’. Previous discussions (Austrin~et al. CRYPTO'22) on the impossibility of QPKE from OWF rely on a seemingly strong conjecture. Our work makes a significant step towards a complete and unconditional quantization of Impagliazzo and Rudich’s results.
Our second main result extends to QPKE with quantum public keys.
The second main result: QPKE with quantum public keys, classical secret keys and ciphertext, does not exist in the QROM, if the key generation only makes classical queries and the quantum public key is either pure or ``efficiently clonable''.
The result is tight due to these existing QPKEs (Barooti et al. TCC'23, Morimae and Yamakawa QIP'24, Malavolta and Walter QIP'24). Our result further gives evidence on why existing QPKEs lose reusability.
To achieve these results, we use a novel argument based on conditional mutual information and quanttum Markov chain by Fawzi and Renner (Communications in Mathematical Physics). We believe the techniques used in the work will find other usefulness in separations in quantum cryptography/complexity.

2024

CRYPTO

How to Construct Quantum FHE, Generically
Abstract

We construct a (compact) quantum fully homomorphic encryption (QFHE) scheme starting from {\em any} (classical) fully homomorphic encryption scheme (with decryption in $\mathsf{NC}^{1}$) together with a dual-mode trapdoor claw-free function family. Compared to previous constructions (Mahadev, FOCS 2018; Brakerski, CRYPTO 2018) which made non-black-box use of similar underlying primitives, our construction provides a pathway to instantiations from different assumptions. Our construction uses the techniques of Dulek, Schaffner and Speelman (CRYPTO 2016) and shows how to make the client in their QFHE scheme classical using claw-free trapdoor functions. As an additional contribution, we show a new instantiation of dual-mode trapdoor claw-free functions from group actions.

2024

CRYPTO

How to Prove Statements Obliviously?
Abstract

Cryptographic applications often require proving statements about hidden secrets satisfying certain circuit relations. Moreover, these proofs must often be generated obliviously, i.e., without knowledge of the secret. This work presents a new technique called --- FRI on hidden values --- for efficiently proving such statements. This technique enables a polynomial commitment scheme for values hidden inside linearly homomorphic primitives, such as linearly homomorphic encryption, linearly homomorphic commitment, group exponentiation, fully homomorphic encryption, etc. Building on this technique, we obtain the following results.
1. An efficient SNARK for proving the honest evaluation of FHE ciphertexts. This allows for an efficiently verifiable private delegation of computation, where the client only needs to perform logarithmic many FHE computations to verify the correctness of the computation.
2. An efficient approach for privately delegating the computation of zkSNARKs to a single untrusted server, without requiring the server to make any non-black-box use of cryptography. All prior works require multiple servers and the assumption that some subset of the servers are honest.
3. A weighted threshold signature scheme that does not require any setup. In particular, parties may sample their own keys independently, and no distributed key generation (DKG) protocol is needed. Furthermore, the efficiency of our scheme is completely independent of the weights.
Prior to this work, there were no known black-box feasibility results for any of these applications.
We also investigate the use of this approach in the context of public proof aggregation. These are only a few representative applications that we explore in this paper. We expect our techniques to be widely applicable in many other scenarios.

2024

CRYPTO

HyperNova: Recursive arguments for customizable constraint systems
Abstract

We introduce HyperNova, a new recursive argument for proving incremental computations whose steps are expressed with CCS (Setty et al. ePrint 2023/552), a customizable constraint system that simultaneously generalizes Plonkish, R1CS, and AIR without overheads. HyperNova makes four contributions, each resolving a major problem in the area of recursive arguments.
First, it provides a folding scheme for CCS where the prover’s cryptographic cost is a single multi-scalar multiplication (MSM) of size equal to the number of variables in the constraint system, which is optimal when using an MSM-based commitment scheme. The folding scheme can fold multiple instances at once, making it easier to build generalizations of IVC such as PCD. Second, when proving program executions on stateful machines (e.g., EVM, RISC-V), the cost of proving a step of a program is proportional only to the size of the circuit representing the instruction invoked by the program step (“a la carte” cost profile). Third, we show how to achieve zero-knowledge for “free” and without the need to employ zero-knowledge SNARKs. Fourth, we show how to efficiently instantiate HyperNova over a cycle of elliptic curves. For this, we provide a general technique, which we refer to as CycleFold, that applies to all modern folding-scheme-based recursive arguments.

2024

CRYPTO

Improved algorithms for finding fixed-degree isogenies between supersingular elliptic curves
Abstract

Finding isogenies between supersingular elliptic curves is a natural algorithmic problem which is known to be equivalent to computing the curves' endomorphism rings.
When the isogeny is additionally required to have a specific known degree $d$, the problem appears to be somewhat different in nature, yet its hardness is also required in isogeny-based cryptography.
Let $E_1,E_2$ be supersingular elliptic curves over $\mathbb{F}_{p^2}$. We present improved classical and quantum algorithms that compute an isogeny of degree $d$ between $E_1$ and $E_2$ if it exists. Let $d \approx p^{1/2+ \epsilon}$ for some $\epsilon>0$.
Our essentially memory-free algorithms have better time complexity than meet-in-the-middle algorithms, which require exponential memory storage, in the range $1/2\leq\epsilon\leq 3/4$ on a classical computer. For quantum computers, we improve the time complexity in the range $0<\epsilon<5/2$.
Our strategy is to compute the endomorphism rings of both curves, compute the reduced norm form associated to $\Hom(E_1,E_2)$ and try to represent the integer $d$ as a solution of this form. We present multiple approaches to solving this problem which combine guessing certain variables exhaustively (or use Grover's search in the quantum case) with methods for solving quadratic Diophantine equations such as Cornacchia's algorithm and multivariate variants of Coppersmith's method. For the different approaches, we provide implementations and experimental results. A solution to the norm form can then be efficiently translated to recover the sought-after isogeny using well-known techniques.
As a consequence of our results we show that a recently introduced signature scheme from~\cite{BassoSIDHsign} does not reach NIST level I security.

2024

CRYPTO

Improved Alternating-Moduli PRFs and Post-Quantum Signatures
Abstract

We revisit the alternating moduli paradigm for constructing symmetric key primitives with a focus on constructing highly efficient protocols to evaluate them using secure multi-party computation (MPC). The alternating moduli paradigm of Boneh et al. (TCC 2018) enables the construction of various symmetric key primitives with the common characteristic that the inputs are multiplied by two linear maps over different moduli, first over F_2 and then over F_3.
The first contribution focuses on efficient two-party evaluation of alternating moduli PRFs, effectively building an oblivious pseudorandom function. We present a generalization of the PRF proposed by Boneh et al. (TCC 18) along with methods to lower the communication and computation. We then provide several variants of our protocols, with different computation and communication tradeoffs, for evaluating the PRF. Most are in the OT/VOLE hybrid model while one is based on specialized garbling. Our most efficient protocol effectively is about 3x faster and requires 1.3x lesser communication.
Our next contribution is the efficient evaluation of the OWF f(x) = B *_3 (A *_2 x) proposed by Dinur et al. (CRYPTO 21) where A \in F^{m x n}_2, B \in F^{t x m}_3 and *_p is multiplication mod p. This surprisingly simple OWF can be evaluated within MPC by secret sharing [x] over F_2, locally computing [v] = A *_2 [x], performing a modulus switching protocol to F_3 shares, followed by locally computing the output shares [y] = B *_3 [v]. We design a bespoke MPC-in-the-Head (MPCitH) signature scheme that evaluates the OWF, achieving state of art performance. The resulting signature has a size ranging from 4.0-5.5 KB, achieving between 2-3x reduction compared to Dinur et al. To the best of our knowledge, this is only 5% larger than the smallest signature based on symmetric key primitives, including the latest NIST PQC competition submissions. We additionally show that our core techniques can be extended to build very small post-quantum ring signatures for small-medium sized rings that are competitive with state-of-the-art lattice based schemes. Our techniques are in fact more generally applicable to set membership in MPCitH.

2024

CRYPTO

Improved Reductions from Noisy to Bounded and Probing Leakages via Hockey-Stick Divergences
Abstract

There exists a mismatch between the theory and practice of cryptography in the presence of leakage. On the theoretical front, the bounded leakage model, where the adversary learns bounded-length but noiseless information about secret components, and the random probing model, where the adversary learns some internal values of a leaking implementation with some probability, are convenient abstractions to analyze the security of numerous designs. On the practical front, side-channel attacks produce long transcripts which are inherently noisy but provide information about all internal computations, and this noisiness is usually evaluated with closely related metrics like the mutual information or statistical distance. Ideally, we would like to claim that resilience to bounded leakage or random probing implies resilience to noisy leakage evaluated according to these metrics. However, prior work (Duc, Dziembowski and Faust, Eurocrypt 2014; Brian et al., Eurocrypt 2021) has shown that proving such reductions with useful parameters is challenging.
In this work, we study noisy leakage models stemming from hockey-stick divergences, which generalize statistical distance and are also the basis of differential privacy. First, we show that resilience to bounded leakage and random probing implies resilience to our new noisy leakage model with improved parameters compared to models based on the statistical distance or mutual information. Second, we establish composition theorems for our model, showing that these connections extend to a setting where multiple leakages are obtained from a leaking implementation. We complement our theoretical results with a discussion of practical relevance, highlighting that (i) the reduction to bounded leakage applies to realistic leakage functions with noise levels that are decreased by several orders of magnitude compared to Brian et al., and (ii) the reduction to random probing usefully generalizes the seminal work of Duc, Dziembowski, and Faust, although it remains limited when the field size in which masking operates grows (i.e., hockey-stick divergences can better hide the field size dependency of the noise requirements, but do not annihilate it).

2024

CRYPTO

Improving Generic Attacks Using Exceptional Functions
Abstract

Over the past ten years, there have been many attacks on symmetric constructions using the statistical properties of random functions. Initially, these attacks targeted iterated hash constructions and their combiners, developing a wide array of methods based on internal collisions and on the average behavior of iterated random functions. More recently, Gilbert et al. (EUROCRYPT 2023) introduced a forgery attack on so called duplex-based Authenticated Encryption modes which was based on exceptional random functions, i.e., functions whose graph admits a large component with an exceptionally small cycle.
In this paper, we expand the use of such functions in generic cryptanalysis with several new attacks. First, we improve the attack of Gilbert et al. from O(2^{3c/4}) to O(2^{2c/3}), where c is the capacity. This new attack uses a nested pair of functions with exceptional behavior, where the second function is defined over the cycle of the first one. Next, we introduce several new generic attacks against hash combiners, notably using small cycles to improve the complexities of the best existing attacks on the XOR combiner, Zipper Hash and Hash-Twice.
Last but not least, we propose the first quantum second preimage attack against Hash-Twice, reaching a quantum complexity O(2^{3n/7}).

2024

CRYPTO

Information-theoretic security with asymmetries
Abstract

In this paper, we study the problem of lower bounding any given cost function depending on the false positive and false negative probabilities of adversaries against indistinguishability security notions in symmetric-key cryptography. We take the cost model as an input, so that this becomes a purely information-theoretical question.
We propose power bounds as an easy-to-use alternative for advantage bounds in the context of indistinguishability with asymmetric cost functions. We show that standard proof techniques such as hybrid arguments and the H-coefficient method can be generalized to the power model, and apply these techniques to the PRP-PRF switching lemma, the Even-Mansour (EM) construction, and the sum-of-permutations (SoP) construction.
As the final and perhaps most useful contribution, we provide two methods to convert single-user power bounds into multi-user power bounds, and investigate their relation to the point-wise proximity method of Hoang and Tessaro (Crypto 2016). These method are applied to obtain tight multi-user power bounds for EM and SoP.

2024

CRYPTO

Is ML-Based Cryptanalysis Inherently Limited? Simulating Cryptographic Adversaries via Gradient-Based Methods
Abstract

Given the recent progress in machine learning (ML), the cryptography community has started exploring the applicability of ML methods to the design of new cryptanalytic approaches. While current empirical results show promise, the extent to which such methods may outperform classical cryptanalytic approaches is still somewhat unclear.
In this work, we initiate exploration of the theory of ML-based cryptanalytic techniques, in particular providing new results towards understanding whether they are fundamentally limited compared to traditional approaches. Whereas most classic cryptanalysis crucially relies on directly processing individual samples (e.g., plaintext-ciphertext pairs), modern ML methods thus far only interact with samples via gradient-based computations that average a loss function over all samples. It is, therefore, conceivable that such gradient-based methods are inherently weaker than classical approaches.
We introduce a unifying framework for capturing both ``sample-based'' adversaries that are provided with direct access to individual samples and ``gradient-based'' ones that are restricted to issuing gradient-based queries that are averaged over all given samples via a loss function. Within our framework, we establish a general feasibility result showing that any sample-based adversary can be simulated by a seemingly-weaker gradient-based one. Moreover, the simulation exhibits a nearly optimal overhead in terms of the gradient-based simulator's running time. Finally, we extend and refine our simulation technique to construct a gradient-based simulator that is fully parallelizable (crucial for avoiding an undesirable overhead for parallelizable cryptanalytic tasks), which is then used to construct a gradient-based simulator that executes the particular and highly useful gradient-descent method.
Taken together, although the extent to which ML methods may outperform classical cryptanalytic approaches is still somewhat unclear, our results indicate that such gradient-based methods are not inherently limited by their seemingly restricted access to the provided samples.

2024

CRYPTO

Laconic Function Evaluation and ABE for RAMs from (Ring-)LWE
Abstract

Laconic function evaluation (LFE) allows us to compress a circuit $f$ into a short digest. Anybody can use this digest as a public-key to efficiently encrypt some input $x$. Decrypting the resulting ciphertext reveals the output $f(x)$, while hiding everything else about $x$. In this work we consider LFE for \emph{Random-Access Machines} (RAM-LFE) where, instead of a circuit $f$, we have a RAM program $f_{\DB}$ that potentially contains some large hard-coded data $\DB$. The decryption run-time to recover $f_{\DB}(x)$ from the ciphertext should be roughly the same as a plain evaluation of $f_{\DB}(x)$ in the RAM model, which can be sublinear in the size of $\DB$. Prior works constructed LFE for circuits under LWE, and RAM-LFE under indisitinguishability obfuscation (iO) and Ring-LWE. In this work, we construct RAM-LFE with essentially optimal encryption and decryption run-times from just Ring-LWE and a standard circular security assumption, without iO.
RAM-LFE directly yields 1-key succinct functional encryption and reusable garbling for RAMs with similar parameters.
If we only want an \emph{attribute-based} LFE for RAMs (RAM-AB-LFE), then we can replace Ring-LWE with plain LWE in the above. Orthogonally, if we only want \emph{leveled} schemes, where the encryption/decryption efficiency can scale with the depth of the RAM computation, then we can remove the need for a circular-security. Lastly, we also get a leveled many-key \emph{attribute-based encryption for RAMs (RAM-ABE)}, from LWE.

2024

CRYPTO

LATKE: A Framework for Constructing Identity-Binding PAKEs
Abstract

Motivated by applications to the internet of things (IoT), Cremers, Naor, Paz, and Ronen (CRYPTO '22) recently considered a setting in which multiple parties share a common password and want to be able to pairwise authenticate. They observed that using standard password-authenticated key exchange (PAKE) protocols in this setting allows for catastrophic impersonation attacks whereby compromise of a single party allows an attacker to impersonate any party to any other. To address this, they proposed the notion of identity-binding PAKE (iPAKE) and showed constructions of iPAKE protocol CHIP.
We present LATKE, a framework for iPAKE that allows us to construct protocols with features beyond what CHIP achieves. In particular, we can instantiate the components of our framework to yield an iPAKE protocol with post-quantum security and identity concealment, where one party hides its identity until it has authenticated the other. This is the first iPAKE protocol with either property.
To demonstrate the concrete efficiency of our framework, we implement various instantiations and compare the resulting protocols to CHIP when run on commodity hardware. The performance of our schemes is very close to that of CHIP, while offering stronger security properties.

2024

CRYPTO

Leakage Certification Made Simple
Abstract

Side channel evaluations benefit from sound characterisations of adversarial leakage models, which are the determining factor for attack success. Two questions are of interest: can we define and estimate a quantity that captures the ideal adversary (who knows all the distributions that are involved in an attack), and can we define and estimate a quantity that captures a concrete adversary (represented by a given leakage model)?
Existing work has led to a proliferation of custom quantities to measure both types of adversaries, which can be data intensive to estimate in the ideal case, even for discrete side channels and especially when the number of dimensions in the side channel traces grows.
In this paper, we show how to define the mutual information between carefully chosen variables of interest and how to instantiate a recently suggested mutual information estimator for practical estimation. We apply our results to real-world data sets and are the first to provide a mutual information-based characterisation of ideal and concrete adversaries utilising up to 30 data points.

2024

CRYPTO

Limits of Black-Box Anamorphic Encryption
Abstract

(Receiver) Anamorphic encryption, introduced by Persiano
et al. at Eurocrypt 2022, considers the question of achieving private
communication in a world where secret decryption keys are under the
control of a dictator. The challenge here is to be able to establish a secret
communication channel to exchange covert (i.e. anamorphic) messages
on top of some already deployed public key encryption scheme.
Over the last few years several works addressed this challenge by show-
ing new constructions, refined notions and extensions. Most of these con-
structions, however, are either ad hoc, in the sense that they build upon
specific properties of the underlying PKE, or impose severe restrictions
on the size of the underlying anamorphic message space.
In this paper we consider the question of whether it is possible to have
realizations of the primitive that are both generic and allow for large
anamorphic message spaces. We give strong indications that, unfortu-
nately, this is not the case.
Our first result shows that any black-box realization of the primitive, i.e.
any realization that accesses the underlying PKE only via oracle calls,
must have an anamorphic message space of size at most O(poly(λ)) (λ
security parameter).
Even worse, if one aims at stronger variants of the primitive (and, specif-
ically, the notion of asymmetric anamorphic encryption, recently pro-
posed by Catalano et al.) we show that such black-box realizations are
plainly impossible, i.e. no matter how small the anamorphic message
space is.
Finally, we show that our impossibility results are rather tight: indeed,
by making more specific assumptions on the underlying PKE, it becomes
possible to build generic AE where the anamorphic message space is of
size Ω(2^λ).

2024

CRYPTO

Limits on the Power of Prime-Order Groups: Separating Q-Type from Static Assumptions
Abstract

Subgroup decision techniques on cryptographic groups and pairings have been critical for numerous applications. Originally conceived in the composite-order setting, there is a large body of work showing how to instantiate subgroup decision techniques in the prime-order setting as well. In this work, we demonstrate the first barrier to this research program, by demonstrating an important setting where composite-order techniques cannot be replicated in the prime-order setting.
In particular, we focus on the case of q-type assumptions, which are ubiquitous in group- and pairing-based cryptography, but unfortunately are less desirable than the more well-understood static assumptions. Subgroup decision techniques have had great success in removing q-type assumptions, even allowing q-type assumptions to be generically based on static assumptions on composite-order groups. Our main result shows that the same likely does \emph{not} hold in the prime order setting. Namely, we show that a large class of q-type assumptions, including the security definition of a number of cryptosystems, cannot be proven secure in a black box way from any static assumption.

2024

CRYPTO

Linear-Communication Asynchronous Complete Secret Sharing with Optimal Resilience
Abstract

Secure multiparty computation (MPC) allows a set of $n$ parties to jointly compute a function on their private inputs. In this work, we focus on the information-theoretic MPC in the \emph{asynchronous network} setting with optimal resilience ($t<n/3$). The best-known result in this setting is achieved by Choudhury and Patra [J. Cryptol '23], which requires $O(n^4\kappa)$ bits per multiplication gate, where $\kappa$ is the size of a field element.
An asynchronous complete secret sharing (ACSS) protocol allows a dealer to share a batch of Shamir sharings such that all parties eventually receive their shares. ACSS is an important building block in AMPC. The best-known result of ACSS is due to Choudhury and Patra [J. Cryptol '23], which requires $O(n^3\kappa)$ bits per sharing. On the other hand, in the synchronous setting, it is known that distributing Shamir sharings can be achieved with $O(n\kappa)$ bits per sharing. There is a gap of $n^2$ in the communication between the synchronous setting and the asynchronous setting.
Our work closes this gap by presenting the first ACSS protocol that achieves $O(n\kappa)$ bits per sharing. When combined with the compiler from ACSS to AMPC by Choudhury and Patra [IEEE Trans. Inf. Theory '17], we obtain an AMPC with $O(n^2\kappa)$ bits per sharing, improving the previously best-known result by a factor of $n^2$. Moreover, with a concurrent work that improves the compiler by Choudhury and Patra by a factor of $n$, we obtain the first AMPC with $O(n\kappa)$ bits per multiplication gate.

2024

CRYPTO

Loquat: A SNARK-Friendly Post-Quantum Signature based on the Legendre PRF with Applications in Ring and Aggregate Signatures
Abstract

We design and implement a novel post-quantum signature scheme based on the Legendre PRF, named Loquat. Prior to this work, efficient approaches for constructing post-quantum signatures with comparable security assumptions mainly used the MPC-in-the-head paradigm or hash trees. Our method departs from these paradigms and, notably, is SNARK-friendly, a feature not commonly found in earlier designs. Loquat requires significantly fewer computational operations for verification than other symmetric-key-based post-quantum signature schemes that support stateless signing. Our Python implementation of Loquat demonstrate a signature size of 46KB, with a signing time of 5.04 seconds and a verification time of 0.21 seconds. Instantiating the random oracle with an algebraic hash function results in the R1CS constraints for signature verification being about 148K, 7 to 175 times smaller than those required for MPC-in-the-head-based signatures and 3 to 9 times less than those for SPHINCS+ [Bernstein et al. CCS’19].
We explore two applications of Loquat. First, we incorporate it into the ID-based ring signature scheme [Buser et al. ACNS’22], achieving a significant reduction in signature size from 1.9 MB to 0.9 MB with stateless signing and practical master key generation. Our second application presents a SNARK-based aggregate signature scheme. We use the implementations of Aurora [Ben-Sasson et al. EC’19] and Fractal [Chiesa et al. EC’20] to benchmark our aggregate signature’s performance. Our findings show that aggregating 32 Loquat signatures using Aurora results in a proving time of about 7 minutes, a verification time of 66 seconds, and an aggregate signature size of 197 KB. Furthermore, by leveraging the recursive proof composition feature of Fractal, we achieve an aggregate signature with a constant size of 145 KB, illustrating Loquat’s potential for scalability in cryptographic applications.

2024

CRYPTO

Lossy Cryptography from Code-Based Assumptions
Abstract

Over the past few decades, we have seen a proliferation of advanced cryptographic primitives with lossy or homomorphic properties built from various assumptions such as Quadratic Residuosity, Decisional Diffie-Hellman, and Learning with Errors. These primitives imply hard problems in the complexity class $\mathcal{SZK}$ (statistical zero-knowledge); as a consequence, they can only be based on assumptions that are broken in $\mathcal{BPP}^{\mathcal{SZK}}$.
This poses a barrier for building advanced cryptography from code-based assumptions such as Learning Parity with Noise (LPN), as LPN is only known to be in $\mathcal{BPP}^{\mathcal{SZK}}$ under an extremely low noise rate $\frac{\log^2 n}{n}$, for which it is broken in quasi-polynomial time.
In this work, we propose a new code-based assumption: Dense-Sparse LPN, that falls in the complexity class $\mathcal{BPP}^{\mathcal{SZK}}$ and is conjectured to be secure against subexponential time adversaries. Our assumption is a variant of LPN that is inspired by McEliece's cryptosystem and random $k\mbox{-}$XOR in average-case complexity. Roughly, the assumption states that
\[(\mathbf{T}\, \mathbf{M}, \mathbf{s} \,\mathbf{T}\, \mathbf{M} + \mathbf{e}) \quad \text{is indistinguishable from}\quad (\mathbf{T} \,\mathbf{M}, \mathbf{u}),\]
for a random (dense) matrix $\mathbf{T}$, random sparse matrix $\mathbf{M}$, and sparse noise vector $\mathbf{e}$ drawn from the Bernoulli distribution with inverse polynomial noise probability.
We leverage our assumption to build lossy trapdoor functions (Peikert-Waters STOC 08). This gives the first post-quantum alternative to the lattice-based construction in the original paper. Lossy trapdoor functions, being a fundamental cryptographic tool, are known to enable a broad spectrum of both lossy and non-lossy cryptographic primitives; our construction thus implies these primitives in a generic manner. In particular, we achieve collision-resistant hash functions with plausible subexponential security, improving over a prior construction from LPN with noise rate $\frac{\log^2 n}{n}$ that is only quasi-polynomially secure.

2024

CRYPTO

Malicious Security for SCALES: Outsourced Computation with Ephemeral Servers
Abstract

SCALES (Small Clients And Larger Ephemeral Servers) model is a recently proposed model for MPC (Acharya et al., TCC 2022). While the SCALES model offers several attractive features for practical large-scale MPC, the result of Acharya et al. only offered semi-honest secure protocols in this model.
We present a new efficient SCALES protocol secure against malicious adversaries, for general Boolean circuits. We start with the base construction of Acharya et al. and design and use a suite of carefully defined building blocks that may be of independent interest. The resulting protocol is UC-secure without honest majority, with a CRS and bulletin-board as setups, and allows publicly identifying deviations from correct execution.

2024

CRYPTO

Mangrove: A Scalable Framework for Folding-based SNARKs
Abstract

We present a framework for building efficient folding-based SNARKs. First we develop a new ``uniformizing'' compiler for NP statements that converts any poly-time computation to a sequence of identical simple steps. The resulting uniform computation is especially well-suited to be processed by a folding-based IVC scheme. Second, we develop two optimizations to folding-based IVC. The first reduces the recursive overhead of the IVC by restructuring the relation to which folding is applied. The second employs a ``commit-and-fold'' strategy to further simplify the relation. Together, these optimizations result in a folding-based SNARK that has a number of attractive features. First, the scheme uses a constant-size transparent common reference string (CRS). Second, the prover has (i) low memory footprint, (ii) makes only two passes over the data, (iii) is highly parallelizable, and (iv) is concretely efficient. Proving time is comparable to leading monolithic SNARKs, and is significantly faster than other streaming SNARKs. For example, for proving $2^{24}$ constraints, we estimate that a Mangrove prover takes about $64$ seconds, $10$ times faster than Spartan SNARK, while using less than 160MB of memory.

2024

CRYPTO

Memory-Sample Lower Bounds for LWE
Abstract

In this work, we show memory-sample lower bounds for the fundamental problem of learning with error (LWE). In this problem, a learner tries to learn a uniformly sampled $x \sim \Z_q^n$ from a stream of inner products plus errors sampled from discrete Gaussians of scale $\sigma$. Any learning algorithm requires either at least $\Omega(k^2 / \log(q / \sigma))$ bits of memory, or at least $2^{\Omega(k)}$ many samples, where $k = \Omega(n \log(1 / (1 - \phi(q)/q)))$. This matches with the information-theoretic upper bound when $q$ is prime.
In addition to LWE, our bounds apply to a wide range of learning problems. Following the work of Garg, Raz, Tal [STOC 2018], we describe a learning problem by a learning matrix $M \colon A \times X \to \{0, 1, \cdots, q-1\}$ together with an error matrix $\vare$. The learner tries to learn $x \sim X$ from a stream of samples, $(a_1, b_1), \cdots, (a_m, b_m)$, where for every $i$, $a_i \sim A$, and $b_i \leftarrow t$ with probability $\vare_{M(a,x),t}$.
We characterize the learning problems that can have memory-sample lower bounds as ``$q$-balanced'', which is a generalization of the $L2$-extractor in [GRT18]. We also show a reduction from $q$-balanced to $L2$-extractor, which provides a general way to prove $q$-balanced and thus apply our bounds.
Our proof builds on [GRT18] and the work of Garg, Kothari, Liu, Raz [APPROX/RANDOM 2021].

2024

CRYPTO

More Efficient Zero-Knowledge Protocols over $\mathbb{Z}_{2^k}$ via Galois Rings
Abstract

A recent line of works on zero-knowledge (ZK) protocols with a vector oblivious linear function evaluation (VOLE)-based offline phase provides a new paradigm for scalable ZK protocols featuring fast proving and small prover memory. Very recently, Baum et al. (Crypto'23) proposed the VOLE-in-the-head technique, allowing such protocols to become publicly verifiable. Many practically efficient protocols for proving circuit satisfiability over any Galois field are implemented, while protocols over rings $\mathbb{Z}_{2^k}$ are significantly lagging behind, with only a proof-of-concept pioneering work called Appenzeller to Brie (CCS'21) and a first proposal called Moz$\mathbb{Z}_{2^k}$arella (Crypto'22). The ring $\mathbb{Z}_{2^{32}}$ or $\mathbb{Z}_{2^{64}}$, though highly important (it captures computation in real-life programming and the computer architectures such as CPU words), presents non-trivial difficulties because, for example, unlike Galois fields $\mathbb{F}_{2^{k}}$, the fraction of units in $\mathbb{Z}_{2^{k}}$ is $1/2$. In this work, we first construct ZK protocols over a high degree Galois ring extension of $\mathbb{Z}_{2^{k}}$ (fraction of units close to $1$) and then convert them to $\mathbb{Z}_{2^k}$ efficiently using amortization techniques. Our results greatly change the landscape of ZK protocols over~$\mathbb{Z}_{2^k}$.
(1) We propose a competing ZK protocol that has many advantages over the state-of-the-art Moz$\mathbb{Z}_{2^k}$arella. We remove the undesirable dependence of communication complexity on the security parameter, and achieve communication complexity {\em strictly} linear in the circuit size. Furthermore, our protocol has better concrete efficiency. For $40,80$ bits soundness on circuits over $\mathbb{Z}_{2^{32}}$ and $\mathbb{Z}_{2^{64}}$, we offer $1.15\times$--$2.9\times$ improvements in communication.
(2) Inspired by the recently proposed interactive message authentication code technique (Weng et al., CCS'22), we construct a constant round ZK protocol over $\mathbb{Z}_{2^k}$ with sublinear (in the circuit size) communication complexity, which was previously achieved only over fields.
(3) We show that the pseudorandom correlation generator approach can be adapted to efficiently implement VOLE over Galois rings, with analysis of the hardness of underlying LPN assumptions over Galois rings.
(4) We adapt the VOLE-in-the-head technique to make it work for $\mathbb{Z}_{2^k}$, yielding {\em publicly verifiable} non-interactive ZK protocols over $\mathbb{Z}_{2^k}$ which preserve most of the efficiency metrics of the VOLE-based ZK protocols.

2024

CRYPTO

MPC for Tech Giants (GMPC): Enabling Gulliver and the Lilliputians to Cooperate Amicably
Abstract

In the current digital world, large organizations (sometimes referred to as tech giants) provide service to extremely large numbers of users. The service provider is often interested in computing various data analyses over the private data of its users, which in turn have their incentives to cooperate, but do not necessarily trust the service provider.
In this work, we introduce the \emph{Gulliver multi-party computation model} (GMPC) to realistically capture the above scenario. The GMPC model considers a single highly powerful party, called the {\em server} or {\em Gulliver}, that is connected to $n$ users over a star topology network (alternatively formulated as a full network, where the server can block any message). The users are significantly less powerful than the server, and, in particular, should have both computation and communication complexities that are polylogarithmic in $n$. Protocols in the GMPC model should be secure against malicious adversaries that may corrupt a subset of the users and/or the server.
Designing protocols in the GMPC model is a delicate task, since users can only hold information about $\polylog(n)$ other users (and, in particular, can only communicate with $\polylog(n)$ other users). In addition, the server can block any message between any pair of honest parties. Thus, reaching an agreement becomes a challenging task. Nevertheless, we design generic protocols in the GMPC model, assuming that at most $\alpha<1/8$ fraction of the users may be corrupted (in addition to the server). Our main contribution is a variant of Feige's committee election protocol [FOCS 1999] that is secure in the GMPC model. Given this tool we show:
1. Assuming fully homomorphic encryption (FHE), any computationally efficient function with $O(n\cdot\polylog(n))$-size output can be securely computed in the GMPC model.
2. Any function that can be computed by a circuit of $O(\polylog(n))$ depth, $O(n\cdot\polylog(n))$ size, and bounded fan-in and fan-out can be securely computed in the GMPC model assuming vector commitment schemes (without assuming FHE).
3. In particular, {\em sorting} can be securely computed in the GMPC model assuming vector commitment schemes. This has important applications for the {\em shuffle model of differential privacy}, and resolves an open question of Bell et al. [CCS 2020].

2024

CRYPTO

MPC in the head using the subfield bilinear collision problem
Abstract

In this paper, we introduce the subfield bilinear collision problem and use it to construct an identification protocol and a signature scheme. This construction is based on the MPC-in-the-head paradigm and uses the Fiat-Shamir transformation to obtain a signature.

2024

CRYPTO

New Approaches for Estimating the Bias of Differential-Linear Distinguishers
Abstract

Differential-linear cryptanalysis was introduced by Langford and Hellman in 1994 and has been extensively studied since then. In 2019, Bar-On et al. presented the Differential-Linear Connectivity Table (DLCT), which connects the differential part and the linear part, thus an attacked cipher is divided to 3 subciphers: the differential part, the DLCT part, and the linear part.
In this paper, we firstly present an accurate mathematical formula which establishes a relation between differential-linear and truncated differential cryptanalysis. Using the formula, the bias estimate of a differential-linear distinguisher can be converted to the probability calculations of a series of truncated differentials. Then, we propose a novel and natural concept, the TDT, which can be used to accelerate the calculation of the probabilities of truncated differentials. Based on the formula and the TDT, we propose two novel approaches for estimating the bias of a differential-linear distinguisher. We demonstrate the accuracy and efficiency of our new approaches by applying them to 5 symmetric-key primitives: Ascon, Serpent, AES, CLEFIA, and KNOT. For Ascon and Serpent, we update the best known differential-linear distinguishers. For AES, CLEFIA, and KNOT, for the first time we give the theoretical differential-linear biases for different rounds.

2024

CRYPTO

Non-Interactive Zero-Knowledge from LPN and MQ
Abstract

We give the first construction of non-interactive zero-knowledge (NIZK) arguments from post-quantum assumptions other than Learning with Errors. In particular, we achieve NIZK under the polynomial hardness of the Learning Parity with Noise (LPN) assumption, and the exponential hardness of solving random underdetermined multivariate quadratic equations (MQ). We also construct NIZK satisfying statistical zero-knowledge assuming a new variant of LPN, Dense-Sparse LPN, introduced by Dao and Jain (ePrint 2024), together with exponentially-hard MQ.
The main technical ingredient of our construction is an extremely natural (but only in hindsight!) construction of correlation-intractable (CI) hash functions from MQ, for a NIZK-friendly sub-class of constant-degree polynomials that we call concatenated constant-degree polynomials. Under exponential security, this hash function also satisfies the stronger notion of approximate CI for concatenated constant-degree polynomials. The NIZK construction then follows from a prior blueprint of Brakerski-Koppula-Mour (CRYPTO 2020). In addition, we also show how to construct (approximate) CI hashing for degree-$d$ polynomials from the (exponential) hardness of solving random degree-$d$ equations, a natural generalization of MQ. To realize NIZK with statistical zero-knowledge, we design a lossy public-key encryption scheme with approximate linear decryption and inverse-polynomial decryption error from Dense-Sparse LPN. These constructions may be of independent interest.
Our work therefore gives a new way to leverage MQ with uniformly random equations, which has found little cryptographic applications to date. Indeed, most applications in the context of encryption and signature schemes make use of structured variants of MQ, where the polynomials are not truly random but posses a hidden planted structure. We believe that the MQ assumption may plausibly find future use in the designing other advanced proof systems.

2024

CRYPTO

Not Just Regular Decoding: Asymptotics and Improvements of Regular Syndrome Decoding Attacks
Abstract

Cryptographic constructions often base security on structured problem variants to enhance efficiency or to enable advanced functionalities. This led to the introduction of the Regular Syndrome Decoding (RSD) problem, which guarantees that a solution to the Syndrome Decoding (SD) problem follows a particular block-wise structure. Despite recent attacks exploiting that structure by Briaud and Øygarden (Eurocrypt ’23) and Carozza, Couteau and Joux (CCJ, Eurocrypt ’23), many questions about the impact of the regular structure on the problem hardness remain open.
In this work we initiate a systematic study of the hardness of the RSD problem starting from its asymptotics. We classify different parameter regimes revealing large regimes for which RSD instances are solvable in polynomial time and on the other hand regimes that lead to particularly hard instances. Against previous perceptions, we show that a classification solely based on the uniqueness of the solution is not sufficient for isolating the worst case parameters. Further, we provide an in-depth comparison between SD and RSD in terms of reducibility and computational complexity, identifying regimes in which RSD instances are actually *harder* to solve.
We provide the first asymptotic analyses of the algorithms presented by CCJ, establishing their worst case decoding complexities as $2^{0.141n}$ and $2^{0.135n}$, respectively. We then introduce *regular-ISD* algorithms by showing how to tailor the whole machinery of advanced Information Set Decoding (ISD) techniques from attacking SD to the RSD setting. The fastest regular-ISD algorithm improves the worst case decoding complexity significantly to $2^{0.113n}$. Eventually, we show that also with respect to suggested parameters regular-ISD outperforms previous approaches in most cases, reducing security levels by up to 30 bits.

2024

CRYPTO

Oblivious issuance of proofs
Abstract

We consider the problem of creating, or issuing, zero-knowledge proofs {\em obliviously}. In this setting, a prover
interacts with a verifier to produce a proof, known only to the verifier.
The resulting proof is transferrable and can be verified non-interactively by anyone. Crucially, the actual proof cannot be linked back to the interaction that produced it. This notion generalizes common approaches to designing blind signatures, which can be seen as the special case of proving ``knowledge of a signing key'', and extends the seminal work of Camenisch and Stadler ('97). We propose a provably secure construction of oblivious proofs, focusing on discrete-logarithm representation equipped with AND-composition.
We also give three applications of our framework. First, we give a publicly verifiable version of the classical Diffie-Hellman based Oblivious PRF. This yields new constructions of blind signatures and publicly verifiable anonymous tokens. Second, we show how to "upgrade" keyed-verification anonymous credentials (Chase et al., CCS'14) to also be concurrently secure blind signatures on the same set of attributes. Crucially, our upgrade maintains the performance and functionality of the credential in the keyed-verification setting, we only change issuance. We observe that the existing issuer proof that the credential is well-formed may be verified by anyone; creating it with our framework makes it a blind signature, adding public verifiability to the credential system. Finally, we provide a variation of the U-Prove credential system that is provably one-more unforgeable with concurrent issuance sessions. This constitutes a fix for the attack illustrated by Benhamouda et al. (EUROCRYPT'21).
Beyond these example applications, as our results are quite general, we expect they may enable modular design of new primitives with concurrent security, a goal that has historically been challenging to achieve.

2024

CRYPTO

On Central Primitives for Quantum Cryptography with Classical Communication
Abstract

Recent work has introduced the “Quantum-Computation
Classical-Communication” (QCCC) (Chung et. al.) setting for cryptog-
raphy. There has been some evidence that One Way Puzzles (OWPuzz)
are the natural central cryptographic primitive for this setting (Khurana
and Tomer). For a primitive to be considered central it should have sev-
eral characteristics. It should be well behaved (which for this paper we
will think of as having amplification, combiners, and universal construc-
tions); it should be implied by a wide variety of other primitives; and
it should be equivalent to some class of useful primitives. We present
combiners, correctness and security amplification, and a universal con-
struction for OWPuzz. Our proof of security amplification uses a new
and cleaner version construction of EFI from OWPuzz (in comparison
to the result of Khurana and Tomer) that generalizes to weak OWPuzz
and is the most technically involved section of the paper. It was pre-
viously known that OWPuzz are implied by other primitives of interest
including commitments, symmetric key encryption, one way state gen-
erators (OWSG), and therefore pseudorandom states (PRS). However we
are able to rule out OWPuzz’s equivalence to many of these primitives
by showing a black box separation between general OWPuzz and a re-
stricted class of OWPuzz (those with efficient verification, which we call
EV − OWPuzz). We then show that EV − OWPuzz are also implied by
most of these primitives, which separates them from OWPuzz as well.
This separation also separates extending PRS from highly compressing
PRS answering an open question of Ananth et. al.

2024

CRYPTO

On cycles of pairing-friendly abelian varieties
Abstract

One of the most promising avenues for realizing scalable proof systems relies on the existence of 2-cycles of pairing-friendly elliptic curves. Such a cycle consists of two elliptic curves E/GF(p) and E'/GF(q) that both have a low embedding degree and also satisfy q = #E and p = #E'. These constraints turn out to be rather restrictive; in the decade that has passed since 2-cycles were first proposed for use in proof systems, no new constructions of 2-cycles have been found.
In this paper, we generalize the notion of cycles of pairing-friendly elliptic curves to study cycles of pairing-friendly abelian varieties, with a view towards realizing more efficient pairing-based SNARKs. We show that considering abelian varieties of dimension larger than 1 unlocks a number of interesting possibilities for finding pairing-friendly cycles, and we give several new constructions that can be instantiated at any security level.

2024

CRYPTO

On round elimination for special-sound multi-round identification and the generality of the hypercube for MPCitH
Abstract

A popular way to build post-quantum signature schemes is by first constructing an identification scheme (IDS) and applying the Fiat-Shamir transform to it. In this work we tackle two open questions related to the general applicability of techniques around this approach that together allow for efficient post-quantum signatures with optimal security bounds in the QROM.
First, we consider a recent work by Aguilar-Melchor, Hülsing, Joseph, Majenz, Ronen, and Yue (Asiacrypt'23) that showed that an optimal bound for three-round commit & open IDS by Don, Fehr, Majenz, and Schaffner (Crypto'22) can be applied to the five-round Syndrome-Decoding in the Head (SDitH) IDS. For this, they first applied a transform that replaced the first three rounds by one. They left it as an open problem if the same approach applies to other schemes beyond SDitH. We answer this question in the affirmative, generalizing their round-elimination technique and giving a generic security proof for it. Our result applies to any IDS with $2n+1$ rounds for $n>1$. However, a scheme has to be suitable for the resulting bound to not be trivial. We find that IDS are suitable when they have a certain form of special-soundness which many commit & open IDS have.
Second, we consider the hypercube technique by Aguilar-Melchor, Gama, Howe, Hülsing, Joseph, and Yue (Eurocrypt'23). An optimization that was proposed in the context of SDitH and is now used by several of the contenders in the NIST signature on-ramp. It was conjectured that the technique applies generically for the MPC-in-the-Head (MPCitH) technique that is used in the design of many post-quantum IDS if they use an additive secret sharing scheme but this was never proven. In this work we show that the technique generalizes to MPCitH IDS that use an additively homomorphic MPC protocol, and we prove that security is preserved.
We demonstrate the application of our results to the identification scheme of RYDE, a contender in the recent NIST signature on-ramp. While RYDE was already specified with the hypercube technique applied, this gives the first QROM proof for RYDE with an optimally tight bound.

2024

CRYPTO

On Sequential Functions and Fine-Grained Cryptography
Abstract

A sequential function is, informally speaking, a function f for which a massively parallel adversary cannot compute "substantially" faster than an honest user with limited parallel computation power. Sequential functions form the backbone of many primitives that are extensively used in blockchains such as verifiable delay functions (VDFs) and time-lock puzzles. Despite this widespread practical use, there has been little work studying the complexity or theory of sequential functions.
Our main result is a black-box oracle separation between sequential functions and one-way functions: in particular, we show the existence of an oracle O that implies a sequential function but not a one-way function. This seems surprising since sequential functions are typically constructed from very strong assumptions that imply one-way functions and also since time-lock puzzles are known to imply one-way functions (Bitansky et al., ITCS '16).
We continue our exploration of the theory of sequential functions. We show that, informally speaking, the decisional, worst-case variant of a certain class of sequential function called a continuous iterative sequential function (CISF) is PSPACE-complete. A CISF is, in a nutshell, a sequential function f that can be written in the form f(k, x) = g^k (x) for some function g where k is an input determining the number of "rounds" the function is evaluated. We then show that more general forms of sequential functions are not contained in PSPACE relative to a random oracle.
Given these results, we then ask if it is possible to build any interesting cryptographic primitives from sequential functions that are not one-way. It turns out that even if we assume just the existence of a CISF that is not one-way, we can build certain "fine-grained" cryptographic primitives where security is defined similarly to traditional primitives with the exception that it is only guaranteed for some (generally polynomial) amount of time. In particular, we show how to build "fine-grained" symmetric key encryption and "fine-grained" MACs from a CISF. We also show how to build fine-grained public-key encryption from a VDF with a few extra natural properties and indistinguishability obfucsation (iO) for null circuits. We do not assume one-way functions. Finally, we define a primitive that we call a commutative sequential function--essentially a sequential function that can be computed in sequence to get the same output in two different ways--and show that it implies fine-grained key exchange.

2024

CRYPTO

On the (In)Security of the BUFF Transform
Abstract

The BUFF transform is a generic transformation for digital signature schemes, with the purpose of obtaining additional security properties beyond standard unforgeability, e.g., exclusive ownership and non-resignability. In the call for additional post-quantum signatures, these were explicitly mentioned by the NIST as ``additional desirable security properties'', and some of the submissions indeed refer to the BUFF transform with the purpose of achieving them, while some other submissions follow the design of the BUFF transform without mentioning it explicitly.
In this work, we show the following negative results regarding the non-resignability property in general, and the BUFF transform in particular. In the plain model, we observe by means of a simple attack that any signature scheme for which the message has a high entropy given the signature does not satisfy the non-resignability property (while non-resignability is trivially not satisfied if the message can be efficiently computed from its signature). Given that the BUFF transform has high entropy in the message given the signature, it follows that the BUFF transform does not achieve non-resignability whenever the random oracle is instantiated with a hash function, no matter what hash function.
When considering the random oracle model (ROM), the matter becomes slightly more delicate since prior works did not rigorously define the non-resignability property in the ROM. For the natural extension of the definition to the ROM, we observe that our impossibility result still holds, despite there having been positive claims about the non-resignability of the BUFF transform in the ROM. Indeed, prior claims of the non-resignability of the BUFF transform rely on faulty argumentation.
On the positive side, we prove that a salted version of the BUFF transform satisfies a slightly weaker variant of non-resignability in the ROM, covering both classical and quantum attacks, if the entropy requirement in the (weakened) definition of non-resignability is statistical; for the computational variant, we show yet another negative result.

2024

CRYPTO

On the practical CPAD security of "exact" and threshold FHE schemes and libraries
Abstract

In their Eurocrypt'21 seminal paper, Li and Micciancio presented a passive attack against the CKKS approximate FHE scheme and introduced the notion of CPAD security. The current status quo is that this line of attacks does not apply to "exact" FHE. In this paper, we challenge this status quo by exhibiting a CPAD key recovery attack on the linearly homomorphic Regev cryptosystem which easily generalizes to other xHE schemes such as BFV, BGV and TFHE showing that these cryptosystems are not CPAD secure in their basic form. We also show that existing threshold variants of BFV, BGV and CKKS are particularily exposed to CPAD attackers and would be CPAD-insecure without proper smudging noise addition after partial decryption. Finally we successfully implement our attack against several mainstream FHE libraries and discuss a number of natural countermeasures as well as their consequences in terms of FHE practice, security and efficiency. The attack itself is quite practical as it typically takes less than an hour on an average laptop PC, requiring a few thousand ciphertexts as well as up to around a million evaluations/decryptions, to perform a full key recovery.

2024

CRYPTO

Pairing-Free Blind Signatures from CDH Assumptions
Abstract

We present the first concurrently-secure blind signatures making black-box use of a pairing-free group for which unforgeability, in the random oracle model, can be proved {\em without} relying on the algebraic group model (AGM), thus resolving a long-standing open question. Prior pairing-free blind signatures without AGM proofs have only been proved secure for bounded concurrency, relied on computationally expensive non-black-box use of NIZKs, or had complexity growing with the number of signing sessions due to the use of boosting techniques.
Our most efficient constructions rely on the chosen-target CDH assumption and can be seen as blind versions of signatures by Goh and Jarecki (EUROCRYPT '03) and Chevallier-Mames (CRYPTO '05). We also give a less efficient scheme with security based on (plain) CDH. The underlying signing protocols consist of four (in order to achieve regular unforgeability) or five moves (for strong unforgeability). All schemes are proved statistically blind in the random oracle model.

2024

CRYPTO

Pairing-Free Blind Signatures from Standard Assumptions in the ROM
Abstract

Blind Signatures are a useful primitive for privacy preserving
applications such as electronic payments, e-voting, anonymous credentials,
and more. However, existing practical blind signature schemes based on
standard assumptions require either pairings or lattices. We present the
first construction of a round-optimal blind signature in the random oracle
model based on standard assumptions without resorting to pairings or
lattices. In particular, our construction is secure under the strong RSA
assumption and DDH (in pairing-free groups). For our construction, we
provide a NIZK-friendly signature based on strong RSA, and efficiently
instantiate a variant of Fischlin’s generic framework (CRYPTO’06). Our
Blind Signature scheme has signatures of size 4.28 KB and communication
cost 10.98 KB. On the way, we develop techniques that might be of
independent interest. In particular, we provide efficient relaxed range-
proofs for large ranges with subversion zero-knowledge and compact
commitments to elements of arbitrary groups.

2024

CRYPTO

PIR with Client-Side Preprocessing: Information-Theoretic Constructions and Lower Bounds
Abstract

It is well-known that classical Private Information Retrieval
(PIR) schemes without preprocessing must suffer from linear server com-
putation per query, and moreover, any classical single-server PIR with
sublinear bandwidth must rely on “public-key operations”. Several re-
cent works showed that these barriers pertaining to classical PIR can be
overcome by introducing a preprocessing phase where each client down-
loads a hint that helps it makes queries subsequently. Notably, the Piano
PIR scheme (and subsequent improvements) showed that with such a
client-specific preprocessing, not only can we have PIR with sublinear
computation and bandwidth per query, somewhat surprisingly, we can
also get it using only symmetric-key operations (i.e., one-way functions).
In this paper, we take the question of minimizing cryptographic assump-
tions to an extreme. Specifically, we are the first to explore the landscape
of information theoretic single-server preprocessing PIR. We make con-
tributions on both the upper- and lower-bounds fronts. First, we show
new information-theoretic constructions with non-trivial performance
bounds. Second, we prove a (nearly) tight lower bound on the client-
space and bandwidth tradeoff. Moreover, we also prove that natural ap-
proaches towards constructing preprocessing PIR with better-than-Piano
client-space/bandwidth tradeoff would imply a hard SZK problem which
cannot be constructed in a black-box fashion from one-way functions or
collision-resistant hashing. This shows that Piano achieves (nearly) opti-
mal client space and bandwidth tradeoff subject to using only symmetric-
key operations. The techniques for proving our new upper- and lower-
bounds can also be of independent interest.

2024

CRYPTO

Plaintext-Ciphertext Matrix Multiplication and FHE Bootstrapping: Fast and Fused
Abstract

Homomorphically multiplying a plaintext matrix with a ciphertext matrix (PC-MM) is a central task for the private evaluation of transformers, commonly used for large language models. We provide several RLWE-based algorithms for PC-MM that consist of multiplications of plaintext matrices (PC-MM) and comparatively cheap pre-processing and post-processing steps: for small and large dimensions compared to the RLWE ring degree, and with and without precomputation. For the algorithms with precomputation, we show how to perform a \pcmm with a single floating-point PC-MM of the same dimensions. This is particularly meaningful for practical purposes as a floating-point PC-MM can be implemented using high-performance BLAS libraries.
The algorithms rely on the multi-secret variant of RLWE, which allows to represent multiple ciphertexts more compactly. We give algorithms to convert from usual shared-secret RLWE ciphertexts to multi-secret ciphertexts and back. Further, we show that this format is compatible with homomorphic addition, plaintext-ciphertext multiplication, and key-switching. This in turn allows us to accelerate the slots-to-coeffs and coeffs-to-slots steps of CKKS bootstrapping when several ciphertexts are bootstrapped at once. Combining batch-bootstrapping with efficient PC-MM results in MaMBo (Matrix Multiplication Bootstrapping), a bootstrapping algorithm that can perform a PC-MM for a limited overhead.

2024

CRYPTO

Polymath: Groth16 Is Not The Limit
Abstract

Shortening the argument (three group elements or 1536 / 3072 bits over the BLS12-381/BLS24-509 curves) of the Groth16 zk-SNARK for R1CS is a long-standing open problem. We propose a zk-SNARK Polymath for the Square
Arithmetic Programming constraint system using the KZG polynomial commitment scheme. Polymath has a shorter argument (1408 / 1792 bits over the same curves) than Groth16. At 192-bit security, Polymath's argument is nearly
half the size, making it highly competitive for high-security future applications. Notably, we handle public inputs in a simple way. We optimized Polymath's prover through an exhaustive parameter search. Polymath's prover does not output $\mathbb{G}_{2}$ elements, aiding in batch verification, SNARK aggregation, and recursion. Polymath's properties make it highly suitable to be the final SNARK in SNARK compositions.

2024

CRYPTO

Polynomial Commitments from Lattices: Post-Quantum Security, Fast Verification and Transparent Setup
Abstract

Polynomial commitment scheme allows a prover to commit to a polynomial $f \in \ring[X]$ of degree $L$, and later prove that the committed function was correctly evaluated at a specified point $x$; in other words $f(x)=u$ for public $x,u \in \ring$. Most applications of polynomial commitments, e.g. succinct non-interactive arguments of knowledge (SNARKs), require that (i) both the commitment and evaluation proof are succinct (i.e., polylogarithmic in the degree $L$) - with the latter being efficiently verifiable, and (ii) no pre-processing step is allowed.
Surprisingly, as far as plausibly quantum-safe polynomial commitments are concerned, the currently most efficient constructions only rely on weak cryptographic assumptions, such as security of hash functions. Indeed, despite making use of the underlying algebraic structure, prior lattice-based polynomial commitments still seem to be much behind the hash-based ones. Moreover, security of the aforementioned lattice constructions against quantum adversaries was never formally discussed.
In this work, we bridge the gap and propose the first (asymptotically and concretely) efficient lattice-based polynomial commitment with transparent setup and post-quantum security. Our interactive variant relies on the standard (Module-)SIS problem, and can be made non-interactive in the random oracle model using Fiat-Shamir transformation. In addition, we equip the scheme with a knowledge soundness proof against quantum adversaries which can be of independent interest. In terms of concrete efficiency, for $L=2^{20}$ our scheme yields proofs of size $2$X smaller than the hash-based \textsf{FRI} commitment (Block et al., Asiacrypt 2023), and $60$X smaller than the very recent lattice-based construction by Albrecht et al. (Eprint 2023/1469).

2024

CRYPTO

Polytopes in the Fiat-Shamir with Aborts Paradigm
Abstract

The Fiat-Shamir with Aborts paradigm (FSwA) uses rejection sampling to remove a secret’s dependency from a given source distribution. Recent results revealed that unlike the uniform distribution in the hypercube, both the continuous Gaussian and the uniform distribution within the hypersphere minimise the rejection rate and the size of the proof of knowledge. However, in practice both these distributions suffer from the complexity of their sampler. So far, those three distributions are the only available alternatives, but none of them offer the best of all worlds: competitive proof of knowledge size and rejection rate with a simple sampler.
We introduce a new generic framework for FSwA using polytope based rejection sampling to enable a wider variety of constructions. As a matter of fact, this framework is the first to generalise these results to integral distributions. To complement the lack of alternatives, we also propose a new polytope construction, whose uniform sampler approaches in simplicity that of the hypercube. At the same time, it provides competitive proof of knowledge sizes compared to those obtained from the Gaussian distribution. Concurrently, we share some experimental improvements of our construction to further shorten the proof size. Finally, we propose a signature based on the FSwA paradigm using both our framework and construction. We prove it to be competitive with Haetae in signature size and with Dilithium on sampler simplicity.

2024

CRYPTO

Privacy-Preserving Dijkstra
Abstract

Given a graph $G(V,E)$, represented as a secret-sharing of an adjacency list, we show how to obliviously convert it into an alternative, MPC-friendly secret-shared representation, so-called $d${\sc-normalized replicated \linebreak adjacency list} (which we abbreviate to $d${\em -normalized}), where the size of our new data-structure is only 4x larger -- compared to the original (secret-shared adjacency list) representation of $G$. Yet, this new data structure enables us to execute oblivious graph algorithms that simultaneously improve underlying graph algorithms' round, computation, and communication complexity.
Our $d$-{\em normalization} proceeds in two steps:
\begin{itemize}
\item First, we show how for any graph $G$, given a secret-shared adjacency list, where vertices are arbitrary alphanumeric strings that fit into a single RAM memory word, we can efficiently and securely rename vertices to integers from $1$ to $V$ that will appear in increasing order in the resulting secret-shared adjacency list. The secure renaming takes $O(\log V)$ rounds and $O((V+E)\log V)$ secure operations. Our algorithm also outputs in a secret-shared form two arrays: a mapping from integers to alphanumeric names and its sorted inverse. Of course, if the adjacency list is already in such an integer format, this step could be skipped.
\item Second, given a secret-shared adjacency list for any graph $G$, where vertices are integers from $1$ to $V$ and are sorted, there exists a $d${\em-normalization}
algorithm that takes $O(1)$ rounds and $O((V+E))$ secure operations.
\end{itemize}
We believe that both conversions are of independent interest. We demonstrate the power of our data structures by designing a privacy-preserving Dijkstra's single-source shortest-path algorithm that simultaneously achieves
$O\left((V +E) \cdot \log V \right)$ secure operations and $O(V \cdot \log V \cdot \log \log\log V)$ rounds. Our secure Dijkstra algorithm works for any adjacency list representation as long as all vertex labels and weights can individually fit into RAM memory word.
Our algorithms work for two or a constant number of servers in the honest but curious setting. The limitation of our result (to only a constant number of servers) is due to our reliance on linear work and constant-round secure shuffle.
\noindent {\bf Keywords}: Oblivious Graph Algorithms, MPC, Oblivious RAM, Distributed \linebreak ORAM, Garbled RAM, Single-Source Shortest Path, Secure Dijkstra.

2024

CRYPTO

Probabilistic Linearization: Internal Differential Collisions in up to 6 Rounds of SHA-3
Abstract

The SHA-3 standard consists of four cryptographic hash functions, called SHA3-224, SHA3-256, SHA3-384 and SHA3-512, and two extendable-output functions (XOFs), called SHAKE128 and SHAKE256. In this paper, we study the collision resistance of the SHA-3 instances. By analyzing the nonlinear layer, we introduce the concept of maximum difference density subspace, and develop a new target internal difference algorithm by probabilistic linearization. We also exploit new strategies for optimizing the internal differential characteristic. Further more, we figure out the expected size of collision subsets in internal differentials, by analyzing the collision probability of the digests rather than the intermediate states input to the last nonlinear layer. These techniques enhance the analysis of internal differentials, leading to the best collision attacks on four round-reduced variants of the SHA-3 instances. In particular, the number of attacked rounds is extended to 5 from 4 for SHA3-384, and to 6 from 5 for SHAKE256.

2024

CRYPTO

Provable security against decryption failure attacks from LWE
Abstract

In a recent work, Hövelmanns, Hülsing and Majenz introduced a new security proof for the Fujisaki-Okamoto transform in the quantum-accessible random oracle model (QROM) used in post-quantum
key encapsulation mechanisms. While having a smaller security loss due to decryption failures present in many constructions, it requires two new security properties of the underlying public-key encryption scheme (PKE).
In this work, we show that one of the properties, Find Non-Generically Failing Plaintexts (FFP-NG) security, is achievable using an efficient lattice-based PKE that does not have perfect correctness. In particular, we show that LWE reduces to breaking FFP-NG security of the PVW scheme, when all LWE errors are discrete Gaussian distributed. The reduction has an arbitrarily small constant multiplicative loss in LWE error size. For the proof, we make use of techniques by Genise, Micciancio, Peikert and Walter to analyse marginal and conditional distributions of sums of discrete Gaussians.

2024

CRYPTO

Pseudorandom Error-Correcting Codes
Abstract

We construct pseudorandom error-correcting codes (or simply pseudorandom codes), which are error-correcting codes with the property that any polynomial number of codewords are pseudorandom to any computationally-bounded adversary. Efficient decoding of corrupted codewords is possible with the help of a decoding key.
We build pseudorandom codes that are robust to bit-flip and deletion errors, where pseudorandomness rests on standard cryptographic assumptions. Specifically, pseudorandomness is based on either $2^{O(\sqrt{n})}$-hardness of LPN, or polynomial hardness of LPN and the planted XOR problem at low density.
As our primary application of pseudorandom codes, we present an undetectable watermarking scheme for outputs of language models that is robust to cropping and a constant rate of random substitutions and deletions. The watermark is undetectable in the sense that any number of samples of watermarked text are computationally indistinguishable from text output by the original model. This is the first undetectable watermarking scheme that can tolerate a constant rate of errors.
Our second application is to steganography, where a secret message is hidden in innocent-looking content. We present a constant-rate stateless steganography scheme with robustness to a constant rate of substitutions. Ours is the first stateless steganography scheme with provable steganographic security and any robustness to errors.

2024

CRYPTO

Public-Key Anamorphism in (CCA-secure) Public-Key Encryption and Beyond
Abstract

The notion of (Receiver-) Anamorphic Encryption was put forth recently to show that a dictator (i.e., an overreaching government), which demands to get the receiver’s private key and even dictates messages to the sender, cannot prevent the receiver from getting an additional covert anamorphic message from a sender. The model required an initial private collaboration to share some secret. There may be settings though where an initial collaboration may be impossible or performance-wise prohibitive, or cases when we need an immediate message to be sent without private key generation (e.g., by any casual sender in need). This situation, to date, somewhat limits the applicability of anamorphic encryption. To overcome this, in this work, we put forth the new notion of “public-key anamorphic encryption,” where, without any initialization, any sender that has not coordinated in any shape or form with the receiver, can nevertheless, under the dictator control of the receiver’s private key, send the receiver an additional anamorphic secret message hidden from the dictator. We define the new notion with its unique new properties, and then prove that, quite interestingly, the known CCA-secure Koppula-Waters (KW) system is, in fact, public-key anamorphic.
We then describe how a public-key anamorphic scheme can support a new hybrid anamorphic encapsulation mode (KDEM) where the public anamorphic part serves a bootstrapping mechanism to activate regular anamorphic messages in the same ciphertext, thus together increasing the anamorphic channel capacity.
Looking at the state of research thus far, we observe that the initial system (Eurocrypt’22) that was shown to have regular anamorphic properties is the CCA-secure Naor-Yung (and other related schemes). Here we identify that the KW CCA-secure scheme also provides a new type of anamorphism. Thus, this situation is hinting that there may be a connection between some types of CCA-secure schemes and some type of anamorphic schemes (in spite of the fact that the goals of the two primitives are fundamentally different); this question is foundational in nature.
Given this, we identify a sufficient condition for a ``CCA-secure scheme which is black-box reduced from a CPA secure scheme'' to directly give rise to an ``anamorphic encryption scheme!'' Furthermore, we identify one extra property of the reduction, that yields a public-key anamorphic scheme as defined here.

2024

CRYPTO

QFESTA: Efficient Algorithms and Parameters for FESTA using Quaternion Algebras
Abstract

In 2023, Basso, Maino, and Pope proposed FESTA~(Fast Encryption from Supersingular Torsion Attacks), an isogeny-based public-key encryption (PKE) protocol that uses the SIDH attack for decryption. In the same paper, they proposed parameters for that protocol, but the parameters require high-degree isogeny computations. In this paper, we introduce QFESTA~(Quaternion Fast Encapsulation from Supersingular Torsion Attacks), a new variant of FESTA that works with better parameters using quaternion algebras and achieves IND-CCA security under QROM. To realize our protocol, we construct a new algorithm to compute an isogeny of non-smooth degree using quaternion algebras and the SIDH attack. Our protocol relies solely on $(2,2)$-isogeny and $3$-isogeny computations, promising a substantial reduction in computational costs. In addition, our protocol has significantly smaller data sizes for public keys and ciphertexts, approximately half size of the original FESTA.

2024

CRYPTO

Quantum Advantage from One-Way Functions
Abstract

Is quantum computing truly faster than classical computing? Demonstrating unconditional quantum computational advantage lies beyond the reach of the current complexity theory, and therefore we have to rely on some complexity assumptions. While various results on quantum advantage have been obtained, all necessitate relatively stronger or less standard assumptions
in complexity theory or classical cryptography. In this paper, we show quantum advantage based on several fundamental assumptions, specifically relying solely on the existence of classically-secure one-way functions. Given the fact that one-way functions are necessary for almost all classical cryptographic primitives, our findings yield a surprising implication: if there is no quantum advantage, then there is no classical cryptography! More precisely, we introduce inefficient-verifier proofs of quantumness (IV-PoQ), and construct it from statistically-hiding and computationally-binding classical bit commitments. IV-PoQ is an interactive protocol between a verifier and a quantum polynomial-time prover consisting of two phases. In the first phase, the verifier is classical probabilistic polynomial-time, and it interacts with the quantum polynomial-time prover over a classical channel. In the second phase, the verifier becomes inefficient, and makes its decision based on the transcript of the first phase. If the quantum prover is honest, the inefficient verifier accepts with high probability, but any classical probabilistic polynomial-time malicious prover only has a small probability of being accepted by the inefficient verifier. In our construction, the inefficient verifier can be a classical deterministic polynomial-time algorithm that queries an NP oracle. Our construction demonstrates the following results based on the known constructions of statistically-hiding and computationally-binding commitments from one-way functions or distributional collision-resistant hash functions:
- If one-way functions exist, then IV-PoQ exist.
- If distributional collision-resistant hash functions exist (which exist if hard-on-average problems in $\mathbf{SZK}$ exist), then constant-round IV-PoQ exist.
We also demonstrate quantum advantage based on worst-case-hard assumptions. We define auxiliary-input IV-PoQ (AI-IV-PoQ) that only require that for any malicious prover, there exist infinitely many auxiliary inputs under which the prover cannot cheat. We construct AI-IV-PoQ from an auxiliary-input version of commitments in a similar way, showing that
- If auxiliary-input one-way functions exist (which exist if $\mathbf{CZK}\not\subseteq\mathbf{BPP), then AI-IV-PoQ exist.
- If auxiliary-input collision-resistant hash functions exist (which is equivalent to $\mathbf{PWPP}\nsubseteq \mathbf{FBPP}$) or $\mathbf{SZK}\nsubseteq \mathbf{BPP}$,
then constant-round AI-IV-PoQ exist.
Finally, we also show that some variants of PoQ can be constructed from quantum-evaluation one-way functions (QE-OWFs), which are similar to classically-secure classical one-way functions except that the evaluation algorithm is not classical but quantum.
QE-OWFs appear to be weaker than classically-secure classical one-way functions, and therefore it demonstrates quantum advantage based on assumptions even weaker than one-way functions.

2024

CRYPTO

Quantum Complexity for Discrete Logarithms and Related Problems
Abstract

This paper studies the quantum computational complexity of the discrete logarithm (DL) and related group-theoretic problems in the context of ``generic algorithms''---that is, algorithms that
do not exploit any properties of the group encoding.
We establish the quantum generic group model and hybrid classical-quantum generic group model as quantum and hybrid analogs of their classical counterpart. This model counts the number of group operations of the underlying cyclic group $G$ as a complexity measure.
Shor's algorithm for the discrete logarithm problem and related algorithms can be described in this model and make $O(\log |G|)$ group operations in their basic form.
We show the quantum complexity lower bounds and (almost) matching algorithms of the discrete logarithm and related problems in these models.
* We prove that any quantum DL algorithm in the quantum generic group model must make $\Omega(\log |G|)$ depth of group operation queries. This shows that Shor's algorithm that makes $O(\log |G|)$ group operations is asymptotically optimal among the generic quantum algorithms, even considering parallel algorithms.
* We observe that some (known) variations of Shor's algorithm can take advantage of classical computations to reduce the number and depth of quantum group operations. We show that these variants are optimal among generic hybrid algorithms up to constant multiplicative factors: Any generic hybrid quantum-classical DL algorithm with a total number of (classical or quantum) group operations $Q$ must make $\Omega(\log |G|/\log Q)$ quantum group operations of depth $\Omega(\log\log |G| - \log\log Q)$.
* When the quantum memory can only store $t$ group elements and use quantum random access classical memory (QRACM) of $r$ group elements, any generic hybrid quantum-classical algorithm must make either $\Omega(\sqrt{|G|})$ group operation queries in total or $\Omega(\log |G|/\log (tr))$ quantum group operation queries. In particular, classical queries cannot reduce the number of quantum queries beyond $\Omega(\log |G|/\log (tr))$.
As a side contribution, we show a multiple discrete logarithm problem admits a better algorithm than solving each instance one by one, refuting a strong form of the quantum annoying property suggested in the context of password-authenticated key exchange protocol.

2024

CRYPTO

Quantum Lattice Enumeration in Limited Depth
Abstract

In 2018, Aono et al. (ASIACRYPT 2018) proposed to use quantum backtracking algorithms (Montanaro, TOC 2018; Ambainis and Kokainis, STOC 2017) to speedup lattice point enumeration. Quantum lattice sieving algorithms had already been proposed (Laarhoven et al., PQCRYPTO 2013), being shown to provide an asymptotic speedup over classical counterparts, but also to lose competitiveness at dimensions relevant to cryptography if practical considerations on quantum computer architecture were taken into account (Albrecht et al., ASIACRYPT 2020). Aono et al.'s work argued that quantum walk speedups can be applied to lattice enumeration, achieving at least a quadratic asymptotic speedup à la Grover search while not requiring exponential amounts of quantum accessible classical memory, as it is the case for sieving. In this work, we explore how to lower bound the cost of using Aono et al.'s techniques on lattice enumeration with extreme cylinder pruning, assuming a limit to the maximum depth that a quantum computation can achieve without decohering, with the objective of better understanding the practical applicability of quantum backtracking in lattice cryptanalysis.

2024

CRYPTO

Quantum One-Wayness of the Single-Round Sponge with Invertible Permutations
Abstract

Sponge hashing is a novel class of cryptographic hash algorithms which underlies the current international hash function standard SHA3. In a nutshell, a sponge function takes as input a bit-stream of any length and processes it via a simple iterative procedure: it repeatedly feeds each block of the input into a so-called block function, and then produces a short digest which consists of a subset of the final output bits. While much is known about the post-quantum security of the sponge in the case when the block function is modeled as a random function or permutation, the case of invertible permutations has so far remained a fundamental open problem.
In this work, we make new progress towards overcoming this barrier and show several results. First, we prove the ``double-sided zero-search'' conjecture proposed by Unruh (eprint' 2021) and show that finding zero-pairs in a random $2n$-bit permutation requires at least $\Omega(2^{n/2})$ many queries---and this is tight due to Grover's algorithm. At the core of our proof lies a novel ``symmetrization argument'' which uses insights from the theory of Young subgroups. Second, we consider more general variants of the double-sided search problem and show similar query lower bounds for them. As an application, we prove the quantum one-wayness of the single-round sponge with invertible permutations in the quantum random oracle model.

2024

CRYPTO

Quantum Public-Key Encryption with Tamper-Resilient Public Keys from One-Way Functions
Abstract

We construct quantum public-key encryption from one-way functions. In our construction, public keys are quantum, but ciphertexts are classical. Quantum public-key encryption from one-way functions (or weaker primitives such as pseudorandom function-like states) are also proposed in some recent works [Morimae-Yamakawa, eprint:2022/1336; Coladangelo, eprint:2023/282; Barooti-Grilo-Malavolta-Sattath-Vu-Walter, TCC 2023]. However, they have a huge drawback: they are secure only when quantum public keys can be transmitted to the sender (who runs the encryption algorithm) without being tampered with by the adversary, which seems to require unsatisfactory physical setup assumptions such as secure quantum channels. Our construction is free from such a drawback: it guarantees the secrecy of the encrypted messages even if we assume only unauthenticated quantum channels. Thus, the encryption is done with adversarially tampered quantum public keys. Our construction is the first quantum public-key encryption that achieves the goal of classical public-key encryption, namely, to establish secure communication over insecure channels, based only on one-way functions. Moreover, we show a generic compiler to upgrade security against chosen plaintext attacks (CPA security) into security against chosen ciphertext attacks (CCA security) only using one-way functions. As a result, we obtain CCA secure quantum public-key encryption based only on one-way functions.

2024

CRYPTO

Raccoon: A Masking-Friendly Signature Proven in the Probing Model
Abstract

This paper present Raccoon, a lattice-based signature scheme submitted to the NIST 2022 call for additional post-quantum signatures. Raccoon has the specificity of always being masked. Concretely, all sensitive intermediate values are shared into $d$ parts. The main design rationale of Raccoon is to be easy to mask at high orders, and this dictated most of its design choices, such as the introduction of new algorithmic techniques for sampling small errors. As a result, Raccoon achieves a masking overhead $O(d \log d)$ that compares favorably with the overheads $O(d^2 \log q)$ observed when masking standard lattice signatures.
In addition, we formally prove the security of Raccoon in the $t$-probing model: an attacker is able to probe $t <d-1$ shares during each execution of the main algorithms (key generation, signing, verification). While for most cryptographic schemes, the black-box security $t$-probing security can be studied in isolation, in Raccoon this analysis is performed jointly.
To that end, a bridge must be made between the black-box game-based EUF-CMA proof and the usual simulation proofs of the ISW model (CRYPTO 2003). In this paper, we formalize an end-to-end masking proof by deploying the probing EUF-CMA introduced by Barthe et al. (Eurocrypt 2018) and exhibiting the simulators of the non-interference properties (Barthe et al. CCS 2016). More precisely, the proof is divided into three novel parts:
- a simulation proof in the ISW model that allows to propagate the dependancy to a restricted number of inputs and random coins,
- a game-based proof showing that the security of Raccoon with probes can be reduced to an instance of Raccoon with smaller parameters,
- a parameter study to ensure that the smaller instance is secure, using a robust generalization of the Rényi divergence.
While we apply our techniques to Raccoon, we expect that the algorithmic and proof techniques we introduce will be helpful for the design and analysis of future masking-friendly schemes.

2024

CRYPTO

Radical Vélu Isogeny Formulae
Abstract

We provide explicit radical N -isogeny formulae for all odd integers N . The formulae are compact closed-form expressions which require one Nth root computation and O(N) basic field operations. The formulae are highly efficient to compute a long chain of N -isogenies, and are extremely beneficial for speeding up certain cryptographic protocols such as CSIDH. Unfortunately, the formulae are conjectured, but we provide ample supporting evidence which strongly suggests their correctness.
For CSIDH-512, we notice an additional 35% speed-up when using radical isogenies up to N = 199, compared to the work by Castryck, Decru, Houben and Vercauteren, which uses radical isogenies up to N = 19 only. The addition of our radical isogenies also speeds up the computation of larger class group actions in a comparable fashion.

2024

CRYPTO

Reducing the CRS Size in Registered ABE Systems
Abstract

Attribute-based encryption (ABE) is a generalization of public-key encryption that enables fine-grained access control to encrypted data. In (ciphertext-policy) ABE, a central trusted authority issues decryption keys for attributes $x$ to users. In turn, ciphertexts are associated with a decryption policy $\mathcal{P}$. Decryption succeeds and recovers the encrypted message whenever $\mathcal{P}(x) = 1$. Recently, Hohenberger, Lu, Waters, and Wu (Eurocrypt 2023) introduced the notion of registered ABE, which is an ABE scheme without a trusted central authority. Instead, users generate their own public/secret keys (just like in public-key encryption) and then register their keys (and attributes) with a key curator. The key curator is a transparent and untrusted entity.
Currently, the best pairing-based registered ABE schemes support monotone Boolean formulas and an a priori bounded number of users $L$. A major limitation of existing schemes is that they require a (structured) common reference string (CRS) of size $L^2 \cdot |\mathcal{U}|$ where $|\mathcal{U}|$ is the size of the attribute universe. In other words, the size of the CRS scales quadratically with the number of users and multiplicatively with the size of the attribute universe. The large CRS makes these schemes expensive in practice and limited to a small number of users and a small universe of attributes.
In this work, we give two ways to reduce the CRS size in pairing-based registered ABE schemes. First, we introduce a combinatoric technique based on progression-free sets that enables registered ABE for the same class of policies but with a CRS whose size is sub-quadratic in the number of users. Asymptotically, we obtain a scheme where the CRS size is nearly linear in the number of users $L$ (i.e., $L^{1 + o(1)}$). If we take a more concrete-efficiency-oriented focus, we can instantiate our framework to obtain a construction with a CRS of size $L^{\log_2 3} \approx L^{1.6}$. For instance, in a scheme for 100,000 users, our approach reduces the CRS by a factor of over $115\times$ compared to previous approaches (and without incurring any overhead in encryption/decryption time). Our second approach for reducing the CRS size is to rely on a partitioning-based argument when arguing security of the registered ABE scheme. Previous approaches took a dual-system approach. Using a partitioning-based argument yields a registered ABE scheme where the size of the CRS is independent of the size of the attribute universe. The cost is the resulting scheme satisfies a weaker notion of static security. Our techniques for reducing the CRS size can be combined, and taken together, we obtain a pairing-based registered ABE scheme that supports monotone Boolean formulas with a CRS size of $L^{1 + o(1)}$. Notably, this is the first pairing-based registered ABE scheme that does not require imposing a bound on the size of the attribute universe during setup time.
As an additional application, we also show how to apply our techniques based on progression-free sets to the batch argument (BARG) for $\mathsf{NP}$ scheme of Waters and Wu (Crypto 2022) to obtain a scheme with a nearly-linear CRS without needing to rely on non-black-box bootstrapping techniques.

2024

CRYPTO

Resettable Statistical Zero-Knowledge for NP
Abstract

Resettable statistical zero-knowledge [Garg--Ostrovsky--Visconti--Wadia, TCC 2012] is a strong privacy notion that guarantees statistical zero-knowledge even when the prover uses the same randomness in multiple proofs.
In this paper, we show an equivalence of resettable statistical zero-knowledge arguments for NP and witness encryption schemes for NP.
- Positive result: For any NP language L, a resettable statistical zero-knowledge argument for L can be constructed from a witness encryption scheme for L under the assumption of the existence of one-way functions.
- Negative result: The existence of even resettable statistical witness-indistinguishable arguments for NP imply the existence of witness encryption schemes for NP under the assumption of the existence of one-way functions.
The positive result is obtained by naturally extending existing techniques (and is likely to be already well-known among experts). The negative result is our main technical contribution.
To explore workarounds for the negative result, we also consider resettable security in a model where the honest party's randomness is only reused with fixed inputs. We show that resettable statistically hiding commitment schemes are impossible even in this model.

2024

CRYPTO

Reusable Online-Efficient Commitments
Abstract

An {\em online-efficient commitment} is a succinct locally-openable commitment, where the bulk of the sender work is done offline, generating an encoding $\tilde x$ of the committed data $x$. In the online phase, both the sender, given random access to $\tilde x$, and receiver run in polylogarithmic time in the length of $x$. Online-efficient commitments were recently constructed under the standard assumption of RingLWE by Lin, Mook, and Wichs, but with a significant caveat: {\em they are not reusable.} Their commitments are privately verifiable and cease to be binding if a malicious sender can learn whether the receiver accepts or rejects in repeated decommitment requests.
We construct the first {\em reusable} online-efficient commitment under a standard assumption, RingLWE. A main component in our analysis is a leakage lemma by Chung, Kalai, Liu, and Raz (CRYPTO `11) introduced in the context of {\em streaming delegation schemes.}

2024

CRYPTO

Revisiting Differential-Linear Attacks via a Boomerang Perspective With Application to AES, Ascon, CLEFIA, SKINNY, PRESENT, KNOT, TWINE, WARP, LBlock, Simeck and SERPENT
Abstract

In 1994, Langford and Hellman introduced differential-linear (DL) cryptanalysis, with the idea of decomposing the block cipher E into two parts, EU and EL, such that EU exhibits a high-probability differential trail, while EL has a high-correlation linear trail.Combining these trails forms a distinguisher for E, assuming independence between EU and EL. The dependency between the two parts of DL distinguishers remained unaddressed until EUROCRYPT 2019, where Bar-On et al. introduced the DLCT framework, resolving the issue up to one S-box layer. However, extending the DLCT framework to formalize the dependency between the two parts for multiple rounds remained an open problem.
In this paper, we first tackle this problem from the perspective of boomerang analysis. By examining the relationships between DLCT, DDT, and LAT, we introduce a set of new tables facilitating the formulation of dependencies between the two parts of the DL distinguisher across multiple rounds. Then, we introduce a highly versatile and easy-to-use automatic tool for exploring DL distinguishers, inspired by automatic tools for boomerang distinguishers. This tool considers the dependency between differential and linear trails across multiple rounds. We apply our tool to various symmetric primitives, and in all applications, we either present the first DL distinguishers or enhance the best-known ones. We achieve successful results against Ascon, AES, SERPENT, PRESENT, SKINNY, TWINE, CLEFIA, WARP, LBlock, Simeck, and KNOT. Furthermore, we demonstrate that, in some cases, DL distinguishers outperform boomerang distinguishers significantly.

2024

CRYPTO

Ring Signatures for Deniable AKEM: Gandalf's Fellowship
Abstract

Ring signatures, a cryptographic primitive introduced by Rivest, Shamir and Tauman (ASIACRYPT 2001), offer signer anonymity within dynamically formed user groups.
Recent advancements have focused on lattice-based constructions to improve efficiency, particularly for large signing rings.
However, current state-of-the-art solutions suffer from significant overhead, especially for smaller rings.
In this work, we present two novel NTRU-based ring signature constructions tailored towards small rings.
Concretely, our schemes offer up to 50% reduction in signature size for ring of size smaller than 18 compared to the state of the art ring signature scheme Raptor (ACNS 2019) and the sublinear ring signature scheme Smile (CRYPTO 2021).
In particular, for rings of size two, our ring signatures are only 1244 bytes.
Additionally, we explore the application of ring signatures in achieving deniability in authenticated key exchange mechanisms (AKEMs), the primitive behind the recent HPKE standard used in MLS and TLS.
We take a fine-grained approach at formalising sender deniability within AKEM and seek to define the strongest possible notions.
Our contributions extend to a black-box construction of a deniable AKEM from a KEM and a ring signature scheme for rings of size two.
Our approach attains the highest level of confidentiality and authenticity, while simultaneously preserving the strongest forms of deniability in two orthogonal settings.
Finally, we present parameter sets for our schemes, and show that our deniable AKEM yields ciphertexts of 2 KB when combined with our new ring signature scheme.

2024

CRYPTO

Robust Additive Randomized Encodings from IO and Pseudo Non-Linear Codes
Abstract

Additive randomized encodings (ARE), introduced by Halevi, Ishai,
Kushilevitz, and Rabin (CRYPTO 2023), reduce the computation of a k-party
function f (x_1, . . . , x_k ) to locally computing encodings hat{x}_i of each input xi and
then adding them together over some Abelian group into an output encoding
hat{y} = ∑ hat{x}_i, which reveals nothing but the result. In robust ARE (RARE)
the sum of any subset of hat{x}_i, reveals only the residual function obtained by
restricting the corresponding inputs. The appeal of (R)ARE comes from the
simplicity of the interactive part of the computation, involving only addition,
which yields for instance non-interactive multi-party computation in the shuffle
model where messages from different parties are anonymously shuffled. Halevi,
Ishai, Kushilevitz, and Rabin constructed ARE from standard assumptions and
RARE in the ideal obfuscation model, leaving open the question of whether
RARE can be constructed in the plain model.
We construct RARE in the plain model from indistinguishability obfuscation,
which is necessary, and a new primitive that we call pseudo-non-linear codes.
We provide two constructions of this primitive assuming either Learning with
Errors or Decision Diffie Hellman. A bonus feature of our construction is that
it is succinct. Specifically, encodings hat{x}_i can be decomposed to non-interactive
parts hat{z}_i, generated in time proportional to the input size, and sent directly to the
evaluator, and group parts hat{g}_i that are added together, and whose size depends
only on the security parameter.

2024

CRYPTO

Robust Quantum Public-Key Encryption with Applications to Quantum Key Distribution
Abstract

Quantum key distribution (QKD) allows Alice and Bob to agree on a shared secret key, while communicating over a public (untrusted) quantum channel. Compared to classical key exchange, it has two main advantages: (i) The key is unconditionally hidden to the eyes of any attacker, and (ii) its security assumes only the existence of authenticated classical channels which, in practice, can be realized using Minicrypt assumptions, such as the existence of digital signatures. On the flip side, QKD protocols typically require multiple rounds of interactions, whereas classical key exchange can be realized with the minimal amount of two messages using public-key encryption. A long-standing open question is whether QKD requires more rounds of interaction than classical key exchange.
In this work, we propose a two-message QKD protocol that satisfies everlasting security, assuming only the existence of quantum-secure one-way functions. That is, the shared key is unconditionally hidden, provided computational assumptions hold during the protocol execution. Our result follows from a new construction of quantum public-key encryption (QPKE) whose security, much like its classical counterpart, only relies on authenticated classical channels.

2024

CRYPTO

Round-Optimal Fully Secure Distributed Key Generation
Abstract

Protocols for distributed (threshold) key generation (DKG) in the discrete-logarithm setting have received a tremendous amount of attention in the past few years. Several synchronous DKG protocols have been proposed, but most such protocols are not fully secure: they either allow a single corrupted party to bias the key, or are not robust and allow a single malicious party to prevent successful generation of a key.
We explore the round complexity of fully secure DKG in the honest-majority setting where it is feasible. We show the impossibility of one-round, unbiased DKG protocols (even satisfying weaker notions of security), regardless of any prior setup. On the positive side, we show various round-optimal protocols for fully secure DKG offering tradeoffs in terms of their efficiency, necessary setup, and required assumptions.

2024

CRYPTO

Scalable Multiparty Computation from Non-linear Secret Sharing
Abstract

A long line of work has investigated the design of scalable secure multiparty computation (MPC) protocols with computational and communication complexity independent of the number of parties (beyond any dependence on the circuit size). We present the first unconditionally-secure MPC protocols for arithmetic circuits over *large fields* with total computation $\bigO{|C|\log|F|}$, where $|C|$ and $F|$ denote the circuit and field size, respectively.
Prior work could either achieve similar complexity only in *communication*, or required highly structured circuits, or expensive circuit transformations. To obtain our results, we depart from the prior approach of share packing in linear secret-sharing schemes; instead, we use an ``unpacking'' approach via *non-linear* secret sharing.

2024

CRYPTO

Secret Sharing with Certified Deletion
Abstract

Secret sharing allows a user to split a secret into many shares so that the secret can be recovered if, and only if, an authorized set of shares is collected. Although secret sharing typically does not require any computational hardness assumptions, its security \emph{does} require that an adversary cannot collect an authorized set of shares. Over long periods of time where an adversary can benefit from multiple data breaches, this may not be a realistic assumption.
We initiate the systematic study of secret sharing \emph{with certified deletion} in order to achieve security \emph{even against an adversary that eventually collects an authorized set of shares}. In secret sharing with certified deletion, a (classical) secret $s$ is split into quantum shares which can be destroyed in a manner verifiable by the dealer. We put forth two natural definitions of security. \textbf{No-signaling security} roughly requires that if multiple non-communicating adversaries delete sufficiently many shares, then their combined view contains negligible information about $s$, even if the total set of corrupted parties forms an authorized set. \textbf{Adaptive security} requires privacy of $s$ against an adversary that can continuously and adaptively corrupt new shares and delete previously-corrupted shares, as long as the total set of corrupted shares minus deleted shares remains unauthorized.
Next, we show that these security definitions are achievable: we show how to construct (i) a secret sharing scheme with no-signaling certified deletion for \emph{any monotone access structure}, and (ii) a \emph{threshold} secret sharing scheme with adaptive certified deletion. Our first construction uses Bartusek and Khurana's (CRYPTO 2023) 2-out-of-2 secret sharing scheme with certified deletion as a building block, while our second construction is built from scratch and requires several new technical ideas. For example, we significantly generalize the ``XOR extractor'' of Agarwal, Bartusek, Khurana, and Kumar (EUROCRYPT 2023) in order to obtain better seedless extraction from certain quantum sources of entropy, and show how polynomial interpolation can double as a high-rate randomness extractor in our context of threshold sharing with certified deletion.

2024

CRYPTO

Secure Multiparty Computation with Identifiable Abort from Vindicating Release
Abstract

In the dishonest-majority setting, secure multiparty computation (MPC) with identifiable abort (IA) guarantees that honest parties can identify and agree upon at least one cheating party if the protocol does not produce an output. Known MPC constructions with IA rely on generic zero-knowledge proofs, adaptively secure oblivious transfer (OT) protocols, or homomorphic primitives, and thus incur a substantial penalty with respect to protocols that abort without identifiability.
We introduce a new, weaker notion of IA called input-revealing IA (IRIA), which can be constructed through selective revealing of committed input values---a technique we call vindicating release. We show that this weaker form of IA can be achieved with small concrete overheads for many interesting protocols in the literature, including the pre-processing protocols needed for several state-of-the-art MPC protocols.
We next show how to assemble these IRIA components into an MPC protocol for any functionality with standard IA. Such a realization differs minimally in terms of cost, techniques, and analysis from the equivalent realization that lacks identifiability, e.g., our total bandwidth overhead incurred is less than 2x, which is an asymptotic improvement over prior work on IA.
On a practical level, we apply our techniques to the problem of threshold ECDSA, and show that the resulting protocol with standard IA is concretely efficient. On a theoretical level, we present a compiler that transforms any secure protocol into one with standard IA assuming only a variant of statically-corruptable ideal OT.

2024

CRYPTO

Solving the Tensor Isomorphism Problem for special orbits with low rank points: Cryptanalysis and repair of an Asiacrypt 2023 commitment scheme
Abstract

The Tensor Isomorphism Problem (TIP) has been shown to be equivalent to the matrix code equivalence problem, making it an interesting candidate on which to build post-quantum cryptographic primitives. These hard problems have already been used in protocol development. One of these, MEDS, is currently in Round 1 of NIST's call for additional post-quantum digital signatures.
In this work, we consider the TIP for a special class of tensors. The hardness of the decisional version of this problem is the foundation of a commitment scheme proposed by D'Alconzo, Flamini, and Gangemi (Asiacrypt 2023). We present polynomial-time algorithms for the decisional and computational versions of TIP for special orbits, which implies that the commitment scheme is not secure. The key observations of these algorithms are that these special tensors contain some low-rank points, and their stabilizer groups are not trivial.
With these new developments in the security of TIP in mind, we give a new commitment scheme based on the general TIP that is non-interactive, post-quantum, and statistically binding, making no new assumptions. Such a commitment scheme does not currently exist in the literature.

2024

CRYPTO

Sometimes You Can't Distribute Random Oracle Based Proofs
Abstract

We investigate the conditions under which straight-line extractable NIZKs in the random oracle model (i.e. without a CRS) permit multiparty realizations that are black-box in the same random oracle. We show that even in the semi-honest setting, any MPC protocol to compute such a NIZK cannot make black-box use of the random oracle or a hash function instantiating it if security against all-but-one corruptions is desired, unless the number of queries made by the verifier to the oracle grows linearly with the number of parties. This presents a fundamental barrier to constructing efficient protocols to securely distribute the computation of NIZKs (and signatures) based on MPC-in-the-head, PCPs/IOPs, and sigma protocols compiled with transformations due to Fischlin, Pass, or Unruh.
When the adversary is restricted to corrupt only a constant fraction of parties, we give a positive result by means of a tailored construction, which demonstrates that our impossibility does not extend to weaker corruption models in general.

2024

CRYPTO

Space-Efficient and Noise-Robust Quantum Factoring
Abstract

We provide two improvements to Regev's recent quantum factoring algorithm (arXiv:2308.06572), addressing its space efficiency and its noise-tolerance.
Our first contribution is to improve the quantum space efficiency of Regev's algorithm while keeping the circuit size the same. Our main result constructs a quantum factoring circuit using $O(n \log n)$ qubits and $O(n^{3/2} \log n)$ gates. We achieve the best of Shor and Regev (upto a logarithmic factor in the space complexity): on the one hand, Regev's circuit requires $O(n^{3/2})$ qubits and $O(n^{3/2} \log n)$ gates, while Shor's circuit requires $O(n^2 \log n)$ gates but only $O(n)$ qubits. As with Regev, to factor an $n$-bit integer $N$, we run our circuit independently $\approx \sqrt{n}$ times and apply Regev's classical postprocessing procedure.
Our optimization is achieved by implementing efficient and reversible exponentiation with Fibonacci numbers in the exponent, rather than the usual powers of 2, adapting work by Kaliski (arXiv:1711.02491) from the classical reversible setting to the quantum setting. This technique also allows us to perform quantum modular exponentiation that is efficient in both space and size without requiring significant precomputation, a result that may be useful for other quantum algorithms. A key ingredient of our exponentiation implementation is an efficient circuit for a function resembling \emph{in-place} quantum-quantum modular multiplication. This implementation works with only black-box access to any quantum circuit for \emph{out-of-place} modular multiplication, which we believe is yet another result of potentially broader interest.
Our second contribution is to show that Regev's classical postprocessing procedure can be modified to tolerate a constant fraction of the quantum circuit runs being corrupted by errors. In contrast, Regev's analysis of his classical postprocessing procedure requires all $\approx \sqrt{n}$ runs to be successful. In a nutshell, we achieve this using lattice reduction techniques to detect and filter out corrupt samples.

2024

CRYPTO

Speeding up Preimage and Key-Recovery Attacks with Highly Biased Differential-Linear Approximations
Abstract

We present a framework for speeding up the search for preimages of candidate one-way functions based on highly biased differential-linear distinguishers. It is naturally applicable to preimage attacks on hash functions. Further, a variant of this framework applied to keyed functions leads to accelerated key-recovery attacks. Interestingly, our technique is able to exploit related-key differential-linear distinguishers in the single-key model without querying the target encryption oracle with unknown but related keys. This is in essence similar to how we speed up the key search based on the well known complementation property of DES, which calls for caution from the designers in building primitives meant to be secure in the single-key setting without a thorough cryptanalysis in the related-key model. We apply the method to sponge-based hash function Ascon-HASH, XOFs XOEsch/Ascon-XOF and AEAD Schwaemm, etc. Accelerated preimage or key-recovery attacks are obtained. Note that all the differential-linear distinguishers employed in this work are highly biased and thus can be experimentally verified.

2024

CRYPTO

STIR: Reed–Solomon Proximity Testing with Fewer Queries
Abstract

We present STIR (Shift To Improve Rate), a concretely efficient interactive oracle proof of proximity (IOPP) for Reed--Solomon codes that achieves the best known query complexity of any concretely efficient IOPP for this problem. Roughly, in order to achieve $\lambda$ bits of security, STIR has query complexity $O(\log d + \lambda \cdot \loglog d )$, while the popular FRI protocol (including variants based on conjectured security assumptions) has query complexity $O(\lambda \cdot \log d )$. STIR relies on a new technique for recursively reducing the degree of the function being tested while simultaneously improving the rate.
We provide an implementation of STIR compiled to a SNARK. Compared to FRI, our implementation achieves an improvement in argument size that ranges from $1.25\times$ to $2.46\times$ depending on the chosen parameters. For example, in order to achieve 128 bits of security for degree $2^{26}$ and rate $1/4$, STIR has argument size $114$~KiB, compared to $211$~KiB for FRI.

2024

CRYPTO

Stochastic Secret Sharing with 1-Bit Shares and Applications to MPC
Abstract

The problem of minimizing the share size of threshold secret-sharing schemes is a basic research question that has been extensively studied. Ideally, one strives for schemes in which the share size equals the secret size. While this is achievable for large secrets (Shamir, CACM '79), no similar solutions are known for the case of binary, single-bit secrets. Current approaches often rely on so-called ramp secret sharing that achieves a constant share size at the expense of a slight gap between the privacy and the correctness thresholds. In the case of single-bit shares, this leads to a large gap which is typically unacceptable. The possibility of a meaningful notion of secret sharing scheme with 1-bit shares and almost optimal threshold has been left wide open. Of special interest is the case of threshold 0.5, which is motivated by information-theoretic honest-majority secure multiparty computation (MPC).
In this work, we present a new stochastic model for secret-sharing where each party is corrupted by the adversary with probability $p$, independently of the other parties, and correctness and privacy are required to hold with high probability over the choice of the corrupt parties. We present new secret sharing schemes with single-bit shares that tolerate any constant corruption probability $p<0.5$. Our construction is based on a novel connection between such stochastic secret-sharing schemes and error-correcting codes that achieve capacity over the binary erasure channel.
Our schemes are linear and multiplicative. We demonstrate the usefulness of the model by using our new schemes to construct MPC protocols with security against an adversary that passively corrupts an arbitrary subset of $0.499n$ of the parties, where the online communication per party consists of a single bit per AND gate and zero communication per XOR gate. Unlike competing approaches for communication-efficient MPC, our solution is applicable even in a real-time model in which the parties should compute a Boolean circuit whose gates arrive in real-time, one at a time, and are not known in advance.

2024

CRYPTO

Structural Lower Bounds on Black-Box Constructions of Pseudorandom Functions
Abstract

We address the black-box complexity of constructing pseudorandom functions (PRF) from pseudorandom generators (PRG). The celebrated GGM construction of Goldreich, Goldwasser, and Micali (Crypto 1984) provides such a construction, which (even when combined with Levin's domain-extension trick) has super-logarithmic depth. Despite many years and much effort, this remains essentially the best construction we have to date. On the negative side, one step is provided by the work of Miles and Viola (TCC 2011), which shows that a black-box construction which just calls the PRG once and outputs one of its output bits, cannot be a PRF.
In this work, we make significant further progress: we rule out black-box constructions of PRF from PRG that follow certain structural constraints, but may call the PRG adaptively polynomially many times. In particular, we define ``tree constructions" which generalize the GGM structure: they apply the PRG $G$ along a tree path, but allow for different choices of functions to compute the children of a node on the tree and to compute the next node on the computation path down the tree. We prove that a tree construction of logarithmic depth cannot be a PRF (while GGM is a tree construction of super-logarithmic depth). Moreover, we prove that there is no PRF construction that uses such a tree construction (returning one bit) as an oracle, even if allowed to call the oracle adaptively polynomially many times with a different input (root value) each time. We also show several other results and discuss the special case of one-call constructions.
Our main results in fact rule out even weak PRF constructions with one output bit. We use the oracle separation methodology introduced by Gertner, Malkin, and Reingold (FOCS 2001), and show that for any candidate black-box construction F^G from G, there exists an oracle relative to which G is a PRG, but F^G is not a PRF.

2024

CRYPTO

Succinctly-Committing Authenticated Encryption
Abstract

Recent attacks and applications have led to the need for symmetric encryption schemes that, in addition to providing the usual authenticity and privacy, are also committing. In response, many committing authenticated encryption schemes have been proposed. However, all known schemes, in order to provide s bits of committing security, suffer an expansion---this is the length of the ciphertext minus the length of the plaintext---of 2s bits. This incurs a cost in bandwidth or storage. (We typically want s=128, leading to 256-bit expansion.) However, it has been considered unavoidable due to birthday attacks. We show how to bypass this limitation. We give authenticated encryption (AE) schemes that provide s bits of committing security, yet suffer expansion only around s as long as messages are long enough, namely more than s bits. We call such schemes succinct. We do this via a generic, ciphertext-shortening transform called SC: given an AE scheme with 2s-bit expansion, SC returns an AE scheme with s-bit expansion while preserving committing security. SC is very efficient; an AES-based instantiation has overhead just two AES calls. As a tool, SC uses a collision-resistant invertible PRF called HtM, that we design, and whose analysis is technically difficult. To add the committing security that SC assumes to a base scheme, we also give a transform CTY that improves Chan and Rogaway's CTX. Our results hold in a general framework for authenticated encryption that includes both classical AEAD and AE2 (also called nonce-hiding AE) as special cases, so that we in particular obtain succinctly-committing AE schemes for both these settings.

2024

CRYPTO

That’s not my signature! Fail-stop signatures for a post-quantum world
Abstract

The Snowden's revelations kick-started a community-wide effort to develop cryptographic tools against mass surveillance. In this work, we propose to add another primitive to that toolbox: Fail-Stop Signatures (FSS) [EC'89]. FSS are digital signatures enhanced with a forgery-detection mechanism that can protect a computationally bounded signer from more powerful attackers. Despite the fascinating concept, research in this area stalled after the '90s. However, the ongoing transition to post-quantum cryptography, with its hiccups due to the novelty of underlying assumptions, has become the perfect use case for FSS. This paper aims to reboot research on FSS with practical use in mind: Our framework for FSS includes ``fine-grained'' security definitions (that assume a powerful, but bounded adversary e.g: can break 128-bit of security, but not 256-bit). As an application, we show new FSS constructions for the post-quantum setting. We show that FSS are equivalent to standard, provably secure digital signatures that do not require rewinding or programming random oracles, and that this implies lattice-based FSS. Our main construction is an FSS version of SPHINCS, which required building FSS versions of all its building blocks: WOTS, XMSS, and FORS. In the process, we identify and provide generic solutions for two fundamental issues arising when deriving a large number of private keys from a single seed, and when building FSS for Hash-and-Sign-based signatures.

2024

CRYPTO

The Algebraic Freelunch: Efficient Gröbner Basis Attacks Against Arithmetization-Oriented Primitives
Abstract

In this paper, we present a new type of algebraic attack that applies to many recent arithmetization-oriented families of permutations, such as those used in Griffin, Anemoi, ArionHash, and XHash8, whose security relies on the hardness of the constrained-input constrained-output (CICO) problem.
We introduce the FreeLunch approach: the monomial ordering is chosen so that the natural polynomial system encoding the CICO problem already is a Gröbner basis. In addition, we present a new dedicated resolution algorithm for FreeLunch systems, of complexity lower than applicable state-of-the-art FGLM algorithms.
We show that the FreeLunch approach challenges the security of full-round instances of Anemoi, Arion and Griffin. We confirm these theoretical results with experimental results on those three permutations. In particular, using the FreeLunch attack combined with a new technique to bypass 3 rounds of Griffin, we recover a CICO solution for 7 out of 10 rounds of Griffin in less than four hours on one core of AMD EPYC 7352 (2.3GHz).

2024

CRYPTO

The Committing Security of MACs with Applications to Generic Composition
Abstract

Message Authentication Codes (MACs) are ubiquitous primitives
deployed in multiple flavours through standards such as HMAC,
CMAC, GMAC, LightMAC and many others. Its versatility makes it
an essential building block in applications necessitating message authentication
and integrity check, in authentication protocols, authenticated
encryption schemes, or as a pseudorandom or key derivation function.
Its usage in this variety of settings makes it susceptible to a broad range
of attack scenarios. The latest attack trends leverage a lack of commitment
or context-discovery security in AEAD schemes and these attacks
are mainly due to the weakness in the underlying MAC part. However,
these new attack models have been scarcely analyzed for MACs themselves.
This paper provides a thorough treatment of MACs committing
and context-discovery security. We reveal that commitment and context-discovery
security of MACs have their own interest by highlighting real-world
vulnerable scenarios. We formalize the required security notions for
MACs, and analyze the security of standardized MACs for these notions.
Additionally, as a constructive application, we analyze generic AEAD
composition and provide simple and efficient ways to build committing
and context-discovery secure AEADs.

2024

CRYPTO

The One-Wayness of Jacobi Signatures
Abstract

We show that under a mild number-theoretic conjecture, recovering an integer from its Jacobi signature modulo $N = p^2 q$, for primes $p$ and $q$, is as hard as factoring $N$. This relates, for the first time, the one-wayness of a pseudorandom generator that Damgård proposed in 1988, to a standard number-theoretic problem. In addition, we show breaking the Jacobi pseudorandom function is no harder than factoring.

2024

CRYPTO

Threshold Encryption with Silent Setup
Abstract

We build a concretely efficient threshold encryption scheme where the joint public key of a set of parties is computed as a \emph{deterministic} function of their locally computed public keys, enabling a \emph{silent} setup phase. By eliminating interaction from the setup phase, our scheme immediately enjoys several highly desirable features such as asynchronous setup, multiverse support, and dynamic threshold.
Prior to our work, the only known constructions of threshold encryption with silent setup relied on heavy cryptographic machinery such as indistinguishability Obfuscation or witness encryption for all of $\mathsf{NP}$. Our core technical innovation lies in building a special purpose witness encryption scheme for the statement ``at least $t$ parties have signed a given message''. Our construction relies on pairings and is proved secure in the Generic Group Model.
Notably, our construction, restricted to the special case of threshold $\thres=1$, gives an alternative construction of the (flexible) distributed broadcast encryption from pairings, which has been the central focus of several recent works.
We implement and evaluate our scheme to demonstrate its concrete efficiency. Both encryption and partial decryption are constant time, taking $<7\,$ms and $<1\,$ms, respectively. For a committee of $1024$ parties, the aggregation of partial decryptions takes $<200\,$ms, when all parties provide partial decryptions. The size of each ciphertext is $\approx 8\times$ larger than an ElGamal ciphertext.

2024

CRYPTO

Tight Characterizations for Preprocessing against Cryptographic Salting
Abstract

Cryptography often considers the strongest yet plausible attacks in the real world. Preprocessing (a.k.a. non-uniform attacks) plays an important role in both theory and practice: an efficient online attacker can take advantage of advice prepared by a time-consuming preprocessing stage.
Salting is a heuristic strategy to counter preprocessing attacks by feeding a small amount of randomness to the cryptographic primitive.
We present general and tight characterizations of preprocessing against cryptographic salting, with upper bounds matching the advantages of the most intuitive attack. Our result quantitatively strengthens the previous work by Coretti, Dodis, Guo, and Steinberger (EUROCRYPT'18). Our proof exploits a novel connection between the non-uniform security of salted games and direct product theorems for memoryless algorithms.
For quantum adversaries, we give similar characterizations for property finding games, resolving an open problem of the quantum non-uniform security of salted collision resistant hash by Chung, Guo, Liu, and Qian (FOCS'20). Our proof extends the compressed oracle framework of Zhandry (CRYPTO'19) to prove quantum strong direct product theorems for property finding games in the average-case hardness.

2024

CRYPTO

Time-Lock Puzzles from Lattices
Abstract

Time-lock puzzles (TLP) are a cryptographic tool that allow one to encrypt a message into
the future, for a predetermined amount of time T . At present, we have only two constructions with provable security: One based on the repeated squaring assumption and the other based on indistinguishability obfuscation (iO). Basing TLP on any other assumption is a long-standing question, further motivated by the fact that know constructions are broken by quantum algorithms.
In this work, we propose a new approach to construct time-lock puzzles based on lattices,
and therefore with plausible post-quantum security. We obtain the following main results:
• In the preprocessing model, where a one-time public-coin preprocessing is allowed, we
obtain a time-lock puzzle with encryption time log(T ).
• In the plain model, where the encrypter does all the computation, we obtain a time-lock
puzzle with encryption time √T .
Both constructions assume the existence of any sequential function f , and the hardness of the circular small-secret learning with errors (LWE) problem.
At the heart of our results is a new construction of succinct randomized encodings (SRE)
for T-folded repeated circuits, where the complexity of the encoding is √T . This is the first
construction of SRE where the overall complexity of the encoding algorithm is sublinear in the runtime T , and which is not based on iO. Using our SRE we directly obtain the first non-
interactive RAM delegation scheme with sublinear complexity (in the number of steps T ), again without iO. Finally, we also propose a new heuristic construction of SREs, and consequently of TLPs, with fully-efficient encoding complexity log(T ). Our scheme is inspired by iO techniques, but carefully sidesteps the regime of zeroizing attacks that plague lattice-based iO candidates.

2024

CRYPTO

Time-memory Trade-offs Sound the Death Knell for GPRS and GSM
Abstract

This paper introduces a practical TMTO-based attack against GSM (A5/3) and GPRS (GEA-3), which are both technologies used in 2G mobile networks. Although designed in the 80s, such networks are still quite active today, especially for embedded systems. While active attacks
against 2G networks with a fake base station were already known for a while, the attack introduced in this paper relies on a passive attacker. We explain in the paper how to find material in GPRS and GSM communications to perform a TMTO attack and we experimented this step with off-the-shelf devices operated in real-life networks. We provide the success probability of the attack and its performances for several real-life scenarios. We optimized the implementation of KASUMI with AVX2 instructions, and we designed a specific TMTO implementation to get around the SSD access latency. For example, an attacker passively eavesdropping a GSM communication between a target and a base station can decrypt any 2-hour call with probability 0.43, in 14 min.

2024

CRYPTO

Towards Achieving Asynchronous MPC with Linear Communication and Optimal Resilience
Abstract

Secure multi-party computation (MPC) allows a set of $n$ parties to jointly compute a function over their private inputs. The seminal works of Ben-Or, Canetti and Goldreich [STOC'93] and Ben-Or, Kelmer and Rabin [PODC'94] settled the feasibility of MPC over asynchronous networks. Despite the significant line of work devoted to improving the communication complexity, current protocols with information-theoretic security and optimal resilience $t<n/3$ communicate $\Omega(n^4C)$ field elements for a circuit with $C$ multiplication gates. In contrast, synchronous MPC protocols with $\Omega(nC)$ communication have long been known.
In this work we make progress towards closing this gap. We provide a novel MPC protocol that makes black-box use of an asynchronous complete secret-sharing (ACSS), where the cost per multiplication reduces to the cost of distributing a constant number of sharings in the ACSS, improving a linear factor over the state of the art by Choudhury and Patra [IEEE Trans. Inf. Theory '17].
Instantiating the ACSS with the protocol by Choudhury and Patra [J. Crypto '23] we achieve an MPC protocol with $\mathcal{O}(n^3C)$ communication. Moreover, with a recent concurrent work achieving ACSS with linear cost per sharing, we achieve an MPC with $\mathcal{O}(nC)$ communication.

2024

CRYPTO

Towards Breaking the Half-barrier of Local Leakage-resilient Shamir's Secret Sharing
Abstract

Advanced methods for repairing Reed-Solomon codes, exemplified by the work of Guruswami and Wooters (STOC 2016), can be exploited to launch local leakage attacks against Shamir secret-sharing schemes over characteristic-2 fields.
Conversely, Benhamouda, Degwekar, Ishai, and Rabin (CRYPTO 2018) proved that high-threshold instances of Shamir's secret sharing over prime fields are resilient to one-bit local leakage. Since then, extensive efforts have been made to lower the threshold. However, even for simple leakage such as quadratic residue, it remains uncertain whether Shamir's scheme is leakage-resilient when the reconstruction threshold $n$ is less than half the number of parties $k$.
As highlighted by Maji, Paskin-Cherniavsky, Suad, and Wang (CRYPTO 2021), the common approach fails to establish the leakage resilience of Shamir's scheme against quadratic residue leakage when $k < n/2$. In many applications, the threshold must not exceed half the number of parties.
This work develops a new framework for studying the local leakage resilience of Shamir's secret sharing over a finite field of prime order $p$.
Our work demonstrates that Shamir secret sharing remains leakage resilient against almost all 1-bit local leakages, including quadratic residue leakage, even when $k = cn$ for any constant $c$, provided the prime field is sufficiently large.
This result extends to any MDS code-based secret sharing.
For the hardness of computation, we propose an explicit 2-bit leakage attack capable of determining the secret in Shamir secret sharing with a reconstruction threshold $k = O(\sqrt{n})$ when $p = \Theta(n)$.
Our attack translates into a repairing algorithm for Reed-Solomon codes.
Technically, our framework relies on additive combinatorics and character sums, specifically higher-order Fourier analysis.
These connections may be of independent interest.

2024

CRYPTO

Towards Permissionless Consensus in the Standard Model via Fine-Grained Complexity
Abstract

We investigate the feasibility of {\em permissionless} consensus (aka Byzantine agreement) under standard assumptions.
A number of protocols have been proposed to achieve permissionless consensus, most notably based on the Bitcoin protocol; however, to date no protocol is known that can be provably instantiated outside of the random oracle model.
In this work, we take the first steps towards achieving permissionless consensus in the standard model. In particular, we demonstrate that worst-case conjectures in fine-grained complexity, in particular the orthogonal vectors conjecture (implied by the Strong Exponential Time Hypothesis),
imply permissionless consensus in the random beacon model---a setting where a fresh random value is delivered to all parties at regular intervals. This gives a remarkable win-win result: \emph{either permissionless
consensus exists relative to a random beacon, or there are non-trivial worst-case algorithmic speed-ups for a host of natural algorithmic problems} (including $\mathsf{SAT}$).
Our protocol achieves resilience against adversaries that control an inverse-polynomial fraction of the honest computational power, i.e.,~adversarial power $A=T^{1-\epsilon}$ for some constant $\epsilon>0$, where $T$ denotes the honest computational power. This relatively low threshold is a byproduct of the slack in the fine-grained complexity conjectures.
One technical highlight is the construction of a \emph{Seeded Proof of Work}: a Proof of Work where many (correlated) challenges can be derived from a single short \emph{public} seed, and yet still no non-trivial amortization is possible.

2024

CRYPTO

Traceable Secret Sharing: Strong Security and Efficient Constructions
Abstract

Suppose Alice uses a $t$-out-of-$n$ secret sharing to store her secret key on $n$ servers. Her secret key is protected as long as $t$ of them do not collude. However, what if a less-than-$t$ subset of the servers decides to offer the shares they have for sale? In this case, Alice should be able to hold them accountable, or else nothing prevents them from selling her shares. With this motivation in mind, Goyal, Song, and Srinivasan (CRYPTO 21) introduced the concept of {\em traceable secret sharing}. In such schemes, it is possible to provably trace the leaked secret shares back to the servers who leaked them. Goyal et al.~presented the first construction of a traceable secret sharing scheme. However, secret shares in their construction are quadratic in the secret size, and their tracing algorithm is quite involved as it relies on Goldreich-Levin decoding.
In this work, we put forth new definitions and practical constructions for traceable secret sharing. In our model, some $f < t$ servers output a reconstruction box~$R$ that may arbitrarily depend on their shares. Given additional $t-f$ shares, $R$ reconstructs and outputs the secret.
The task is to trace $R$ back to the corrupted servers given
black-box access to $R$.
Unlike Goyal et al., we do not assume that the tracing algorithm has any information on how the corrupted servers constructed~$R$ from the shares in their possession.
We then present two very efficient constructions of traceable secret sharing based on two classic secret sharing schemes.
In both of our schemes, shares are only twice as large as the secret, improving over the quadratic overhead of Goyal et al.
Our first scheme is obtained by presenting a new practical tracing algorithm for the widely-used Shamir secret sharing scheme.
Our second construction is based on an extension of Blakley's secret sharing scheme. Tracing in this scheme is optimally efficient, and requires just one successful query to $R$.
We believe that our constructions are an important step towards bringing traceable secret-sharing schemes to practice.
This work also raises several interesting open problems that we describe
in the paper.

2024

CRYPTO

Two-Round Threshold Signature from Algebraic One-More Learning with Errors
Abstract

Threshold signatures have recently seen a renewed interest due to applications in cryptocurrency while NIST has released a call for multi-party threshold schemes, with a deadline for submission expected for the first half of 2025. So far, all lattice-based threshold signatures requiring less than two-rounds are based on heavy tools such as (fully) homomorphic encryption (FHE) and homomorphic trapdoor commitments (HTDC). This is not unexpected considering that most efficient two-round signatures from classical assumptions either rely on idealized model such as algebraic group models or on one-more type assumptions, none of which we have a nice analogue in the lattice world.
In this work, we construct the first efficient two-round lattice-based threshold signature without relying on FHE or HTDC. It has an offline- online feature where the first round can be reprocessed without knowing message or the signer sets, effectively making the signing phase non-interactive. The signature size is small and shows great scalability. For example, even for a threshold as large as 1024 signers, we achieve a signature size roughly 11 KB. At the heart of our construction is a new lattice-based assumption called the algebraic one-more learning with errors (AOM-MLWE) assumption. We believe this to be a strong inclusion to our lattice toolkits with an independent interest. We establish the selective security of AOM-MLWE based on the standard MLWE and MSIS assumptions, and provide an in depth analysis of its adaptive security, which our threshold signature is based on.

2024

CRYPTO

Unconditionally Secure Commitments with Quantum Auxiliary Inputs
Abstract

We show the following unconditional results on quantum commitments in two related yet different models:
1. We revisit the notion of quantum auxiliary-input commitments introduced by Chailloux, Kerenidis, and Rosgen (Comput. Complex. 2016) where both the committer and receiver take the same quantum state, which is determined by the security parameter,
as quantum auxiliary inputs. We show that computationally-hiding and statistically-binding quantum auxiliary-input commitments exist unconditionally, i.e., without relying on any unproven assumption, while Chailloux et al. assumed a complexity-theoretic assumption, ${\bf QIP}\not\subseteq{\bf QMA}$. On the other hand, we observe that achieving both statistical hiding and statistical binding at the same time is impossible even in the quantum auxiliary-input setting. To the best of our knowledge, this is the first example of unconditionally proving computational security of any form of (classical or quantum) commitments for which statistical security is impossible. As intermediate steps toward our construction, we introduce and unconditionally construct post-quantum sparse pseudorandom distributions and quantum auxiliary-input EFI pairs which may be of independent interest.
2. We introduce a new model which we call the common reference quantum state (CRQS) model where both the committer and receiver take the same quantum state that is randomly sampled by an efficient setup algorithm. We unconditionally prove that there exist statistically hiding and statistically binding commitments in the CRQS model, circumventing the impossibility in the plain model.
We also discuss their applications to zero-knowledge proofs, oblivious transfers, and multi-party computations.

2024

CRYPTO

Unconditionally secure quantum commitments with preprocessing
Abstract

We demonstrate how to build computationally secure commitment schemes with the aid of quantum auxiliary inputs without unproven complexity assumptions. Furthermore, the quantum auxiliary input can be either sampled in uniform exponential time or prepared in at most doubly exponential time, without relying on an external trusted third party. Classically this remains impossible without first proving P ≠ NP.

2024

CRYPTO

Universal Composable Transaction Serialization with Order Fairness
Abstract

Order fairness in the context of distributed ledgers has received recently significant attention due to a range of attacks that exploit the reordering and adaptive injection of transactions (violating what is known as ``input causality''). To address such concerns an array of definitions for order fairness has been put forth together with impossibility and feasibility results highlighting the difficulty and multifaceted nature of fairness in transaction serialization. Motivated by this we present a comprehensive modeling of order fairness capitalizing on the universal composition (UC) setting. Our results capture the different flavors of sender order fairness and input causality (which is arguably one of the most critical aspects of ledger transaction processing with respect to serialization attacks) and we parametrically illustrate what are the limits of feasibility for realistic constructions via an impossibility result. Our positive result, a novel distributed ledger protocol utilizing trusted enclaves, complements tightly our impossibility result, hence providing an \emph{optimal} sender order fairness ledger construction that is also eminently practical.

2024

CRYPTO

Zero-knowledge IOPs Approaching Witness Length
Abstract

Interactive Oracle Proofs (IOPs) allow a probabilistic verifier interacting with a prover to verify the validity of an NP statement while reading only few bits from the prover messages. IOPs generalize standard Probabilistically-Checkable Proofs (PCPs) to the interactive setting, and in the few years since their introduction have already exhibited major improvements in main parameters of interest (such as the proof length and prover and verifier running times), which in turn led to significant improvements in constructions of succinct arguments. {\em Zero-Knowledge} (ZK) IOPs additionally guarantee that the view of any query-bounded (possibly malicious) verifier can be efficiently simulated. ZK-IOPs are the main building block of succinct {\em ZK} arguments which use the underlying cryptographic object (e.g., a collision-resistant hash function) {\em as a black box}.
In this work, we construct the first {\em ZK-IOPs approaching the witness length} for a natural NP problem. More specifically, we design constant-query and constant-round IOPs for 3SAT in which the total communication is $(1+\gamma)m$, where $m$ is the number of variables and $\gamma>0$ is an arbitrarily small constant, and ZK holds against verifiers querying $m^\beta$ bits from the prover's messages, for a constant $\beta>0$. This gives a ZK variant of a recent result of Ron-Zewi and Rothblum (FOCS `20), who construct (non-ZK) IOPs approaching the witness length for a large class of NP languages. Previous constructions of {\em ZK}-IOPs incurred an (unspecified) large constant multiplicative overhead in the proof length, even when restricting to ZK against the {\em honest} verifier.
We obtain our ZK-IOPs by improving the two main building blocks underlying most ZK-IOP constructions, namely ZK codes and ZK-IOPs for sumcheck. More specifically, we give the first ZK-IOPs for sumcheck that achieve both {\em sublinear} communication for sumchecking a {\em general} tensor code, and a ZK guarantee. We also show a strong ZK preservation property for tensors of ZK codes, which extends a recent result of Bootle, Chiesa, and Liu (EC `22). Given the central role of these objects in designing ZK-IOPs, these results might be of independent interest.