International Association
for Cryptologic Research

$\mathbb{Z}^n$ is one of the simplest types of lattices, but the computational problems on its rotations, such as $\mathbb{Z}$SVP and $\mathbb{Z}$LIP, have been of great interest in cryptography. Recent advances have been made in building cryptographic primitives based on these problems, as well as in developing new algorithms for solving them. However, the theoretical complexity of $\mathbb{Z}$SVP and $\mathbb{Z}$LIP are still not well understood.

In this work, we study the problems on rotations of $\mathbb{Z}^n$ by exploiting the symmetry property. We introduce a randomization framework that can be roughly viewed as `applying random automorphisms’ to the output of an oracle, without accessing the automorphism group. Using this framework, we obtain new reduction results for rotations of $\mathbb{Z}^n$. First, we present a reduction from $\mathbb{Z}$LIP to $\mathbb{Z}$SCVP. Here $\mathbb{Z}$SCVP is the problem of finding the shortest characteristic vectors, which is a special case of CVP where the target vector is a deep hole of the lattice. Moreover, we prove a reduction from $\mathbb{Z}$SVP to $\gamma$-$\mathbb{Z}$SVP for any constant $\gamma = O(1)$ in the same dimension, which implies that $\mathbb{Z}$SVP is as hard as its approximate version for any constant approximation factor. Second, we investigate the problem of finding a nontrivial automorphism for a given lattice, which is called LAP. Specifically, we use the randomization framework to show that $\mathbb{Z}$LAP is as hard as $\mathbb{Z}$LIP. We note that our result can be viewed as a $\mathbb{Z}^n$-analogue of Lenstra and Silverberg's result in [JoC2017], but with a different assumption: they assume the $G$-lattice structure, while we assume the access to an oracle that outputs a nontrivial automorphism.

Auerbach, Cash, Fersch, and Kiltz (CRYPTO 2017) initiated the study of memory tightness of reductions in cryptography in addition to the standard tightness related to advantage and running time and showed the importance of memory tightness when the underlying problem can be solved efficiently with large memory. Diemert, Geller, Jager, and Lyu (ASIACRYPT 2021) and Ghoshal, Ghosal, Jaeger, and Tessaro (EUROCRYPT 2022) gave memory-tight proofs for the multi-challenge security of digital signatures in the random oracle model.

This paper studies the memory-tight reductions for _post-quantum_ signature schemes in the _quantum_ random oracle model. Concretely, we show that signature schemes from lossy identification are multi-challenge secure in the quantum random oracle model via memory-tight reductions. Moreover, we show that the signature schemes from lossy identification achieve more enhanced securities considering _quantum_ signing oracles proposed by Boneh and Zhandry (CRYPTO 2013) and Alagic, Majenz, Russel, and Song (EUROCRYPT 2020). We additionally show that signature schemes from preimage-sampleable functions achieve those securities via memory-tight reductions.

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 homomorphic encryption with composable preprocessing. We realize this concept on RLWE encryption schemes, and thanks to the composibility of this technique we are able to preprocess almost all the expensive parts of the homomorphic computation and reuse across multiple executions. As a concrete application, we achieve very efficient matrix vector multiplication that allows us to build HintlessPIR. For a database of size 8GB, HintlessPIR achieves throughput about 3.7GB/s without requiring any client or server state. We additionally formalize the matrix vector multiplication protocol as LinPIR primitive, which may be of independent interests.

In our second construction TensorPIR we reduce the communications of HintlessPIR from square root to cubic root in the database size. For this purpose we extend our HE with preprocessing techniques to composition of key-switching keys and the query expansion algorithm. 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 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.

Masking is a well-known and provably secure countermeasure against side-channel attacks. However, due to additional redundant computations, integrating masking schemes is expensive in terms of performance. The performance overhead of integrating masking countermeasures is heavily influenced by the design choices of a cryptographic algorithm and is often not considered during the design phase. In this work, we deliberate on the effect of design choices on integrating masking techniques into lattice-based cryptography. We select Scabbard, a suite of three lattice-based post-quantum key-encapsulation mechanisms (KEM), namely Florete, Espada, and Sable. We provide arbitrary-order masked implementations of all the constituent KEMs of the Scabbard suite by exploiting their specific design elements. We show that the masked implementations of Florete, Espada, and Sable outperform the masked implementations of Kyber in terms of speed for any order masking. Masked Florete exhibits a $73\%$, $71\%$, and $70\%$ performance improvement over masked Kyber corresponding to the first-, second-, and third-order. Similarly, Espada exhibits $56\%$, $59\%$, and $60\%$ and Sable exhibits $75\%$, $74\%$, and $73\%$ enhanced performance for first-, second-, and third-order masking compared to Kyber respectively. Our results show that the design decisions have a significant impact on the efficiency of integrating masking countermeasures into lattice-based cryptography.

Physical attacks are serious threats to cryptosystems deployed in the real world. In this work, we propose a microarchitectural end-to-end attack methodology on generic lattice-based post-quantum key encapsulation mechanisms to recover the long-term secret key. Our attack targets a critical component of a Fujisaki-Okamoto transform that is used in the construction of almost all lattice-based key encapsulation mechanisms. We demonstrate our attack model on practical schemes such as Kyber and Saber by using Rowhammer. We show that our attack is highly practical and imposes little preconditions on the attacker to succeed. As an additional contribution, we propose an improved version of the plaintext checking oracle, which is used by almost all physical attack strategies on lattice-based key-encapsulation mechanisms. Our improvement reduces the number of queries to the plaintext checking oracle by as much as 39% for Saber and approximately 23% for Kyber768. This can be of independent interest and can also be used to reduce the complexity of other attacks.

We show an explicit construction of an efficiently decodable family of $n$-dimensional lattices whose minimum distances achieve $\Omega(\sqrt{n} / (\log n)^{\varepsilon+o(1)})$ for $\varepsilon>0$. It improves upon the state-of-the-art construction due to Mook-Peikert (IEEE Trans.\ Inf.\ Theory, no. 68(2), 2022) that provides lattices with minimum distances $\Omega(\sqrt{n/ \log n})$. These lattices are construction-D lattices built from a sequence of BCH codes. We show that replacing BCH codes with subfield subcodes of Garcia-Stichtenoth tower codes leads to a better minimum distance. To argue on decodability of the construction, we adapt soft-decision decoding techniques of Koetter-Vardy (IEEE Trans.\ Inf.\ Theory, no.\ 49(11), 2003) to algebraic-geometric codes.

Secure Multiparty Computation (MPC) protocols enable secure evaluation of a circuit by several parties, even in the presence of an adversary who maliciously corrupts all but one of the parties. These MPC protocols are constructed using the well-known secret-sharing-based paradigm (SPDZ and SPD$\mathbb{Z}_{2^k}$), where the protocols ensure security against a malicious adversary by computing Message Authentication Code (MAC) tags on the input shares and then evaluating the circuit with these input shares and tags. However, this tag computation adds a significant runtime overhead, particularly for machine learning (ML) applications with computationally intensive linear layers, such as convolutions and fully connected layers.

To alleviate the tag computation overhead, we introduce CompactTag, a lightweight algorithm for generating MAC tags specifically tailored for linear layers in ML. Linear layer operations in ML, including convolutions, can be transformed into Toeplitz matrix multiplications. For the multiplication of two matrices with dimensions T1 × T2 and T2 × T3 respectively, SPD$\mathbb{Z}_{2^k}$ required O(T1 · T2 · T3) local multiplications for the tag computation. In contrast, CompactTag only requires O(T1 · T2 + T1 · T3 + T2 · T3) local multiplications, resulting in a substantial performance boost for various ML models.

We empirically compared our protocol to the SPD$\mathbb{Z}_{2^k}$ protocol for various ML circuits, including ResNet Training-Inference, Transformer Training-Inference, and VGG16 Training-Inference. SPD$\mathbb{Z}_{2^k}$ dedicated around 30% of its online runtime for tag computation. CompactTag speeds up this tag computation bottleneck by up to 23×, resulting in up to 1.47× total online phase runtime speedups for various ML workloads.

In LWE based cryptosystems, using small (polynomially large) ciphertext modulus improves both efficiency and security. In threshold encryption, one often needs "simulation security": the ability to simulate decryption shares without the secret key. Existing lattice-based threshold encryption schemes provide one or the other but not both. Simulation security has seemed to require superpolynomial flooding noise, and the schemes with polynomial modulus use Rényi divergence based analyses that are sufficient for game-based but not simulation security.

In this work, we give the first construction of simulation-secure lattice-based threshold PKE with polynomially large modulus. The construction itself is relatively standard, but we use an improved analysis, proving that when the ciphertext noise and flooding noise are both Gaussian, simulation is possible even with very small flooding noise. Our modulus is small not just asymptotically but also concretely: this technique gives parameters roughly comparable to those of highly optimized non-threshold schemes like FrodoKEM. As part of our proof, we show that LWE remains hard in the presence of some types of leakage; these results and techniques may also be useful in other contexts where noise flooding is used.

Envelope encryption is a method to encrypt data with two distinct keys in its basic form. Data is first encrypted with a data-encryption key, and then the data-encryption key is encrypted with a key-encryption key. Despite its deployment in major cloud services, as far as we know, envelope encryption has not received any formal treatment. To address this issue, we first formalize the syntax and security requirements of envelope encryption in the symmetric-key setting. Then, we show that it can be constructed by combining encryptment and authenticated encryption with associated data (AEAD). Encryptment is one-time AEAD satisfying that a small part of a ciphertext works as a commitment to the corresponding secret key, message, and associated data. Finally, we show that the security of the generic construction is reduced to the security of the underlying encryptment and AEAD.

We construct a new post-quantum cryptosystem which consists of enhancing CSIDH and similar cryptosystems by adding a full level $N$ structure. We discuss the size of the isogeny graph in this new cryptosystem which consists of components which are acted on by the ray class group for the modulus $N$. We conclude by showing that, if we can efficiently find rational isogenies between elliptic curves, then we can efficiently find rational isogenies that preserve the level structure. We show that one can reduce the group action problem for the ray class group to the group action problem for the ideal class group. This reduces the security of this new cryptosystem to that of the original one

For any prime number $p$, we provide two classes of linear codes with few weights over a $p$-ary alphabet. These codes are based on a well-known generic construction (the defining-set method), stemming on a class of monomials and a class of trinomials over finite fields. The considered monomials are Dembowski-Ostrom monomials $x^{p^{\alpha}+1}$, for a suitable choice of the exponent $\alpha$, so that, when $p>2$ and $n\not\equiv 0 \pmod{4}$, these monomials are planar. We study the properties of such monomials in detail for each integer $n$ greater than two and any prime number $p$. In particular, we show that they are $t$-to-one, where the parameter $t$ depends on the field $\mathbb{F}_{p^n}$ and it takes the values $1, 2$ or $p+1$. Moreover, we give a simple proof of the fact that the functions are $\delta$-uniform with $\delta \in \{1,4,p\}$. This result describes the differential behaviour of these monomials for any $p$ and $n$. For the second class of functions, we consider an affine equivalent trinomial to $x^{p^{\alpha}+1}$, namely, $x^{p^{\alpha}+1}+\lambda x^{p^{\alpha}}+\lambda^{p^{\alpha}}x$ for $\lambda\in \mathbb{F}_{p^n}^*$. We prove that these trinomials satisfy certain regularity properties, which are useful for the specification of linear codes with three or four weights that are different than the monomial construction. These families of codes contain projective codes and optimal codes (with respect to the Griesmer bound). Remarkably, they contain infinite families of self-orthogonal and minimal $p$-ary linear codes for every prime number $p$. Our findings highlight the utility of studying affine equivalent functions, which is often overlooked in this context.

In a traitor tracing system there are $n$ parties and each party holds a secret key. A broadcaster uses an encryption key to encrypt a message $m$ to a ciphertext $c$ so that every party can decrypt~$c$ using its secret key and obtain $m$. Suppose a subset of parties ${\cal J} \subseteq [n]$ combine their secret keys to create a pirate decoder $D(\cdot)$ that can decrypt ciphertexts from the broadcaster. Then it is possible to trace $D$ to at least one member of ${\cal J}$ using only blackbox access to the decoder. Traitor tracing received much attention over the years and multiple schemes have been developed.

In this paper we explore how to do traitor tracing in the context of a threshold decryption scheme. Again, there are $n$ parties and each party has a secret key, but now~$t$ parties are needed to decrypt a ciphertext~$c$, for some $t>1$. If a subset ${\cal J}$ of at least $t$ parties use their secret keys to create a pirate decoder $D(\cdot)$, then it must be possible to trace $D$ to at least one member of ${\cal J}$. This problem has not yet been explored in the literature, however, it has recently become quite important due to the use of encrypted mempools, as we explain in the paper.

We develop the theory of traitor tracing for threshold decryption. 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.

We present a deterministic synchronous protocol for binary Byzantine Agreement against a corrupt minority with adaptive $O(n\cdot f)$ communication complexity, where $f$ is the exact number of corruptions. Our protocol improves the previous best-known deterministic Byzantine Agreement protocol developed by Momose and Ren (DISC 2021), whose communication complexity is quadratic, independent of the exact number of corruptions. Our approach combines two distinct primitives that we introduce and implement with $O(n\cdot f)$ communication, Reliable Voting, and Weak Byzantine Agreement. In Reliable Voting, all honest parties agree on the same value only if all honest parties start with that value, but there is no agreement guarantee in the general case. In Weak Byzantine Agreement, we achieve agreement, but validity requires that the inputs to the protocol satisfy certain properties. Our Weak Byzantine Agreement protocol is an adaptation of the recent Cohen et al. protocol (OPODIS 2022), in which we identify and address various issues.

Active fault injection is a credible threat to real-world digital systems computing on sensitive data. Arguing about security in the presence of faults is non-trivial, and state-of-the-art criteria are overly conservative and lack the ability of fine-grained comparison. However, comparing two alternative implementations for their security is required to find a satisfying compromise between security and performance. In addition, the comparison of alternative fault scenarios can help optimize the implementation of effective countermeasures.

In this work, we use quantitative information flow analysis to establish a vulnerability metric for hardware circuits under fault injection that measures the severity of an attack in terms of information leakage. Potential use cases range from comparing implementations with respect to their vulnerability to specific fault scenarios to optimizing countermeasures. We automate the computation of our metric by integrating it into a state-of-the-art evaluation tool for physical attacks and provide new insights into the security under an active fault attacker.

We propose a new method to encode the problems of optimizing S-box implementations into SAT problems. By considering the inputs and outputs of gates as Boolean functions, the fundamental idea of our method is representing the relationships between these inputs and outputs according to their algebraic normal forms. Based on this method, we present several encoding schemes for optimizing S-box implementations according to various criteria, such as multiplicative complexity, bitslice gate complexity, gate complexity, and circuit depth complexity. The experimental results of these optimization problems show that, compared to the encoding method proposed in FSE 2016, which represents these relationships between Boolean functions by their truth tables, our new encoding method can significantly reduce accelerate the subsequent solving process by 2-100 times for the majority of instances. To further improve the solving efficiency, we propose several strategies to eliminate the redundancy of the derived equation system and break the symmetry of the solution space. We apply our method in the optimizations of the S-boxes used in Ascon, ICEPOLE, PRIMATEs, Keccak/Ketje/Keyak, Joltik/Piccolo, LAC, Minalpher, Prøst, and RECTANGLE. We achieve some new improved implementations and narrow the range of the optimal values for different optimization criteria of these S-boxes.

There has been a recent interest in proposing quantum protocols whose security relies on weaker computational assumptions than their classical counterparts. Importantly to our work, it has been recently shown that public-key encryption (PKE) from one-way functions (OWF) is possible if we consider quantum public keys. Notice that we do not expect classical PKE from OWF given the impossibility results of Impagliazzo and Rudich (STOC'89). However, the distribution of quantum public keys is a challenging task. Therefore, the main question that motivates our work is if quantum PKE from OWF is possible if we have classical public keys. Such protocols are impossible if ciphertexts are also classical, given the impossibility result of Austrin et al. (CRYPTO'22) of quantum enhanced key-agreement (KA) with classical communication. In this paper, we focus on black-box separation for PKE with classical public key and quantum ciphertext from OWF under the polynomial compatibility conjecture, first introduced in Austrin et al.. More precisely, we show the separation when the decryption algorithm of the PKE does not query the OWF. We prove our result by extending the techniques of Austrin et al. and we show an attack for KA in an extended classical communication model where the last message in the protocol can be a quantum state.

This paper presents MQ on my Mind (MQOM), a digital signature scheme based on the difficulty of solving multivariate systems of quadratic equations (MQ problem). MQOM has been submitted to the NIST call for additional post-quantum signature schemes. MQOM relies on the MPC-in-the-Head (MPCitH) paradigm to build a zero-knowledge proof of knowledge (ZK-PoK) for MQ which is then turned into a signature scheme through the Fiat-Shamir heuristic. The underlying MQ problem is non-structured in the sense that the system of quadratic equations defining an instance is drawn uniformly at random. This is one of the hardest and most studied problems from multivariate cryptography which hence constitutes a conservative choice to build candidate post-quantum cryptosystems. For the efficient application of the MPCitH paradigm, we design a specific MPC protocol to verify the solution of an MQ instance. Compared to other multivariate signature schemes based on non-structured MQ instances, MQOM achieves the shortest signatures (6.3-7.8 KB) while keeping very short public keys (few dozen of bytes). Other multivariate signature schemes are based on structured MQ problems (less conservative) which either have large public keys (e.g. UOV) or use recently proposed variants of these MQ problems (e.g. MAYO).

The LowMC family of SPN block cipher proposed by Albrecht et al. was designed specifically for MPC-/FHE-/ZKP-friendly use cases. It is especially used as the underlying block cipher of PICNIC, one of the alternate third-round candidate digital signature algorithms for NIST post-quantum cryptography standardization. The security of PICNIC is highly related to the difficulty of recovering the secret key of LowMC from a given plaintext/ciphertext pair, which raises new challenges for security evaluation under extremely low data complexity.

In this paper, we improve the attacks on LowMC under low data complexity, i.e. 1 or 2 chosen plaintext/ciphertext pairs. For the difference enumeration attack with 2 chosen plaintexts, we propose new algebraic methods to better exploit the nonlinear relation inside the introduced variables based on the attack framework proposed by Liu et al. at ASIACRYPT 2022. With this technique, we significantly extend the number of attack rounds for LowMC with partial nonlinear layers and improve the success probability from around 0.5 to over 0.9. The security margin of some instances can be reduced to only 3/4 rounds. For the key-recovery attack using a single plaintext, we adopt a different linearization strategy to reduce the huge memory consumption caused by the polynomial methods for solving multivariate equation systems. The memory complexity reduces drastically for all 5-/6-round LowMC instances with full nonlinear layers at the sacrifice of a small factor of time complexity. For 5-round LowMC instances with a block size of 129, the memory complexity decreases from $2^{86.46}$ bits to $2^{48.18}$ bits while the time complexity even slightly reduces. Our results indicate that the security for different instances of LowMC under extremely low data complexity still needs further exploration.

Central Bank Digital Currencies refer to the digitization of lifecycle's of central bank money in a way that meets first of a kind requirements for transparency in transaction processing, interoperability with legacy or new world, and resilience that goes beyond the traditional crash fault tolerant model. This comes in addition to legacy system requirements for privacy and regulation compliance, that may differ from central bank to central bank.

This paper introduces a novel framework for Central Bank Digital Currency settlement that outputs a system of record---acting a a trusted source of truth serving interoperation, and dispute resolution/fraud detection needs---, and brings together resilience in the event of parts of the system being compromised, with throughput comparable to crash-fault tolerant systems. Our system further exhibits agnosticity of the exact cryptographic protocol adopted for meeting privacy, compliance and transparency objectives, while ensuring compatibility with the existing protocols in the literature. For the latter, performance is architecturally guaranteed to scale horizontally. We evaluated our system's performance using an enhanced version of Hyperledger Fabric, showing how a throughput of >100K TPS can be supported even with computation-heavy privacy-preserving protocols are in place.

Although we have known about fully homomorphic encryption (FHE) from circular security assumptions for over a decade [Gentry, STOC '09; Brakerski–Vaikuntanathan, FOCS '11], there is still a significant gap in understanding related homomorphic primitives supporting all *unrestricted* polynomial-size computations. One prominent example is attribute-based encryption (ABE). The state-of-the-art constructions, relying on the hardness of learning with errors (LWE) [Gorbunov–Vaikuntanathan–Wee, STOC '13; Boneh et al., Eurocrypt '14], only accommodate circuits up to a *predetermined* depth, akin to leveled homomorphic encryption. In addition, their components (master public key, secret keys, and ciphertexts) have sizes polynomial in the maximum circuit depth. Even in the simpler setting where a single key is published (or a single circuit is involved), the depth dependency persists, showing up in constructions of 1-key ABE and related primitives, including laconic function evaluation (LFE), 1-key functional encryption (FE), and reusable garbling schemes. So far, the only approach of eliminating depth dependency relies on indistinguishability obfuscation. An interesting question that has remained open for over a decade is whether the circular security assumptions enabling FHE can similarly benefit ABE.

In this work, we introduce new lattice-based techniques to overcome the depth-dependency limitations:

- Relying on a circular security assumption, we construct LFE, 1-key FE, 1-key ABE, and reusable garbling schemes capable of evaluating circuits of unbounded depth and size.

- Based on the *evasive circular* LWE assumption, a stronger variant of the recently proposed *evasive* LWE assumption [Wee, Eurocrypt '22; Tsabary, Crypto '22], we construct a full-fledged ABE scheme for circuits of unbounded depth and size.

Our LFE, 1-key FE, and reusable garbling schemes achieve optimal succinctness (up to polynomial factors in the security parameter). Their ciphertexts and input encodings have sizes linear in the input length, while function digest, secret keys, and garbled circuits have constant sizes independent of circuit parameters (for Boolean outputs). In fact, this gives the first constant-size garbled circuits without relying on indistinguishability obfuscation. Our ABE schemes offer short components, with master public key and ciphertext sizes linear in the attribute length and secret key being constant-size.