## CryptoDB

### Papers from PKC 2021

**Year**

**Venue**

**Title**

2021

PKC

A Geometric Approach to Homomorphic Secret Sharing
📺 Abstract

An (n,m,t)-homomorphic secret sharing (HSS) scheme allows n clients to share their inputs across m servers, such that the inputs are hidden from any t colluding servers, and moreover the servers can evaluate functions over the inputs locally by mapping their input shares to compact output shares. Such compactness makes HSS a useful building block for communication-efficient secure multi-party computation (MPC).
In this work, we propose a simple compiler for HSS evaluating multivariate polynomials based on two building blocks: (1) homomorphic encryption for linear functions or low-degree polynomials, and (2) information-theoretic HSS for low-degree polynomials. Our compiler leverages the power of the first building block towards improving the parameters of the second.
We use our compiler to generalize and improve on the HSS scheme of Lai, Malavolta, and Schröder [ASIACRYPT'18], which is only efficient when the number of servers is at most logarithmic in the security parameter. In contrast, we obtain efficient schemes for polynomials of higher degrees and an arbitrary number of servers. This application of our general compiler extends techniques that were developed in the context of information-theoretic private information retrieval (Woodruff and Yekhanin [CCC'05]), which use partial derivatives and Hermite interpolation to support the computation of polynomials of higher degrees.
In addition to the above, we propose a new application of HSS to MPC with preprocessing. By pushing the computation of some HSS servers to a preprocessing phase, we obtain communication-efficient MPC protocols for low-degree polynomials that use fewer parties than previous protocols based on the same assumptions. The online communication of these protocols is linear in the input size, independently of the description size of the polynomial.

2021

PKC

Adventures in Crypto Dark Matter: Attacks and Fixes for Weak Pseudorandom Functions
📺 Abstract

A weak pseudorandom function (weak PRF) is one of the most important cryptographic primitives for its efficiency although it has lower security than a standard PRF.
Recently, Boneh et al. (TCC'18) introduced two types of new weak PRF candidates, which are called a basic Mod-2/Mod-3 and alternative Mod-2/Mod-3 weak PRF.
Both use the mixture of linear computations defined on different small moduli to satisfy conceptual simplicity, low complexity (depth-2 ${\sf ACC^0}$) and MPC friendliness. In fact, the new candidates are conjectured to be exponentially secure against any adversary that allows exponentially many samples, and a basic Mod-2/Mod-3 weak PRF is the only candidate that satisfies all features above. However, none of the direct attacks which focus on basic and alternative Mod-2/Mod-3 weak PRFs use their own structures.
In this paper, we investigate weak PRFs from two perspectives; attacks, fixes.
We first propose direct attacks for an alternative Mod-2/Mod-3 weak PRF and a basic Mod-2/Mod-3 weak PRF when a circulant matrix is used as a secret key.
For an alternative Mod-2/Mod-3 weak PRF, we prove that the adversary's advantage is at least $2^{-0.105n}$, where $n$ is the size of the input space of the weak PRF. Similarly, we show that the advantage of our heuristic attack to the weak PRF with a circulant matrix key is larger than $2^{-0.21n}$, which is contrary to the previous expectation that `structured secret key' does not affect the security of a weak PRF. Thus, for an optimistic parameter choice $n = 2\lambda$ for the security parameter $\lambda$, parameters should be increased to preserve $\lambda$-bit security when an adversary obtains exponentially many samples.
Next, we suggest a simple method for repairing two weak PRFs affected by our attack while preserving the
parameters.

2021

PKC

An Alternative Approach for SIDH Arithmetic
Abstract

In this paper, we present new algorithms for the field arithmetic layers of supersingular isogeny Diffie-Hellman; one of the fifteen remaining candidates in the NIST post-quantum standardization process. Our approach uses a polynomial representation of the field elements together with mechanisms to keep the coefficients within bounds during the arithmetic operations. We present timings and comparisons for SIKEp503 and suggest a novel 736-bit prime that offers a 1.17x speedup compared to SIKEp751 for a similar level of security.

2021

PKC

An Efficient and Generic Construction for Signal's Handshake (X3DH): Post-Quantum, State Leakage Secure, and Deniable
📺 Abstract

The Signal protocol is a secure instant messaging protocol that underlies the security of numerous applications such as WhatsApp, Skype, Facebook Messenger among many others. The Signal protocol consists of two sub-protocols known as the X3DH protocol and the double ratchet protocol, where the latter has recently gained much attention. For instance, Alwen, Coretti, and Dodis (Eurocrypt'19) provided a concrete security model along with a generic construction based on simple building blocks that are instantiable from versatile assumptions, including post-quantum ones. In contrast, as far as we are aware, works focusing on the X3DH protocol seem limited.
In this work, we cast the X3DH protocol as a specific type of authenticated key exchange (AKE) protocol, which we call a Signal-conforming AKE protocol, and formally define its security model based on the vast prior work on AKE protocols. We then provide the first efficient generic construction of a Signal-conforming AKE protocol based on standard cryptographic primitives such as key encapsulation mechanisms (KEM) and signature schemes.
Specifically, this results in the first post-quantum secure replacement of the X3DH protocol on well-established assumptions. Similar to the X3DH protocol, our Signal-conforming AKE protocol offers a strong (or stronger) flavor of security, where the exchanged key remains secure even when all the non-trivial combinations of the long-term secrets and session-specific secrets are compromised. Moreover, our protocol has a weak flavor of deniability and we further show how to strengthen it using ring signatures. Finally, we provide a full-fledged, generic C implementation of our (weakly deniable) protocol. We instantiate it with several Round 3 candidates (finalists and alternates) to the NIST post-quantum standardization process and compare the resulting bandwidth and computation performances. Our implementation is publicly available.

2021

PKC

Analysis of Multivariate Encryption Schemes: Application to Dob
📺 Abstract

In this paper, we study the effect of two modifications to multivariate public key encryption schemes: internal perturbation (ip), and Q_+. Focusing on the Dob encryption scheme, a construction utilising these modifications, we accurately predict the number of degree fall polynomials produced in a Gröbner basis attack, up to and including degree five. The predictions remain accurate even when fixing variables. Based on this new theory we design a novel attack on the Dob encryption scheme, which breaks Dob using the parameters suggested by its designers.
While our work primarily focuses on the Dob encryption scheme, we also believe that the presented techniques will be of particular interest to the analysis of other big-field schemes.

2021

PKC

Banquet: Short and Fast Signatures from AES
📺 Abstract

In this work we introduce Banquet, a digital signature scheme with post-quantum security, constructed using only symmetric-key primitives. The design is based on the MPC-in-head paradigm also used by Picnic (CCS 2017) and BBQ (SAC 2019). Like BBQ, Banquet uses only standardized primitives, namely AES and SHA-3, but signatures are more than 50\% shorter, making them competitive with Picnic (which uses a non-standard block cipher to improve performance). The MPC protocol in Banquet uses a new technique to verify correctness of the AES S-box computations, which is efficient because the cost is amortized with a batch verification strategy.
Our implementation and benchmarks also show that both signing and verification can be done in under 10ms on a current x64 CPU. We also explore the parameter space to show the range of trade-offs that are possible with the Banquet design, and show that Banquet can nearly match the signature sizes possible with Picnic (albeit with slower, but still practical run times) or have speed within a factor of two of Picnic (at the cost of larger signatures).

2021

PKC

BETA: Biometric-Enabled Threshold Authentication
📺 Abstract

In the past decades, user authentication has been dominated by server-side password-based solutions that rely on ``what users know". This approach is susceptible to breaches and phishing attacks, and poses usability challenges. As a result, the industry is gradually moving to biometric-based client-side solutions that do not store any secret information on servers. This shift necessitates the safe storage of biometric templates and private keys, which are used to generate tokens, on user devices.
We propose a new generic framework called Biometric Enabled Threshold Authentication (BETA) to protect sensitive client-side information like biometric templates and cryptographic keys. Towards this, we formally introduce the notion of Fuzzy Threshold Tokenizer (FTT) where an initiator can use a ``close'' biometric measurement to generate an authentication token if at least t (the threshold) devices participate. We require that the devices only talk to the initiator, and not to each other, to capture the way user devices are connected in the real world. We use the universal composability (UC) framework to model the security properties of FTT, including the unforgeability of tokens and the privacy of the biometric values (template and measurement), under a malicious adversary. We construct three protocols that meet our definition.
Our first two protocols are general feasibility results that work for any distance function, any threshold t and tolerate the maximal (i.e. t-1) amount of corruption. They are based on any two round UC-secure multi-party computation protocol in the standard model (with a CRS) and threshold fully homomorphic encryption, respectively. We show how to effectively use these primitives to build protocols in a constrained communication model with just four rounds of communication.
For the third protocol, we consider inner-product based distance metrics (cosine similarity, Euclidean distance, etc.) specifically, motivated by the recent interest in its use for face recognition. We use Paillier encryption, efficient NIZKs for specific languages, and a simple garbled circuit to build an efficient protocol for the common case of n=3 devices with one compromised.

2021

PKC

Beyond Security and Efficiency: On-Demand Ratcheting with Security Awareness
📺 Abstract

Secure asynchronous two-party communication applies ratcheting to strengthen privacy, in the presence of internal state exposures. Security with ratcheting is provided in two forms: forward security and post-compromise security. There have been several such secure protocols proposed in the last few years. However, they come with a high cost.
In this paper, we propose two generic constructions with favorable properties. Concretely, our first construction achieves security awareness. It allows users to detect non-persistent active attacks, to determine which messages are not safe given a potential leakage pattern, and to acknowledge for deliveries.
In our second construction, we define a hybrid system formed by combining two protocols: typically, a weakly secure "light" protocol and a strongly secure "heavy" protocol. The design goals of our hybrid construction are, first, to let the sender decide which one to use in order to obtain an efficient protocol with ratchet on demand; and second, to restore the communication between honest participants in the case of a message loss or an active attack.
We can apply our generic constructions to any existing protocol.

2021

PKC

Bootstrapping fully homomorphic encryption over the integers in less than one second
📺 Abstract

One can bootstrap LWE-based fully homomorphic encryption (FHE) schemes
in less than one second, but bootstrapping AGCD-based FHE schemes,
also known as FHE over the integers, is still very slow.
In this work we propose fast bootstrapping methods for FHE over the integers,
closing thus this gap between these two types of schemes.
We use a variant of the AGCD problem to construct a new GSW-like scheme
that can natively encrypt polynomials, then, we show how the single-gate
bootstrapping method proposed by
Ducas and Micciancio (EUROCRYPT 2015)
can be adapted to FHE over the
integers using our scheme, and we implement a bootstrapping that,
using around 400 MB of key material,
runs in less than one second in a common personal computer.

2021

PKC

Compact Zero-Knowledge Proofs for Threshold ECDSA with Trustless Setup
📺 Abstract

Threshold ECDSA signatures provide a higher level of security to a crypto wallet since it requires more than t parties out of n parties to sign a transaction. The state-of-the-art bandwidth efficient threshold ECDSA used the additive homomorphic Castagnos and Laguillaumie (CL) encryption based on an unknown order group G, together with a number of zero-knowledge proofs in G. In this paper, we propose compact zero-knowledge proofs for threshold ECDSA to lower the communication bandwidth, as well as the computation cost. The proposed zero-knowledge proofs include the discrete-logarithm relation in G and the well-formedness of a CL ciphertext.
When applied to two-party ECDSA, we can lower the bandwidth of the key generation algorithm by 47%, and the running time for the key generation and signing algorithms are boosted by about 35% and 104% respectively. When applied to threshold ECDSA, our first scheme is more optimized for the key generation algorithm (about 70% lower bandwidth and 70% faster computation in key generation, at a cost of 20% larger bandwidth in signing), while our second scheme has an all-rounded performance improvement (about 60% lower bandwidth, 27% faster computation in key generation without additional cost in signing).

2021

PKC

Cryptographic Pseudorandom Generators Can Make Cryptosystems Problematic
📺 Abstract

Randomness is an essential resource for cryptography. For practical randomness generation, the security notion of pseudorandom generators (PRGs) intends to automatically preserve (computational) security of cryptosystems when used in implementation. Nevertheless, some opposite case such as in computational randomness extractors (Barak et al., CRYPTO 2011) is known (but not yet systematically studied so far) where the security can be lost even by applying secure PRGs. The present paper aims at pushing ahead the observation and understanding about such a phenomenon; we reveal such situations at layers of primitives and protocols as well, not just of building blocks like randomness extractors. We present three typical types of such cases: (1) adversaries can legally see the seed of the PRGs (including the case of randomness extractors); (2) the set of "bad" randomness may be not efficiently recognizable; (3) the formulation of a desired property implicitly involves non-uniform distinguishers for PRGs. We point out that the semi-honest security of multiparty computation also belongs to Type 1, while the correctness with negligible decryption error probability for public key encryption belongs to Types 2 and 3. We construct examples for each type where a secure PRG (against uniform distinguishers only, for Type 3) does not preserve the security/correctness of the original scheme; and discuss some countermeasures to avoid such an issue.

2021

PKC

Efficient Adaptively-Secure IB-KEMs and VRFs via Near-Collision Resistance
📺 Abstract

We construct more efficient cryptosystems with provable security against adaptive attacks, based on simple and natural hardness
assumptions in the standard model. Concretely, we describe:
– An adaptively-secure variant of the efficient, selectively-secure LWE-
based identity-based encryption (IBE) scheme of Agrawal, Boneh,
and Boyen (EUROCRYPT 2010). In comparison to the previously
most efficient such scheme by Yamada (CRYPTO 2017) we achieve
smaller lattice parameters and shorter public keys of size O(log \lambda),
where \lambda is the security parameter.
– Adaptively-secure variants of two efficient selectively-secure pairing-
based IBEs of Boneh and Boyen (EUROCRYPT 2004). One is based
on the DBDH assumption, has the same ciphertext size as the cor-
responding BB04 scheme, and achieves full adaptive security with
public parameters of size only O(log \lambda). The other is based on a q-
type assumption and has public key size O(\lambda), but a ciphertext is
only a single group element and the security reduction is quadrat-
ically tighter than the corresponding scheme by Jager and Kurek
(ASIACRYPT 2018).
– A very efficient adaptively-secure verifiable random function where
proofs, public keys, and secret keys have size O(log \lambda).
As a technical contribution we introduce blockwise partitioning, which
leverages the assumption that a cryptographic hash function is weak
near-collision resistant to prove full adaptive security of cryptosystems.

2021

PKC

Exact Lattice Sampling from Non-Gaussian Distributions
📺 Abstract

We propose a new framework for (trapdoor) sampling over lattices. Our framework can be instantiated in a number of ways. It allows for example to sample from uniform, affine and “product affine” distributions. Another salient point of our framework is that the output distributions of our samplers are perfectly indistinguishable from ideal ones, in contrast with classical samplers that are statistically indistinguishable. One caveat of our framework is that all our current instantiations entail a rather large standard deviation.

2021

PKC

Flexible and Efficient Verifiable Computation on Encrypted Data
📺 Abstract

We consider the problem of verifiable and private delegation of computation [Gennaro et al. CRYPTO'10] in which a client stores private data on an untrusted server and asks the server to compute functions over this data. In this scenario we aim to achieve three main properties: the server should not learn information on inputs and outputs of the computation (privacy), the server cannot return wrong results without being caught (integrity), and the client can verify the correctness of the outputs faster than running the computation (efficiency). A known paradigm to solve this problem is to use a (non-private) verifiable computation (VC) to prove correctness of a homomorphic encryption (HE) evaluation on the ciphertexts. Despite the research advances in obtaining efficient VC and HE, using these two primitives together in this paradigm is concretely expensive. Recent work [Fiore et al. CCS'14, PKC'20] addressed this problem by designing specialized VC solutions that however require the HE scheme to work with very specific parameters; notably HE ciphertexts must be over $\mathbb{Z}_q$ for a large prime $q$.
In this work we propose a new solution that allows a flexible choice of HE parameters, while staying modular (based on the paradigm combining VC and HE) and efficient (the VC and the HE schemes are both executed at their best efficiency). At the core of our new protocol are new homomorphic hash functions for Galois rings. As an additional contribution we extend our results to support non-deterministic computations on encrypted data and an additional privacy property by which verifiers do not learn information on the inputs of the computation.

2021

PKC

Generic Negation of Pair Encodings
📺 Abstract

Attribute-based encryption (ABE) is a cryptographic primitive which supports fine-grained access control on encrypted data, making it an appealing building block for many applications. Pair encodings (Attrapadung, EUROCRYPT 2014) are simple primitives that can be used for constructing fully secure ABE schemes associated to a predicate relative to the encoding. We propose a generic transformation that takes any pair encoding scheme (PES) for a predicate P and produces a PES for its negated predicate \bar{P} . This construction finally solves a problem that was open since 2015. Our techniques bring new insight to the expressivity and generality of PES and can be of independent interest. We also provide, to the best of our knowledge, the first pair encoding scheme for negated doubly spatial encryption (obtained with our transformation) and explore several other consequences of our results.

2021

PKC

Group Encryption: Full Dynamicity, Message Filtering and Code-Based Instantiation
📺 Abstract

Group encryption (\textsf{GE}), introduced by Kiayias, Tsiounis and Yung (Asiacrypt'07), is the encryption analogue of group signatures. It allows to send verifiably encrypted messages satisfying certain requirements to certified members of a group, while keeping the anonymity of the receivers. Similar to the tracing mechanism in group signatures, the receiver of any ciphertext can be identified by an opening authority - should the needs arise. The primitive of \textsf{GE} is motivated by a number of interesting privacy-preserving applications, including the filtering of encrypted emails sent to certified members of an organization.
This paper aims to improve the state-of-affairs of \textsf{GE} systems. Our first contribution is the formalization of fully dynamic group encryption (\textsf{FDGE}) - a \textsf{GE} system simultaneously supporting dynamic user enrolments and user revocations. The latter functionality for \textsf{GE} has not been considered so far. As a second contribution, we realize the message filtering feature for \textsf{GE} based on a list of $t$-bit keywords and $2$ commonly used policies: ``permissive'' - accept the message if it contains at least one of the keywords as a substring; ``prohibitive'' - accept the message if all of its $t$-bit substrings are at Hamming distance at least $d$ from all keywords, for $d \geq 1$. This feature so far has not been substantially addressed in existing instantiations of \textsf{GE} based on DCR, DDH, pairing-based and lattice-based assumptions. Our third contribution is the first instantiation of GE under code-based assumptions. The scheme is more efficient than the lattice-based construction of Libert et al. (Asiacrypt'16) - which, prior to our work, is the only known instantiation of \textsf{GE} under post-quantum assumptions. Our scheme supports the $2$ suggested policies for message filtering, and in the random oracle model, it satisfies the stringent security notions for \textsf{FDGE} that we put forward.

2021

PKC

Group Signatures with User-Controlled and Sequential Linkability
📺 Abstract

Group signatures allow users to create signatures on behalf of a group while remaining anonymous. Such signatures are a powerful tool to realize privacy-preserving data collections, where e.g., sensors, wearables or vehicles can upload authenticated measurements into a data lake. The anonymity protects the user’s privacy yet enables basic data processing of the uploaded unlinkable information. For many applications, full anonymity is often neither desired nor useful though, and selected parts of the data must eventually be correlated after being uploaded. Current solutions of group signatures do not provide such functionality in a satisfactory way: they either rely on a trusted party to perform opening or linking of signatures, which clearly conflicts with the core privacy goal of group signatures; or require the user to decide upon the linkability of signatures before they are generated.
In this paper we propose a new variant of group signatures that provides linkability in a flexible and user-centric manner. Users – and only they – can decide before and after signature creation whether they should remain linkable or be correlated. To prevent attacks where a user omits certain signatures when a sequence of events in a certain section (e.g., time frame), should be linked, we further extend this new primitive to allow for sequential link proofs. Such proofs guarantee that the provided sequence of data is not only originating from the same signer, but also occurred in that exact order and contains all of the user’s signatures within the time frame. We formally define the desired security and privacy properties, propose a provably secure construction based on DL-related assumptions and report on a prototypical implementation of our scheme.

2021

PKC

How Provably Secure are (EC)DSA Signatures?
📺 Abstract

★Invited talk

Today, digital signatures are an omnipresent cryptographic primitive. They are extensively used for message and entity authentication and find widespread application in real-world protocols. Without much doubt, the specific schemes deployed most often are the RSA-based PKCS#1 v1.5, and the discrete logarithm-based DSA and ECDSA. For instance, current versions of TLS - the standard technology for securing internet connections - exclusively employ signatures of these types to authenticate servers. Furthermore, most cryptocurrencies like Bitcoin and Ethereum use ECDSA for signing transactions. The popularity of (EC)DSA signatures stands in stark contrast to the absence of rigorous security analyses. In this talk we will survey known provable security results about DSA and ECDSA. We will also discuss limitations of current provable security approaches.

2021

PKC

Impossibility on Tamper-Resilient Cryptography with Uniqueness Properties
📺 Abstract

In this work, we show negative results on the tamper-resilience of a wide class of cryptographic primitives with uniqueness properties, such as unique signatures, verifiable random functions, signatures with unique keys, injective one-way functions, and encryption schemes with a property we call unique-message property. Concretely, we prove that for these primitives, it is impossible to derive their (even extremely weak) tamper-resilience from any common assumption, via black-box reductions. Our proofs exploit the simulatable attack paradigm proposed by Wichs (ITCS ’13), and the tampering model we treat is the plain model, where there is no trusted setup.

2021

PKC

Improving Revocation for Group Signature with Redactable Signature
📺 Abstract

Group signature is a major cryptographic tool allowing anonymous access to a service. However, in practice, access to a service is usually granted for some periods of time, which implies that the signing rights must be deactivated the rest of the time. This requirement thus calls for complex forms of revocation, reminiscent of the concept of time-bound keys. However, schemes implementing this concept are rare and only allow revocation with limited granularity. That is, signing keys are associated with an expiry time and become definitively useless once the latter has passed.
In this paper, we revisit the notion of group signatures with time-bound keys with several contributions. Firstly, we extend this notion to allow high granularity revocation: a member's signing key can in particular be deactivated at some moments and then be automatically reinstated. Secondly, we show that this complex property is actually simple to achieve using redactable signature. In particular, we consider in this context a recent redactable signature scheme from PKC 20 that we improve by dramatically reducing the size of the public key. The resulting construction is of independent interest.

2021

PKC

Isogeny-based key compression without pairings
📺 Abstract

SIDH/SIKE-style protocols benefit from key compression to minimize their bandwidth requirements, but proposed key compression mechanisms rely on computing bilinear pairings.
Pairing computation is a notoriously expensive operation, and, unsurprisingly, it is typically one of the main efficiency bottlenecks in SIDH key compression, incurring processing time penalties that are only mitigated at the cost of trade-offs with precomputed tables.
We address this issue by describing how to compress isogeny-based keys without pairings.
As a bonus, we also substantially reduce the storage requirements of other operations involved in key compression.

2021

PKC

Lattices and Factoring (Invited Talk)
Abstract

In this talk, I would like to re-popularize two dual ideas that relate Lattices and Factoring. Such a connection may appear surprising at first, but is only one logarithm away: after all, factoring is nothing more than a {\em multiplicative} knapsack problem, i.e. a subset product problem, where the weights are given by the set of small enough primes.
The first of the two ideas, we owe to Schnorr (1991) and to Adleman (1995). It consists in finding close or short vectors in a carefully crafted lattice, in the hope that they will provide so-called factoring relations. While this idea does not appear to lead to faster factoring algorithms, it remains fascinating and has in fact lead to other major results. Indeed, the Schnorr-Adleman lattice plays a key role in the proof by Ajtai (1998) of the NP-hardness of the shortest vector problem.
The second idea, due to Chor and Rivest (1988) shows a reverse connection: constructing the lattice this time using {\em discrete} logarithms, they instead solve the bounded distance decoding (BDD) problem through easy factoring instances. Revisiting their idea, Pierrot and I (2018) showed that this was a quite close to an optimal construction for solving BDD in polynomial time. It was in fact the best known such construction until some recent work by Peikert and Mook (2020).
I wish to conclude with an invitation to explore the cryptographic potential of other lattices than the random q-ary lattices ---the lattices underlying the Learning with Error problem (LWE) and the Short Integer Solution problem (SIS). While SIS and LWE have shown to be very convenient for constructing the most advanced schemes and protocols, I believe that more general lattices have a yet untapped potential for cryptography.

2021

PKC

Masked Triples: Amortizing Multiplication Triples across Conditionals
📺 Abstract

A classic approach to MPC uses preprocessed multiplication triples to evaluate arbitrary Boolean circuits. If the target circuit features conditional branching, e.g. as the result of a IF program statement, then triples are wasted: one triple is consumed per AND gate, even if the output of the gate is entirely discarded by the circuit’s conditional behavior.
In this work, we show that multiplication triples can be re-used across conditional branches. For a circuit with b branches, each having n AND gates, we need only a total of n triples, rather than the typically required bn. Because preprocessing triples is often the most expensive step in protocols that use them, this significantly improves performance.
Prior work similarly amortized oblivious transfers across branches in the classic GMW protocol (Heath et al., Asiacrypt 2020, [HKP20]). In addition to demonstrating conditional improvements are possible for a different class of protocols, we also concretely improve over [HKP20]: their maximum improvement is bounded by the topology of the circuit. Our protocol yields improvement independent of topology: we need triples proportional to the size of the program’s longest execution path, regardless of the structure of the program branches.
We implemented our approach in C++. Our experiments show that we significantly improve over a "naive" protocol and over prior work: for a circuit with 16 branches and in terms of total communication, we improved over naive by 12x and over [HKP20] by an average of 2.6x.
Our protocol is secure against the semi-honest corruption of p-1 parties.

2021

PKC

Master-Key KDM-Secure ABE via Predicate Encoding
📺 Abstract

In this paper, we propose the first generic framework for attribute-based encryptions (ABE) with master-secret-key-dependent-message security (mKDM security) for affine functions via predicate encodings by Chen, Gay and Wee [Eurocrypt 2015]. The construction is adaptively secure under standard $k$-Lin assumption in prime-order bilinear groups. By this, we obtain a set of new mKDM-secure ABE schemes with high expressiveness that have never been reached before: we get the first hierarchical IBE (HIBE) scheme and the first ABE scheme for arithmetic branching program (ABP) with mKDM security for affine functions. Thanks to the expressiveness (more concretely, delegability like HIBE), we can obtain mKDM-secure ABE against chosen-ciphertext attack (i.e., CCA security) via a classical CPA-to-CCA transformation that works well in the context of mKDM.

2021

PKC

More Efficient Digital Signatures with Tight Multi-User Security
📺 Abstract

We construct the currently most efficient signature schemes with tight multi-user security against adaptive corruptions. It is the first generic construction of such schemes, based on lossy identification schemes (Abdalla etal; JoC 2016), and the first to achieve strong existential unforgeability. It also has significantly more compact signatures than the previously most efficient construction by Gjosteen and Jager (CRYPTO 2018). When instantiated based on the decisional Diffie-Hellman assumption, a signature consists of only three exponents.
We propose a new variant of the generic construction of signatures from sequential OR-proofs by Abe, Ohkubo, and Suzuki (ASIACRYPT 2002) and Fischlin, Harasser, and Janson (EUROCRYPT 2020).
In comparison to Fischlin etal, who focus on constructing signatures in the non-programmable random oracle model (NPROM), we aim to achieve tight security against adaptive corruptions, maximize efficiency, and to directly achieve strong existential unforgeability (also in the NPROM).
This yields a slightly different construction and we use slightly different and additional properties of the lossy identification scheme.
Signatures with tight multi-user security against adaptive corruptions are a commonly-used standard building block for tightly-secure authenticated key exchange protocols. We also show how our construction improves the efficiency of all existing tightly-secure AKE protocols.

2021

PKC

Multi-Client Functional Encryption for Separable Functions
📺 Abstract

In this work, we provide a compiler that transforms a single-input functional encryption scheme for the class of polynomially bounded circuits
into a multi-client functional encryption (MCFE) scheme for the class of separable functions. An $n$-input function $f$ is called separable if it can be described as a list of polynomially bounded circuits $f^1,..., f^n$ s.t. $f(x_1,..., x_n)= f^1(x_1)+ ... + f^n(x_n)$ for all $x_1,..., x_n$.
Our compiler extends the works of Brakerski et al. [Eurocrypt 2016] and of Komargodski et al. [Eurocrypt 2017] in which a generic compiler is proposed to obtain multi-input functional encryption (MIFE) from single-input functional encryption. Our construction achieves the stronger notion of MCFE but for the less generic class of separable functions. Prior to our work, a long line of results has been proposed in the setting of MCFE for the inner-product functionality, which is a special case of a separable function.
We also propose a modified version of the notion of decentralized MCFE introduced by Chotard et al. [Asiacrypt 2018] that we call outsourceable mulit-client functional encryption (OMCFE). Intuitively, the notion of OMCFE makes it possible to distribute the load of the decryption procedure among at most $n$ different entities, which will return decryption shares that can be combined (e.g., additively) thus obtaining the output of the computation. This notion is especially useful in the case of a very resource consuming decryption procedure, while the combine algorithm is non-time consuming. We also show how to extend the presented MCFE protocol to obtain an OMCFE scheme for the same functionality class.

2021

PKC

Multi-Party Threshold Private Set Intersection with Sublinear Communication
📺 Abstract

In multi-party threshold private set intersection (PSI), $n$ parties each with a private set wish to compute the intersection of their sets if the intersection is sufficiently large. Previously, Ghosh and Simkin (CRYPTO 2019) studied this problem for the two-party case and demonstrated interesting lower and upper bounds on the communication complexity. In this work, we investigate the communication complexity of the multi-party setting $(n\geq 2)$. We consider two functionalities for multi-party threshold PSI. In the first, parties learn the intersection if each of their sets and the intersection differ by at most $T$. In the second functionality, parties learn the intersection if the union of all their sets and the intersection differ by at most $T$.
For both functionalities, we show that any protocol must have communication complexity $\Omega(nT)$. We build protocols with a matching upper bound of $O(nT)$ communication complexity for both functionalities assuming threshold FHE. We also construct a computationally more efficient protocol for the second functionality with communication complexity $\widetilde{O}(nT)$ under a weaker assumption of threshold additive homomorphic encryption. As a direct implication, we solve one of the open problems in the work of Ghosh and Simkin (CRYPTO 2019) by designing a two-party protocol with communication cost $\widetilde{O}(T)$ from assumptions weaker than FHE.
As a consequence of our results, we achieve the first "regular" multi-party PSI protocol where the communication complexity only grows with the size of the set difference and does not depend on the size of the input sets.

2021

PKC

Multiparty Cardinality Testing for Threshold Private Set Intersection
📺 Abstract

Threshold Private Set Intersection (PSI) allows multiple parties to compute the intersection of their input sets if and only if the intersection is larger than $n-t$, where $n$ is the size of the sets and $t$ is some threshold. The main appeal of this primitive is that, in contrast to standard PSI, known upper-bounds on the communication complexity only depend on the threshold $t$ and not on the sizes of the input sets.
Current Threshold PSI protocols split themselves into two components: A Cardinality Testing phase, where parties decide if the intersection is larger than some threshold; and a PSI phase, where the intersection is computed. The main source of inefficiency of Threshold PSI is the former part.
In this work, we present a new Cardinality Testing protocol that allows $N$ parties to check if the intersection of their input sets is larger than $n-t$. The protocol incurs in $\tilde{ \mathcal{O}} (Nt^2)$ communication complexity. We thus obtain a Threshold PSI scheme for $N$ parties with communication complexity $\tilde{ \mathcal{O}}(Nt^2)$.

2021

PKC

Multivariate Public Key Cryptosystem from Sidon Spaces
📺 Abstract

A Sidon space is a subspace of an extension field over a base field in which the product of any two elements can be factored uniquely, up to constants. This paper proposes a new a public-key cryptosystem of the multivariate type which is based on Sidon spaces, and has the potential to remain secure even if quantum supremacy is attained. This system, whose security relies on the hardness of the well-known MinRank problem, is shown to be resilient to several straightforward algebraic attacks. In particular, it is proved that the two popular attacks on the MinRank problem, the kernel attack and the minor attack, succeed only with exponentially small probability. The system is implemented in software, and its hardness is demonstrated experimentally.

2021

PKC

Non-Interactive CCA2-Secure Threshold Cryptosystems: Achieving Adaptive Security in the Standard Model Without Pairings
📺 Abstract

We consider threshold public-key encryption, where the decryption servers distributively hold the private key shares, and we need a threshold of these servers to decrypt the message (while the system remains secure when less than the threshold is corrupt). We investigate the notion of chosen-ciphertext secure threshold systems which has been historically hard to achieve. We further require the systems to be, both, adaptively secure (i.e., secure against a strong adversary making corruption decisions dynamically during the protocol), and non-interactive (i.e., where decryption servers do not interact amongst themselves but rather efficiently contribute, each, a single message). To date, only pairing-based implementations were known to achieve security in the standard security model without relaxation (i.e., without assuming the random oracle idealization) under the above stringent requirements. Here, we investigate how to achieve the above using other assumptions (in order to understand what other algebraic building blocks and mathematical assumptions are needed to extend the domain of encryption methods achieving the above). Specifically, we show realizations under the Decision Composite Residuosity (DCR) and Learning-With-Errors (LWE) assumptions.

2021

PKC

On Publicly-Accountable Zero-Knowledge and Small Shuffle Arguments
📺 Abstract

Constructing interactive zero-knowledge arguments from simple assumptions with small communication complexity and good computational efficiency is an important, but difficult problem.
In this work, we study interactive arguments with noticeable soundness error in their full generality and for the specific purpose of constructing concretely efficient shuffle arguments.
To counterbalance the effects of a larger soundness error, we show how to transform such three-move arguments into publicly-accountable ones which allow the verifier to convince third parties of detected misbehavior by a cheating prover.
This may be particularly interesting for applications where a malicious prover has to balance the profits it can make from cheating successfully and the losses it suffers from being caught.
We construct interactive, public-coin, zero-knowledge arguments with noticeable soundness error for proving that a target vector of commitments is a pseudorandom permutation of a source vector.
Our arguments do not rely on any trusted setup and only require the existence of collision-resistant hash functions.
The communication complexity of our arguments is \emph{independent} of the length of the shuffled vector.
For a soundness error of $2^{-5}=1/32$, the communication cost is $153$ bytes without and $992$ bytes with public accountability, meaning that our arguments are shorter than shuffle arguments realized using Bulletproofs (IEEE S\&P 2018) and even competitive in size with SNARKs, despite only relying on simple assumptions.

2021

PKC

On Selective-Opening Security of Deterministic Primitives
Abstract

Classically, selective-opening attack (SOA) has been studied for \emph{randomized} primitives, like randomized encryption schemes and commitments. The study of SOA for deterministic primitives, which presents some unique challenges, was initiated by Bellare \emph{et al.} (PKC 2015), who showed negative results. Subsequently, Hoang \emph{et al.} (ASIACRYPT 2016) showed positive results in the non-programmable random oracle model. Here we show the first positive results for SOA security of deterministic primitives in the \emph{standard} (RO devoid) model. Our results are:
\begin{itemize}
\item Any $2t$-wise independent hash function is SOA secure for an unbounded number of ``$t$-correlated'' messages, meaning any group of up to $t$ messages are arbitrarily correlated.
\item A construction of a deterministic encryption scheme with analogous security, combining a regular lossy trapdoor function with a $2t$-wise independent hash function.
\item The one-more-RSA problem of Bellare \emph{et al.} (J.~Cryptology 2003), which can be seen as a form of SOA, is hard under the $\Phi$-Hiding Assumption with large enough encryption exponent.
\end{itemize}
Somewhat surprisingly, the last result yields the first proof of RSA-based Chaum's blind signature scheme (CRYPTO 1982) based on a ``standard'' computational assumption. Notably, it avoids the impossibility result of Pass (STOC 2011) because lossiness of RSA endows the scheme with non-unique signatures.

2021

PKC

On the (In)Security of the Diffie-Hellman Oblivious PRF with Multiplicative Blinding
📺 Abstract

Oblivious Pseudorandom Function (OPRF) is a protocol between a client holding input x and a server holding key k for a PRF F. At the end, the client learns F_k(x) and nothing else while the server learns nothing. OPRF's have found diverse applications as components of larger protocols, and the currently most efficient instantiation, with security proven in the UC model, is F_k(x)=H2(x,(H1(x))^k) computed using so-called exponential blinding, i.e., the client sends a=(H1(x))^r for random r, the server responds b=a^k, which the client ublinds as v=b^{1/r} to compute F_k(x)=H2(x,v).
However, this protocol requires two variable-base exponentiations on the client, while a more efficient multiplicative blinding scheme replaces one or both client exponentiations with fixed-base exponentiation, leading to the decrease of the client's computational cost by a factor between two to six, depending on pre-computation.
We analyze the security of the above OPRF with multiplicative blinding, showing surprising weaknesses that offer attack avenues which are not present using exponential blinding. We characterize the security of this OPRF implementation as a "Revised OPRF" functionality, a relaxation of UC OPRF functionality used in prior work.
On the positive side, we show that the Revised OPRF suffices for the security of OPAQUE, the asymmetric PAKE protocol, hence allowing OPAQUE the computational advantages of multiplicative blinding. Unfortunately, we also show examples of other OPRF applications which become insecure when using such blinding. The conclusion is that usage of multiplicative blinding for F_k(x) defined as above, in settings where correct value g^k (needed for multiplicative blinding) is not authenticated, and OPRF inputs are of low entropy, must be carefully analyzed, or avoided all together. We complete the picture by showing a simple and safe alternative definition of function F_k(x) which offers (full) UC OPRF security using either form of blinding.

2021

PKC

On the CCA Compatibility of Public-Key Infrastructure
📺 Abstract

In this work, we put forth the notion of compatibility of any key generation or setup algorithm. We focus on the specific case of encryption, and say that a key generation algorithm KeyGen is X-compatible (for X \in {CPA, CCA1, CCA2}) if there exist encryption and decryption algorithms that together with KeyGen, result in an X-secure public-key encryption scheme.
We study the following question: Is every CPA-compatible key generation algorithm also CCA-compatible? We obtain the following answers:
- Every sub-exponentially CPA-compatible KeyGen algorithm is CCA1-compatible, assuming the existence of hinting PRGs and sub-exponentially secure keyless collision resistant hash functions.
- Every sub-exponentially CPA-compatible KeyGen algorithm is also CCA2-compatible, assuming the existence of non-interactive CCA2 secure commitments, in addition to sub-exponential security of the assumptions listed in the previous bullet.
Here, sub-exponentially CPA-compatible KeyGen refers to any key generation algorithm for which there exist encryption and decryption algorithms that result in a CPA-secure public-key encryption scheme {\em against sub-exponential adversaries}.
This gives a way to perform CCA secure encryption given any public key infrastructure that has been established with only (sub-exponential) CPA security in mind. The resulting CCA encryption makes black-box use of the CPA scheme and all other underlying primitives.

2021

PKC

On the Integer Polynomial Learning with Errors Problem
📺 Abstract

Several recent proposals of efficient public-key encryption are based on variants of the polynomial learning with errors problem (\textsf{PLWE}$^f$) in which the underlying \emph{polynomial} ring $\mZ_q[x]/f$ is replaced with the (related) modular \emph{integer} ring $\mZ_{f(q)}$; the corresponding problem is known as \emph{Integer Polynomial Learning with Errors} (\textsf{I-PLWE}$^f$). Cryptosystems based on \textsf{I-PLWE}$^f$ and its variants can
exploit optimised big-integer arithmetic to achieve good practical performance, as exhibited by the \textsf{ThreeBears} cryptosystem.
Unfortunately, the average-case hardness of \textsf{I-PLWE}$^f$
and its relation to more established lattice problems have to date remained unclear.
We describe the first polynomial-time average-case reductions for the search variant of \textsf{I-PLWE}$^f$, proving its computational equivalence with the search variant of its counterpart problem \textsf{PLWE}$^f$. Our reductions apply to a large class of defining polynomials~$f$. To obtain our results, we employ a careful adaptation of R\'{e}nyi divergence analysis techniques to bound the impact of the integer ring arithmetic carries on the error distributions.
As an application, we present a deterministic public-key cryptosystem over integer rings. Our cryptosystem, which resembles \textsf{ThreeBears}, enjoys one-way (OW-CPA) security provably based on the search variant of~\textsf{I-PLWE}$^f$.

2021

PKC

On the Success Probability of Solving Unique SVP via BKZ
📺 Abstract

As lattice-based key encapsulation, digital signature, and fully homomorphic encryption schemes near standardisation, ever more focus is being directed to the precise estimation of the security of these schemes.
The primal attack reduces key recovery against such schemes to instances of the unique Shortest Vector Problem (uSVP).
Dachman-Soled et al. (Crypto 2020) recently proposed a new approach for fine-grained estimation of the cost of the primal attack when using Progressive BKZ for lattice reduction.
In this paper we review and extend their technique to BKZ 2.0 and provide extensive experimental evidence of its accuracy.
Using this technique we also explain results from previous primal attack experiments by Albrecht et al. (Asiacrypt 2017) where attacks succeeded with smaller than expected block sizes.
Finally, we use our simulators to reestimate the cost of attacking the three lattice KEM finalists of the NIST Post Quantum Standardisation Process.

2021

PKC

Private Set Operations from Oblivious Switching
📺 Abstract

Private set intersection reveals the intersection of two private sets, but many real-world applications require the parties to learn $\textit{only}$ partial information} about the intersection.
In this paper, we introduce a new approach for computing arbitrary functions of the intersection, provided that it is safe to also reveal the cardinality of the intersection. In the most general case, our new protocol provides the participants with secret shares of the intersection, which can be fed into any generic 2PC protocol. Certain computations on the intersection can also be done even more directly and efficiently, avoiding this secret-sharing step. These cases include computing $\textit{only}$ the cardinality of the intersection, or the ``cardinality-sum'' application proposed in Ion $\textit{et al.}$ (ePrint 2017). Compared to the state-of-the-art protocol for computing on the intersection (Pinkas et al., Eurocrypt 2019), our protocol has about $2.5-3\times$ less communication and has faster running time on slower (50Mbps) networks.
Our new techniques can also be used to privately compute the {\em union} of two sets as easily as computing the intersection. Our protocol concretely improves the leading private set union protocol (Kolesnikov et al., Asiacrypt 2020) by a factor of $2-2.5\times$, depending on the network speed. We then show how private set union can be used in a simple way to realize the ``Private-ID'' functionality suggested by Buddhavarapu et al.~(ePrint 2020). Our protocol is significantly faster than the prior Private-ID protocol, especially on fast networks.
All of our protocols are in the two-party setting and are secure against semi-honest adversaries.

2021

PKC

Publicly Verifiable Zero Knowledge from (Collapsing) Blockchains
📺 Abstract

Publicly Verifiable Zero-Knowledge proofs are known to exist only from setup assumptions such as a trusted common reference string or a random oracle. Unfortunately, the former requires a trusted party while the latter does not exist.
Blockchains are distributed systems that already exist and provide certain security properties (under some honest majority assumption), hence, a natural recent research direction has been to use a blockchain as an alternative setup assumption.
In TCC 2017 Goyal and Goyal proposed a construction of a publicly verifiable zero-knowledge (pvZK) proof system for some proof-of-stake blockchains.
The zero-knowledge property of their construction however relies on some
additional and not fully specified assumptions about the current and future behavior of honest blockchain players.
In this paper, we provide several contributions.
First, we show that when using a blockchain to design a provably secure protocol, it is dangerous to rely on demanding additional requirements on behaviors of the blockchain players.
We do so by showing an ``attack of the clones'' whereby a malicious verifier can use a smart contract to slyly (not through bribing) clone capabilities of honest stakeholders and use those to invalidate the zero-knowledge property of the proof system by Goyal and Goyal.
Second, we propose a new publicly verifiable zero-knowledge proof system that
relies on non-interactive commitments and on an assumption on the min-entropy of some blocks appearing on the blockchain.
Third, motivated by the fact that blockchains are a recent innovation and their resilience, in the long run, is still controversial, we introduce the concept of collapsing blockchain, and we prove that the zero-knowledge property of our scheme holds even if the blockchain eventually becomes insecure and all blockchain players eventually become dishonest.

2021

PKC

QCCA-Secure Generic Key Encapsulation Mechanism with Tighter Security in the Quantum Random Oracle Model
📺 Abstract

Xagawa and Yamakawa (PQCrypto 2019) proved the transformation SXY can tightly turn DS secure PKEs into IND-qCCA secure KEMs in the quantum random oracle model (QROM). But transformations such as KC, TPunc that turn PKEs with standard security (OW-CPA or IND-CPA) into DS secure PKEs still suffer from quadratic security loss in the QROM. In this paper, we give a tighter security reduction for the transformation KC that turns OW-CPA secure deterministic PKEs into modified DS secure PKEs in the QROM. We use the Measure-Rewind-Measure One-Way to Hiding Lemma recently introduced by Kuchta et al. (EUROCRYPT 2020) to avoid the square-root advantage loss. Moreover, we extend it to the case that underlying PKEs are not perfectly correct. Combining with other transformations, we finally obtain a generic KEM from any IND-CPA secure PKE. Our security reduction has roughly the same tightness as the result of Kuchta et al. without any other assumptions and we achieve the stronger IND-qCCA security. We also give a similar result for another KEM transformation achieving the same security notion from any OW-CPA secure deterministic PKE.

2021

PKC

Rate-1 Key-Dependent Message Security via Reusable Homomorphic Extractor against Correlated-Source Attacks
📺 Abstract

In this work, we first present general methods to construct information rate-1 PKE that is $\KDM^{(n)}$-secure with respect to \emph{block-affine} functions for any unbounded polynomial $n$.
To achieve this, we propose a new notion of extractor that satisfies \emph{reusability}, \emph{homomorphic}, and \emph{security against correlated-source attacks}, and show how to use this extractor to improve the information rate of the \KDM-secure PKE of Brakerski et al.~(Eurocrypt 18).
Then, we show how to amplify \KDM~security from block-affine function class into general bounded size circuits via a variant of the technique of Applebaum (Eurocrypt 11), achieving better efficiency.
Furthermore, we show how to generalize these approaches to the IBE setting.
Additionally, our PKE and IBE schemes are also leakage resilient, with leakage rates $1-o(1)$ against a slightly smaller yet still general class -- block leakage functions. We can instantiate the required building blocks from $\LWE$ or $\DDH$.

2021

PKC

Revisiting (R)CCA Security and Replay Protection
📺 Abstract

This paper takes a fresh approach to systematically characterizing, comparing, and understanding CCA-type security definitions for public-key encryption (PKE), a topic with a long history. The justification for a concrete security definition X is relative to a benchmark application (e.g. confidential communication): Does the use of a PKE scheme satisfying X imply the security of the application? Because unnecessarily strong definitions may lead to unnecessarily inefficient schemes or unnecessarily strong computational assumptions, security definitions should be as weak as possible, i.e. as close as possible to (but above) the benchmark. Understanding the hierarchy of security definitions, partially ordered by the implication (i.e. at least as strong) relation, is hence important, as is placing the relevant applications as benchmark levels within the hierarchy.
CCA-2 security is apparently the strongest notion, but because it is arguably too strong, Canetti, Krawczyk, and Nielsen (Crypto 2003) proposed the relaxed notions of Replayable CCA security (RCCA) as perhaps the weakest meaningful definition, and they investigated the space between CCA and RCCA security by proposing two versions of Detectable RCCA (d-RCCA) security which are meant to ensure that replays of ciphertexts are either publicly or secretly detectable (and hence preventable).
The contributions of this paper are three-fold. First, following the work of Coretti, Maurer, and Tackmann (Asiacrypt 2013), we formalize the three benchmark applications of PKE that serve as the natural motivation for security notions, namely the construction of certain types of (possibly replay-protected) confidential channels (from an insecure and an authenticated communication channel). Second, we prove that RCCA does not achieve the confidentiality benchmark and, contrary to previous belief, that the proposed d-RCCA notions are not even relaxations of CCA-2 security. Third, we propose the natural security notions corresponding to the three benchmarks: an appropriately strengthened version of RCCA to ensure confidentiality, as well as two notions for capturing public and secret replay detectability.

2021

PKC

Round-optimal Verifiable Oblivious Pseudorandom Functions from Ideal Lattices
📺 Abstract

Verifiable Oblivious Pseudorandom Functions (VOPRFs) are protocols that allow a client to learn verifiable pseudorandom function (PRF) evaluations on inputs of their choice. The PRF evaluations are computed by a server using their own secret key. The security of the protocol prevents both the server from learning anything about the client's input, and likewise the client from learning anything about the server's key. VOPRFs have many applications including password-based authentication, secret-sharing, anonymous authentication and efficient private set intersection. In this work, we construct the first round-optimal (online) VOPRF protocol that retains security from well-known subexponential lattice hardness assumptions. Our protocol requires constructions of non-interactive zero-knowledge arguments of knowledge (NIZKAoK). Using recent developments in the area of post-quantum zero-knowledge arguments of knowledge, we show that our VOPRF may be securely instantiated in the quantum random oracle model. We construct such arguments as extensions of prior work in the area of lattice-based zero-knowledge proof systems.

2021

PKC

Shorter Lattice-Based Zero-Knowledge Proofs via One-Time Commitments
📺 Abstract

There has been a lot of recent progress in constructing efficient zero-knowledge proofs for showing knowledge of an $\vec{\bm{s}}$ with small coefficients satisfying $\bm{A}\vec{\bm{s}}=\vec{\bm{t}}$. For typical parameters, the proof sizes have gone down from several megabytes to a bit under $50$KB (Esgin et al., Asiacrypt 2020). These are now within an order of magnitude of the sizes of lattice-based signatures, which themselves constitute proof systems which demonstrate knowledge of something weaker than the aforementioned equation. One can therefore see that this line of research is approaching optimality. In this paper, we modify a key component of these proofs, as well as apply several other tweaks, to achieve a further reduction of around $30\%$ in the proof output size. We also show that this savings propagates itself when these proofs are used in a general framework to construct more complex protocols.

2021

PKC

Single-to-Multi-Theorem Transformations for Non-Interactive Statistical Zero-Knowledge
📺 Abstract

Non-interactive zero-knowledge proofs or arguments allow a prover to show validity of a statement without further interaction. For non-trivial statements such protocols require a setup assumption in form of a common random or reference string (CRS). Generally, the CRS can only be used for one statement (single-theorem zero-knowledge) such that a fresh CRS would need to be generated for each proof. Fortunately, Feige, Lapidot and Shamir (FOCS 1990) presented a transformation for any non-interactive zero-knowledge proof system that allows the CRS to be reused any polynomial number of times (multi-theorem zero-knowledge). This FLS transformation, however, is only known to work for either computational zero-knowledge or requires a structured, non-uniform common reference string.
In this paper we present FLS-like transformations that work for non-interactive statistical zero-knowledge arguments in the common random string model. They allow to go from single-theorem to multi-theorem zero-knowledge and also preserve soundness, for both properties in the adaptive and non-adaptive case. Our first transformation is based on the general assumption that one-way permutations exist, while our second transformation uses lattice-based assumptions. Additionally, we define different possible soundness notions for non-interactive arguments and discuss their relationships.

2021

PKC

Steel: Composable Hardware-based Stateful and Randomised Functional Encryption
📺 Abstract

Trusted execution enviroments (TEEs) enable secure execution of program on untrusted hosts and cryptographically attest the correctness of outputs. As these are complex systems, it is hard to capture the exact security achieved by protocols employing TEEs. Crucially TEEs are typically employed in multiple protocols at the same time, thus composable security (with global subroutines) is a natural goal for such systems.
We show that under an attested execution setup $\Gatt$ we can realise cryptographic functionalities that are unrealizable in the standard model. We propose a new primitive of Functional Encryption for Stateful and Randomised functionalities (FESR) and an associated protocol, Steel, that realizes it. We show that Steel UC-realises FESR in the universal composition with global subroutines model (TCC 2020). Our work is also a validation of the compositionality of earlier work (Iron}, CCS 2017) capturing (non-stateful) hardware-based functional encryption.
As the existing functionality for attested execution of Pass et al. (Eurocrypt 2017) is too strong for real world use, we propose a weaker functionality that allows the adversary to conduct rollback and forking attacks. We show that the stateful variant of $\Steel$, contrary to the stateless variant corresponding to Iron, is not secure in this setting and propose several mitigation techniques.

2021

PKC

Subversion-Resilient Public Key Encryption with Practical Watchdogs
📺 Abstract

Restoring the security of maliciously implemented cryptosystems has been widely considered challenging due to the fact that the subverted implementation could arbitrarily deviate from the official specification. Achieving security against adversaries that can arbitrarily subvert implementations seems to inherently require trusted component assumptions and/or architectural properties. At ASIACRYPT 2016, Russell et al. proposed a very useful model where a watchdog is used to test and approve individual components of implementation before or during deployment. Such a detection-based strategy has been shown very useful for designing a broad class of cryptographic schemes that are provable resilient to subversion.
We consider Russell et al.'s watchdog model from a practical perspective. We find that the asymptotic definitional framework, while permitting strong positive theoretical results, does not yet provide practical solutions, due to the fact that the running time of a watchdog is only bounded by an abstract polynomial. Hence, in the worst case, the running time of the watchdog might exceed the running time of the adversary, which seems not very practical. We adopt Russell et al.'s watchdog model to the concrete security setting. We design the first subversion-resilient public-key encryption scheme, which additionally allows for extremely efficient watchdogs with only linear running time.
At the core of our construction is a new variant of a combiner for key encapsulation mechanisms (KEMs) by Giacon et al. (PKC'18). We combine this construction with a new subversion-resilient randomness generator that also can be checked by a very efficient watchdog, even in constant time, which could be of independent interest for the design of other subversion-resilient cryptographic schemes with practical watchdogs. Our work thus shows how to apply Russell et al.'s watchdog model to design subversion-resilient cryptography with efficient and very practical watchdogs.

2021

PKC

The Convergence of Slide-type Reductions
📺 Abstract

In this work, we apply the dynamical systems analysis of Hanrot et al. (CRYPTO'11) to a class of lattice block reduction algorithms that includes (natural variants of) slide reduction and block-Rankin reduction. This implies sharper bounds on the polynomial running times (in the query model) for these algorithms and opens the door to faster practical variants of slide reduction. We give heuristic arguments showing that such variants can indeed speed up slide reduction significantly in practice. This is confirmed by experimental evidence, which also shows that our variants are competitive with state-of-the-art reduction algorithms.

2021

PKC

Transferable E-cash: A Cleaner Model and the First Practical Instantiation
📺 Abstract

Transferable e-cash is the most faithful digital analog of physical cash, as it allows users to transfer coins between them in isolation, that is, without interacting with a bank or a ``ledger''. Appropriate protection of user privacy and, at the same time, providing means to trace fraudulent behavior (double-spending of coins) have made instantiating the concept notoriously hard. Baldimtsi et al.\ (PKC'15) gave a first instantiation, but, as it relies on a powerful cryptographic primitive, the scheme is not practical. We also point out a flaw in their scheme.
In this paper we revisit the model for transferable e-cash and propose simpler yet stronger security definitions. We then provide the first concrete construction, based on bilinear groups, give rigorous proofs that it satisfies our model, and analyze its efficiency in detail.

2021

PKC

Two-Party Adaptor Signatures From Identification Schemes
📺 Abstract

Adaptor signatures are a novel cryptographic primitive with important applications for cryptocurrencies. They have been used to construct second layer solutions such as payment channels or cross-currency swaps. The basic idea of an adaptor signature scheme is to tie the signing process to the revelation of a secret value in the sense that, much like a regular signature scheme, an adaptor signature scheme can authenticate messages, but simultaneously leaks a secret to certain parties. Recently, Aumayr et al. provide the first formalization of adaptor signature schemes, and present provably secure constructions from ECDSA and Schnorr signatures. Unfortunately, the formalization and constructions given in this work have two limitations: (1) current schemes are limited to ECDSA and Schnorr signatures, and no generic transformation for constructing adaptor signatures is known; (2) they do not offer support for aggregated two-party signing, which can significantly reduce the blockchain footprint in applications of adaptor signatures.
In this work, we address these two shortcomings. First, we show that signature schemes that are constructed from identification (ID) schemes, which additionally satisfy certain homomorphic properties, can generically be transformed into adaptor signature schemes. We further provide an impossibility result which proves that unique signature schemes (e.g., the BLS scheme) cannot be transformed into an adaptor signature scheme. In addition, we define two-party adaptor signature schemes with aggregatable public keys and show how to instantiate them via a generic transformation from ID-based signature schemes. Finally, we give instantiations of our generic transformations for the Schnorr, Katz-Wang and Guillou-Quisquater signature schemes.

2021

PKC

Two-round n-out-of-n and Multi-Signatures and Trapdoor Commitment from Lattice
📺 Abstract

Although they have been studied for a long time, distributed signature
protocols have garnered renewed interest in recent years in view of novel
applications to topics like blockchains. Most recent works have focused
on distributed versions of ECDSA or variants of Schnorr signatures,
however, and in particular, little attention has been given to
constructions based on post-quantum secure assumptions like the hardness
of lattice problems. A few lattice-based threshold signature and
multi-signature schemes have been proposed in the literature, but they
either rely on hash-and-sign lattice signatures (which tend to be
comparatively inefficient), use expensive generic transformations, or
only come with incomplete security proofs.
In this paper, we construct several lattice-based distributed signing
protocols with low round complexity following the Fiat--Shamir with
Aborts (FSwA) paradigm of Lyubashevsky (Asiacrypt 2009). Our protocols can be seen as distributed
variants of the fast Dilithium-G signature scheme and the full security proof can
be made assuming the hardness of module SIS and LWE problems. A key step to achieving
security (unexplained in some earlier papers) is to prevent the leakage
that can occur when parties abort after their first message---which can
inevitably happen in the Fiat--Shamir with Aborts setting. We manage to
do so using homomorphic commitments.
Exploiting the similarities between FSwA and Schnorr-style signatures,
our approach makes the most of observations from recent advancements in the
discrete log setting, such as Drijvers et al.'s seminal work on two-round multi-signatures (S&P 2019).
In particular, we observe that the use of commitment not only resolves the
subtle issue with aborts, but also makes it possible to realize secure two-round
n-out-of-n distributed signing and multi-signature
in the plain public key model, by equipping the commitment with a trapdoor feature.
The construction of suitable trapdoor commitment from
lattices is a side contribution of this paper.

2021

PKC

Two-server Distributed ORAM with Sublinear Computation and Constant Rounds
📺 Abstract

Distributed ORAM (DORAM) is a multi-server variant of Oblivious RAM. Originally proposed to lower bandwidth, DORAM has recently been of great interest due to its applicability to secure computation in the RAM model, where the circuit complexity and rounds of communication are equally important metrics of efficiency. All prior DORAM constructions either involve linear work per server (e.g., Floram) or logarithmic rounds of communication between servers (e.g., square root ORAM). In this work, we construct the first DORAM schemes in the 2-server, semi-honest setting that simultaneously achieve sublinear server computation and constant rounds of communication. We provide two constant-round constructions, one based on square root ORAM that has O(sqrt{N} log N) local computation and another based on secure computation of a doubly efficient PIR that achieves local computation of O(N^e) for any e > 0 but that allows the servers to distinguish between reads and writes. As a building block in the latter construction, we provide secure computation protocols for evaluation and interpolation of multi- variate polynomials based on the Fast Fourier Transform, which may be of independent interest.

2021

PKC

Universal Proxy Re-Encryption
📺 Abstract

We put forward the notion of universal proxy re-encryption (UPRE). A UPRE scheme enables a proxy to convert a ciphertext under a (delegator) public key of any existing public-key encryption (PKE) scheme into another ciphertext under a (delegatee) public key of any existing PKE scheme (possibly different from the delegator one). The proxy has a re-encryption key generated from the delegator's secret key and the delegatee public key. Thus UPRE generalizes proxy re-encryption by supporting arbitrary PKE schemes and allowing to convert ciphertexts into ones of possibly different PKE schemes. In this work, we
- provide syntax and definitions for both UPRE and a variant we call relaxed UPRE. The relaxed variant means that decryption algorithms for re-encrypted ciphertexts are slightly modified but still only use the original delegatee secret keys for decryption.
- construct a UPRE based on probabilistic indistinguishability obfuscation (PIO). It allows us to re-encrypt ciphertexts polynomially many times.
- construct relaxed UPRE from garbled circuits (GCs). We provide two variants of this construction, one which allows us to re-encrypt ciphertexts polynomially many times, and a second one which satisfies a stronger security requirement but only allows us to re-encrypt ciphertexts a constant number of times.

2021

PKC

Updatable Signatures and Message Authentication Codes
📺 Abstract

Cryptographic objects with updating capabilities have been proposed by Bellare, Goldreich and Goldwasser (CRYPTO'94) under the umbrella of incremental cryptography. They have recently seen increased interest, motivated by theoretical questions (Ananth et al., EC'17) as well as concrete practical motivations (Lehmann et al., EC'18; Groth et al. CRYPTO'18; Klooß et al., EC'19). In this work, the form of updatability we are particularly interested in is that primitives are key-updatable and allow to update ''old'' cryptographic objects, e.g., signatures or message authentication codes, from the ''old'' key to the updated key at the same time without requiring full access to the new key (i.e., only via a so-called update token).
Inspired by the rigorous study of updatable encryption by Lehmann and Tackmann (EC'18) and Boyd et al. (CRYPTO'20), we introduce a definitional framework for updatable signatures (USs) and message authentication codes (UMACs). We discuss several applications demonstrating that such primitives can be useful in practical applications, especially around key rotation in various domains, as well as serve as building blocks in other cryptographic schemes. We then turn to constructions and our focus there is on ones that are secure and practically efficient. In particular, we provide generic constructions from key-homomorphic primitives (signatures and PRFs) as well as direct constructions. This allows us to instantiate these primitives from various assumptions such as DDH or CDH (latter in bilinear groups), or the (R)LWE and the SIS assumptions. As an example, we obtain highly practical US schemes from BLS signatures or UMAC schemes from the Naor-Pinkas-Reingold PRF.

2021

PKC

Verifiable Random Functions with Optimal Tightness
📺 Abstract

Verifiable random functions (VRFs), introduced by Micali,
Rabin and Vadhan (FOCS’99), are the public-key equivalent of pseudo-
random functions. A public verification key and proofs accompanying the
output enable all parties to verify the correctness of the output. How-
ever, all known standard model VRFs have a reduction loss that is much
worse than what one would expect from known optimal constructions of
closely related primitives like unique signatures. We show that:
1. Every security proof for a VRF has to lose a factor of Q, where Q is
the number of adversarial queries. To that end, we extend the meta-
reduction technique of Bader et al. (EUROCRYPT’16) to also cover
VRFs.
2. This raises the question: Is this bound optimal? We answer this
question in the affirmative by presenting the first VRF that achieves
this tightness.
We thus paint a complete picture of the achievability of tight verifiable
random functions: We show that a security loss of Q is unavoidable and
present the first construction that achieves this bound.