Committing security has gained considerable attention in the field of authenticated encryption (AE). This can be traced back to a line of recent attacks, which entail that AE schemes used in practice should not only provide confidentiality and authenticity, but also committing security. Roughly speaking, a committing AE scheme guarantees that ciphertexts will decrypt only for one key. Despite the recent research effort in this area, the finalists of the NIST lightweight cryptography standardization process have not been put under consideration yet. We close this gap by providing an analysis of these schemes with respect to their committing security. Despite the structural similarities the finalists exhibit, our results are of a quite heterogeneous nature: We break four of the schemes with effectively no costs, while for two schemes our attacks are costlier, yet still efficient. For the remaining three schemes ISAP, Ascon, and (a slightly modified version of) Schwaemm, we give formal security proofs. Our analysis reveals that sponges are well-suited for building committing AE schemes. Furthermore, we show several negative results when applying the zero-padding method to the NIST finalists.

Digital signature schemes with specific properties have recently seen various real-world applications with a strong emphasis on privacy-enhancing technologies. They have been extensively used to develop anonymous credentials schemes and to achieve an even more comprehensive range of functionalities in the decentralized web. Substantial work has been done to formalize different types of signatures where an allowable set of transformations can be applied to message-signature pairs to obtain new related pairs. Most of the previous work focused on transformations with respect to the message being signed, but little has been done to study what happens when transformations apply to the signing keys. A first attempt to thoroughly formalize such aspects was carried by Derler and Slamanig (ePrint'16, Designs, Codes and Cryptography'19), followed by the more recent efforts by Backes et al. (ASIACRYPT'18) and Eaton et al. (ePrint'23). However, the literature on the topic is vast and different terminology is used across contributions, which makes it difficult to compare related works and understand the range of applications covered by a given construction. In this work, we present a unified view of signatures with randomizable keys and revisit their security properties. We focus on state-of-the-art constructions and related applications,identifying existing challenges. Our systematization allows us to highlight gaps, open questions and directions for future research on signatures with randomizable keys.

The min-hash sketch is a well-known technique for low-communication approximation of the Jaccard index between two input sets. Moreover, there is a folklore belief that min-hash sketch based protocols protect the privacy of the inputs. In this paper, we investigate this folklore to quantify the privacy of the min-hash sketch. We begin our investigation by considering the privacy of min-hash in a centralized setting where the hash functions are chosen by the min-hash functionality and are unknown to the participants. We show that in this case the min-hash output satisfies the standard definition of differential privacy (DP) without any additional noise. This immediately yields a privacy-preserving sublinear-communication semi-honest 2-PC protocol based on FHE where the hash function is evaluated homomorphically. To improve the efficiency of this protocol, we next consider an implementation in the random oracle model. Here, the protocol participants jointly sample public prefixes for domain separation of the random oracle, and locally evaluate the resulting hash functions on their input sets. Unfortunately, we show that in this public hash function setting, the min-hash output is no longer DP. We therefore consider the notion of distributional differential privacy (DDP) introduced by Bassily et al.(FOCS 2013). We show that if the honest party's set has sufficiently high min-entropy then the output of the min-hash functionality achieves DDP, again without any added noise. This yields a more efficient semi-honest two-party protocol in the random oracle model, where parties first locally hash their input sets and then perform a 2PC for comparison. By proving that our protocols satisfy DP and DDP respectively, our results formally confirm and qualify the folklore belief that min-hash based protocols protect the privacy of their inputs.

The threat posed by quantum computing has precipitated an urgent need for post-quantum cryptography. Recently, the post-quantum digital signature draft FIPS 204 has been published, delineating the details of the ML-DSA, which is derived from the CRYSTALS-Dilithium. Despite these advancements, server environments, especially those equipped with GPU devices necessitating high-throughput signing, remain entrenched in classical schemes. A conspicuous void exists in the realm of GPU implementation or server-specific designs for ML-DSA. In this paper, we propose the first server-oriented GPU design tailored for the ML-DSA signing procedure in high-throughput servers. We introduce several innovative theoretical optimizations to bolster performance, including depth-prior sparse ternary polynomial multiplication, the branch elimination method, and the rejection-prioritized checking order. Furthermore, exploiting server-oriented features, we propose a comprehensive GPU hardware design, augmented by a suite of GPU implementation optimizations to further amplify performance. Additionally, we present variants for sampling sparse polynomials, thereby streamlining our design. The deployment of our implementation on both server-grade and commercial GPUs demonstrates significant speedups, ranging from 170.7× to 294.2× against the CPU baseline, and an improvement of up to 60.9% compared to related work, affirming the effectiveness and efficiency of the proposed GPU architecture for ML-DSA signing procedure.

In this paper a reduced set of submatrices for a faster evaluation of the MDS property of a circulant matrix, with entries that are powers of two, is proposed. A proposition is made that under the condition that all entries of a t × t circulant matrix are powers of 2, it is sufficient to check only its 2x2 submatrices in order to evaluate the MDS property in a prime field. Although there is no theoretical proof to support this proposition at this point, the experimental results conducted on a sample of 100 thousand randomly generated matrices indicate that this proposition is true. There are benefits of the proposed MDS test on the efficiency of search methods for the generation of circulant MDS matrices, regardless of the correctness of this proposition. However, if this proposition is correct, its impact on the speed of search methods for circulant MDS matrices will be huge, which will enable generation of MDS matrices of large sizes. Also, a modified version of the make_binary_powers function is presented. Based on this modified function and the proposed MDS test, some examples of efficient 16 x 16 MDS matrices are presented. Also, an examples of efficient 24 x 24 matrices are generated, whose MDS property should be further validated.

We present a construction, called Kirby, for building a variable-input-length pseudorandom function (VIL-PRF) from a $b$-bit permutation. For this construction we prove a tight bound of $b/2$ bits of security on the PRF distinguishing advantage in the random permutation model and in the multi-user setting. Similar to full-state keyed sponge/duplex, it supports full-state absorbing and additionally supports full-state squeezing, while the sponge/duplex can squeeze at most $b-c$ bits per permutation call, for a security level of $c$ bits. This advantage is especially relevant on constrained platforms when using a permutation with small width $b$. For instance, for $b=256$ at equal security strength the squeezing rate of Kirby is twice that of keyed sponge/duplex. This construction could be seen as a generalization of the construction underlying the stream cipher family Salsa. Furthermore, we define a simple mode on top of Kirby that turns it into a deck function with parallel expansion. This is similar to Farfalle but it has a much smaller memory footprint. Furthermore we prove that in the Kirby construction, the leakage of intermediate states does not allow recovering the key or earlier states.

With the increasing scale and complexity of online activities, accountability, as an after-the-fact mechanism, has become an effective complementary approach to ensure system security. Decades of research have delved into the connotation of accountability. They fail, however, to achieve practical accountability of decryption. This paper seeks to address this gap. We consider the scenario where a client (called encryptor, her) encrypts her data and then chooses a delegate (a.k.a. decryptor, him) that stores data for her. If the decryptor initiates an illegitimate decryption on the encrypted data, there is a non-negligible probability that this behavior will be detected, thereby holding the decryptor accountable for his decryption. We make three contributions. First, we review key definitions of accountability known so far. Based on extensive investigations, we formalize new definitions of accountability specifically targeting the decryption process, denoted as accountable decryption, and discuss the (im)possibilities when capturing this concept. We also define the security goals in correspondence. Secondly, we present a novel Trusted Execution Environment(TEE)-assisted solution aligning with definitions. Instead of fully trusting TEE, we take a further step, making TEE work in the "trust, but verify" model where we trust TEE and use its service, but empower users (i.e., decryptors) to detect the potentially compromised state of TEEs. Thirdly, we implement a full-fledged system and conduct a series of evaluations. The results demonstrate that our solution is efficient. Even in a scenario involving $300,000$ log entries, the decryption process concludes in approximately $5.5$ms, and malicious decryptors can be identified within $69$ms.

Lookup arguments allow to prove that the elements of a committed vector come from a (bigger) committed table. They enable novel approaches to reduce the prover complexity of general-purpose zkSNARKs, implementing ``non-arithmetic operations" such as range checks, XOR and AND more efficiently. We extend the notion of lookup arguments along two directions and improve their efficiency: (1) we extend vector lookups to matrix lookups (where we can prove that a committed matrix is a submatrix of a committed table). (2) We consider the notion of zero-knowledge lookup argument that keeps the privacy of both the sub-vector/sub-matrix and the table. (3) We present new zero-knowledge lookup arguments, dubbed cq+, zkcq+ and cq++, more efficient than the state of the art, namely the recent work by Eagen, Fiore and Gabizon named cq. Finally, we give a novel application of zero-knowledge matrix lookup argument to the domain of zero-knowledge decision tree where the model provider releases a commitment to a decision tree and can prove zero-knowledge statistics over the committed data structure. Our scheme based on lookup arguments has succinct verification, prover's time complexity asymptotically better than the state of the art, and is secure in a strong security model where the commitment to the decision tree can be malicious.

Modern block ciphers designed for hardware and masked with Threshold Implementations (TIs) provide provable security against first-order attacks. However, the application of TIs leaves designers to deal with a trade-off between its security and its cost, for example, the process to generate its required random bits. This generation cost comes with an increased overhead in terms of area and latency. Decreasing the number of random bits for the masking allows to reduce the aforementioned overhead. We propose to reduce the randomness to mask the secrets, like the plaintext. For that purpose, we suggest relaxing the requirement for the uniformity of the input shares and reuse randomness for their masking in first-order TIs. We apply our countermeasures to first-order TIs of the Prince and Midori64 ciphers with three shares. Since the designs with non-uniform masks are no longer perfect first-order probing secure, we provide further analysis by calculating bounds on the advantage of a noisy threshold-probing adversary. We then make use of the PROLEAD tool, which implements statistical tests verifying the robust probing security to compare its output with our estimates. Finally, we evaluate the designs on FPGA to highlight the practical security of our solution. We observe that their security holds while requiring four times less randomness over uniform TIs.

Bitcoin demonstrated the possibility of a financial ledger that operates without the need for a trusted central authority. However, concerns persist regarding its security and considerable energy consumption. We assess the consensus protocols that underpin Bitcoin’s functionality, questioning whether they can ensure economically meaningful security while maintaining a permissionless design that allows free entry of operators. We answer this affirmatively by constructing a protocol that guarantees economic security and preserves Bitcoin's permissionless design. This protocol's security does not depend on monetary payments to miners or immense electricity consumption, which our analysis suggests are ineffective. Our framework integrates economic theory with distributed systems theory, and highlights the role of the protocol's user community.

Key Transparency (KT) refers to a public key distribution system with transparency mechanisms proving its correct operation, i.e., proving that it reports consistent values for each user's public key. While prior work on KT systems have offered new designs to tackle this problem, relatively little attention has been paid on the issue of scalability. Indeed, it is not straightforward to actually build a scalable and practical KT system from existing constructions, which may be too complex, inefficient, or non-resilient against machine failures. In this paper, we present OPTIKS, a full featured and optimized KT system that focuses on scalability. Our system is simpler and more performant than prior work, supporting smaller storage overhead while still meeting strong notions of security and privacy. Our design also incorporates a crash-tolerant and scalable server architecture, which we demonstrate by presenting extensive benchmarks. Finally, we address several real-world problems in deploying KT systems that have received limited attention in prior work, including account decommissioning and user-to-device mapping.

This paper presents a semantic characterization of leakage-freeness through timing side-channels for Jasmin programs. Our characterization covers probabilistic Jasmin programs that are not constant-time. In addition, we provide a characterization in terms of probabilistic relational Hoare logic and prove the equivalence between both definitions. We also prove that our new characterizations are compositional and relate our new definitions to existing ones from prior work, which could only be applied to deterministic programs. To provide practical evidence, we use the Jasmin framework to develop a rejection sampling algorithm and provide an EasyCrypt proof that ensures the algorithm's implementation is leakage-free while not being constant-time.

The KHAPE-HMQV protocol is a state-of-the-art highly efficient asymmetric password-authenticated key exchange protocol that provides several desirable security properties, but has the drawback of being vulnerable to quantum adversaries due to its reliance on discrete logarithm-based building blocks: solving a single discrete logarithm allows the attacker to perform an offline dictionary attack and recover the password. We show how to modify KHAPE-HMQV to make the protocol quantum-annoying: a classical adversary who has the additional ability to solve discrete logarithms can only break the protocol by solving a discrete logarithm for each guess of the password. While not fully resistant to attacks by quantum computers, a quantum-annoying protocol could offer some resistance to quantum adversaries for whom discrete logarithms are relatively expensive. Our modification to the protocol is small: encryption (using an ideal cipher) is added to one message. Our analysis uses the same ideal cipher model assumption as the original analysis of KHAPE, and quantum annoyingness is modelled using an extension of the generic group model which gives a classical adversary a discrete logarithm oracle.

In this work we study the problem of minimizing the round complexity for securely evaluating multiparty functionalities while making black-box use of polynomial time assumptions. In Eurocrypt 2016, Garg et al. showed that, assuming all parties have access to a broadcast channel, then at least four rounds of communication are required to securely realize non-trivial functionalities in the plain model. A sequence of works follow-up the result of Garg et al. matching this lower bound under a variety of assumptions. Unfortunately, none of these works make black-box use of the underlying cryptographic primitives. In Crypto 2021, Ishai, Khurana, Sahai, and Srinivasan came closer to matching the four-round lower bound, obtaining a five-round protocol that makes black-box use of oblivious transfer and PKE with pseudorandom public keys. In this work, we show how to realize any input-less functionality (e.g., coin-tossing, generation of key-pairs, and so on) in four rounds while making black-box use of two-round oblivious transfer. As an additional result, we construct the first four-round MPC protocol for generic functionalities that makes black-box use of the underlying primitives, achieving security against non-aborting adversaries. Our protocols are based on a new primitive called list two-party computation. This primitive offers relaxed security compared to the standard notion of secure two-party computation. Despite this relaxation, we argue that this tool suffices for our applications. List two-party computation is of independent interest, as we argue it can also be used for the generation of setups, like oblivious transfer correlated randomness, in three rounds. Prior to our work, generating such a setup required at least four rounds of interactions or a trusted third party.

In 2022, Moriya, Onuki, Aikawa, and Takagi proposed a new framework named generalized Montgomery coordinates to treat one-coordinate type formulas to compute isogenies. This framework generalizes some already known one-coordinate type formulas of elliptic curves. Their result shows that a formula to compute image points under isogenies is unique in the framework of generalized Montogmery coordinates; however, a formula to compute image curves is not unique. Therefore, we have a question: What formula is the most efficient to compute image curves in the framework of generalized Montogmery coordinates? In this paper, we analyze the costs of formulas to compute image curves of $3$-isogenies in the framework of generalized Montgomery coordinates. From our result, the lower bound of the costs is $1\mathbf{M}+1\mathbf{S}$ as a formula whose output and input are in affine coordinates, $2\mathbf{S}$ as an affine formula whose output is projective, and $2\mathbf{M}+3\mathbf{S}$ as a projective formula.

Private information retrieval (PIR) protocols allow clients to access database entries without revealing the queried indices. They have many real-world applications, including privately querying patent-, compromised credential-, and contact databases. While existing PIR protocols that have been implemented perform reasonably well in practice, they all have suboptimal asymptotic complexities. A line of work has explored so-called doubly-efficient PIR (DEPIR), which refers to single-server PIR protocols with optimal asymptotic complexities. Recently, Lin, Mook, and Wichs (STOC 2023) presented the first protocol that completely satisfies the DEPIR constraints and can be rigorously proven secure. Unfortunately, their proposal is purely theoretical in nature. It is even speculated that such protocols are completely impractical, and hence no implementation of any DEPIR protocol exists. In this work, we challenge this assumption. We propose several optimizations for the protocol of Lin, Mook, and Wichs that improve both asymptotic and concrete running times, as well as storage requirements, by orders of magnitude. Furthermore, we implement the resulting protocol and show that for batch queries it outperforms state-of-the-art protocols.

In [1], Sarier presents a practical biometric-based non-transferable credential scheme that maintains the efficiency of the underlying Brands credential. In this paper, we design a new Blockchain-Based E-Voting (BBEV) scheme that combines the system of [1] with encrypted Attribute Based Credentials for a non-transferable code-voting approach to achieve efficient, usable, anonymous, transparent, auditable, verifiable, receipt-free and coercion-resistant remote voting system for small/medium scale elections. To the best of our knowledge, the system is the first user-centric BBEV scheme that depends on the one-show Brands' Credential both for biometric authentication and pre-encrypted ballot generation leading to a natural prevention against double voting. Even though the system is instantiated with Bitcoin Blockchain due to its prevalence and various coin mixers available for anonymity, the system is designed to be generic, i.e. independent of the cryptocurrency. Thus, the new BBEV scheme can be extended to large-scale elections for public Blockchains with higher throughput/cheaper transaction fees. Finally, a cost analysis based on the last USA presidential election data shows that, the new BBEV is advantageous over the traditional one if implemented for three consecutive elections.

Learning with Errors (LWE) is an important problem for post-quantum cryptography (PQC) that underlines the security of several NIST PQC selected algorithms. Several recent papers have claimed improvements on the complexity of so-called dual attacks on LWE. These improvements make dual attacks comparable to or even better than primal attacks in certain parameter regimes. Unfortunately, those improvements rely on a number of untested and hard-to-test statistical assumptions. Furthermore, a recent paper claims that the whole premise of those improvements might be incorrect. The goal of this paper is to improve the situation by proving the correctness of a dual attack without relying on any statistical assumption. Although our attack is greatly simplified compared to the recent ones, it shares many important technical elements with those attacks and can serve as a basis for the analysis of more advanced attacks. We provide some rough estimates on the complexity of our simplified attack on Kyber using a Monte Carlo Markov Chain discrete Gaussian sampler. Our main contribution is to clearly identify a set of parameters under which our attack (and presumably other recent dual attacks) can work. Furthermore, our analysis completely departs from the existing statistics-based analysis and is instead rooted in geometry. We also compare the regime in which our algorithm works to the ``contradictory regime'' of [Ducas and Pulles,2023]. We observe that those two regimes are essentially complementary. Finally, we give a quantum version of our algorithm to speed up the computation. The algorithm is inspired by [Albrecht, and Shen,2022] but is completely formal and does not rely on any heuristics.

Byzantine agreement (BA) asks for a set of parties to reach agreement in an adversarial setting. A central question is how to construct efficient BA protocols that scale well with the number of parties. In particular, the communication complexity is a critical barrier for large-scale implementations. State-of-the-art, scalable BA protocols typically work by sampling a small, unpredictable committee of parties that will send messages in each round. These messages must reach all honest parties, to allow the next round's committee to function. In practice, this is usually accomplished by propagating messages over a gossip network, implemented over a partial communication graph. Most formulations of gossip networks have an ideal guarantee that every message delivered to any honest party will be delivered to every other honest party. Unfortunately, realizing this guarantee necessarily makes the protocol vulnerable to denial-of-service attacks, since an adversary can flood the network with many messages that the protocol must deliver to all parties. In this paper, we make several contributions towards realizing the goal of efficient, scalable byzantine agreement over a gossip network: 1. We define ``gossip with abort,'' a relaxed gossip model that can be efficiently realized with minor modifications to existing gossip protocols, yet allows for significant savings in communication compared to the full point-to-point model. 2. Our protocols work in a graded PKI model, in which honest parties only have partial agreement about the set of participants in the protocol. This model arises naturally in settings without trusted setup, such as the ``permissionless'' setting underlying many blockchain protocols. 3. We construct a new, player-replaceable BA protocol in the graded PKI model. The concrete communication complexity of our protocol, for typical parameter values, is more than 25 times better than the current state-of-the-art BA protocols in the honest-majority setting.

Isogeny-based cryptography is one of the candidates for post-quantum cryptography. One of the benefits of using isogeny-based cryptography is its compactness. In particular, a key exchange scheme SIDH allowed us to use a $4\lambda$-bit prime for the security parameter $\lambda$. Unfortunately, SIDH was broken in 2022 by some studies. After that, some isogeny-based key exchange and public key encryption schemes have been proposed; however, most of these schemes use primes whose sizes are not guaranteed as linearly related to the security parameter $\lambda$. As far as we know, the remaining schemes have not been implemented due to the computation of isogenies of high dimensional abelian varieties, or they need to use a ``weak" curve (\textit{i.e.}, a curve whose endomorphism ring is known) as the starting curve. In this study, we propose a novel compact isogeny-based key encapsulation mechanism named IS-CUBE via Kani's theorem and a $3$-dimensional SIDH diagram. A prime used in IS-CUBE is of the size of about $8\lambda$ bits, and we can use a random supersingular elliptic curve for the starting curve. The public key of IS-CUBE is about $3$ times larger than that of SIKE, and the ciphertext of IS-CUBE is about $4$ times larger than that of SIKE from theoretical estimation. In practice, compared to FESTA, the public key of IS-CUBE is slightly larger and its ciphertext is slightly smaller. The core idea of IS-CUBE comes from the hardness of some already known computational problems and a novel computational problem (the Long Isogeny with Torsion (LIT) problem), which is the problem to compute a hidden isogeny from two given supersingular elliptic curves and information of torsion points of relatively small order.

This paper explores the challenges and potential solutions of implementing the recommended upcoming post-quantum cryptography standards (the CRYSTALS-Dilithium and CRYSTALS-Kyber algorithms) on resource constrained devices. The high computational cost of polynomial operations, fundamental to cryptography based on ideal lattices, presents significant challenges in an efficient implementation. This paper proposes a hardware/software co-design strategy using RISC-V extensions to optimize resource utilization and speed up the number-theoretic transformations (NTTs). The primary contributions include a lightweight custom arithmetic logic unit (ALU), integrated into a 4-stage pipeline 32-bit RISC-V processor. This ALU is tailored towards the NTT computations and supports modular arithmetic as well as NTT butterfly operations. Furthermore, an extension to the RISC-V instruction set is introduced, with ten new instructions accessing the custom ALU to perform the necessary operations. The new instructions reduce the cycle count of the Kyber and Dilithium NTTs by more than 80% compared to optimized assembly, while being more lightweight than other works that exist in the literature.

In the algebraic group model (AGM), an adversary has to return with each group element a linear representation with respect to input group elements. In many groups, it is easy to sample group elements obliviously without knowing such linear representations. Since the AGM does not model this, it can be used to prove the security of spurious knowledge assumptions. We show several well-known zk-SNARKs use such assumptions. We propose AGM with oblivious sampling (AGMOS), an AGM variant where the adversary can access an oracle that allows sampling group elements obliviously from some distribution. We show that AGM and AGMOS are different by studying the family of ``total knowledge-of-exponent'' assumptions, showing that they are all secure in the AGM, but most are not secure in the AGMOS if the DL holds. We show an important separation in the case of the KZG commitment scheme. We show that many known AGM reductions go through also in the AGMOS, assuming a novel falsifiable assumption TOFR. We prove that TOFR is secure in a version of GGM with oblivious sampling.

Zero-Knowledge Proofs (ZKPs), especially Succinct Non-interactive ARguments of Knowledge (SNARKs), have garnered significant attention in modern cryptographic applications. Given the multitude of emerging tools and libraries, assessing their strengths and weaknesses is nuanced and time-consuming. Often, claimed results are generated in isolation, and omissions in details render them irreproducible. The lack of comprehensive benchmarks, guidelines, and support frameworks to navigate the ZKP landscape effectively is a major barrier in the development of ZKP applications. In response to this need, we introduce zk-Bench, the first benchmarking framework and estimator tool designed for performance evaluation of public-key cryptography, with a specific focus on practical assessment of general-purpose ZKP systems. To simplify navigating the complex set of metrics and qualitative properties, we offer a comprehensive open-source evaluation platform, which enables the rigorous dissection and analysis of tools for ZKP development to uncover their trade-offs throughout the entire development stack; from low-level arithmetic libraries, to high-level tools for SNARK development. Using zk-Bench, we (i) collect data across $13$ different elliptic curves implemented across $9$ libraries, (ii) evaluate $5$ tools for ZKP development and (iii) provide a tool for estimating cryptographic protocols, instantiated for the $\mathcal{P}\mathfrak{lon}\mathcal{K}$ proof system, achieving an accuracy of 6 − 32% for ZKP circuits with up to millions of gates. By evaluating zk-Bench for various hardware configurations, we find that certain tools for ZKP development favor compute-optimized hardware, while others benefit from memory-optimized hardware. We observed performance enhancements of up to $40$ % for memory-optimized configurations and $50$ % for compute-optimized configurations, contingent on the specific ZKP development tool utilized.

The security level of a cipher is a key parameter. While general-purpose quantum computers significantly threaten modern symmetric ciphers, other quantum approaches like quantum annealing have been less concerning. However, this paper argues that a quantum annealer specifically designed to attack Grain 128 and Grain 128a ciphers could soon be technologically feasible. Such an annealer would require 5,751 (6,751) qubits and 77,496 (94,708) couplers, with a qubit connectivity of 225 (249). Notably, the forthcoming D-Wave Advantage 2 with Zephyr topology will feature over 7,000 qubits and 60,000 couplers and a qubit connectivity 20. This work also shows that modern stream ciphers like Grain 128 and Grain 128a could be vulnerable to quantum annealing attacks. Although the exact complexity of quantum annealing is unknown, heuristic estimates suggest a \(\sqrt{N}\) exponential advantage over simulated annealing for problems with \(N\) variables. We detail how to transform algebraic attacks on Grain ciphers into the QUBO problem, making our attack potentially more efficient than classical brute-force methods. We also show that applying our attack to rescaled versions of the Grain cipher, namely Grain \( l \) and Grain \( la \) versions, where \( l \) represents the key size, leads to our attack overtaking both brute-force and Grover's attacks for sufficiently large \( l \). This is true, provided that quantum annealing has an exponential advantage over simulated annealing. Specifically, it is sufficient for the time complexity of quantum annealing for problems with \( N \) variables to be $e^{N^{\beta}}$ for any \( \beta < 1 \). Finally, given the general nature of our attack method, all new ciphers should be scrutinized for vulnerability to quantum annealing attacks and at least match the AES cipher in terms of security level.

We provide two improvements to Regev's quantum factoring algorithm (Journal of the ACM 2025), addressing its space efficiency and its noise-tolerance. Our first contribution is to improve the quantum space efficiency of Regev's algorithm while keeping the circuit size the same. Our main result constructs a quantum factoring circuit using $O(n \log n)$ qubits and $O(n^{3/2} \log n)$ gates. We achieve the best of Shor and Regev (upto a logarithmic factor in the space complexity): on the one hand, Regev's circuit requires $O(n^{3/2})$ qubits and $O(n^{3/2} \log n)$ gates, while Shor's circuit requires $O(n^2 \log n)$ gates but only $O(n \log n)$ qubits. As with Regev, to factor an $n$-bit integer $N$, we run our circuit independently $O(\sqrt{n})$ times and apply Regev's classical postprocessing procedure. Our optimization is achieved by implementing efficient and reversible exponentiation with Fibonacci numbers in the exponent, rather than the usual powers of 2, adapting work by Kaliski (arXiv:1711.02491) from the classical reversible setting to the quantum setting. This technique also allows us to perform quantum modular exponentiation that is efficient in both space and size without requiring significant precomputation, a result that may be useful for other quantum algorithms. A key ingredient of our exponentiation implementation is an efficient circuit for a function resembling \emph{in-place} quantum-quantum modular multiplication. This implementation works with only black-box access to any quantum circuit for \emph{out-of-place} modular multiplication, which we believe is yet another result of potentially broader interest. Our second contribution is to show that Regev's classical postprocessing procedure can be modified to tolerate a constant fraction of the quantum circuit runs being corrupted by errors. In contrast, Regev's analysis of his classical postprocessing procedure requires all $O(\sqrt{n})$ runs to be successful. In a nutshell, we achieve this using lattice reduction techniques to detect and filter out corrupt samples.

A succinct non-interactive argument (SNARG) is called holographic if the verifier runs in time sub-linear in the input length when given oracle access to an encoding of the input. We present holographic SNARGs for P and Batch-NP under the learning with errors (LWE) assumption. Our holographic SNARG for P has a verifier that runs in time $\mathsf{poly}(\lambda, \log T, \log n)$ for $T$-time computations and $n$-bit inputs ($\lambda$ is the security parameter), while our holographic SNARG for Batch-NP has a verifier that runs in time $\mathsf{poly}(\lambda, T, \log k)$ for $k$ instances of $T$-time computations. Before this work, constructions with the same asymptotic efficiency were known in the designated-verifier setting or under the sub-exponential hardness of the LWE assumption. We obtain our holographic SNARGs (in the public-verification setting under the polynomial hardness of the LWE assumption) by constructing holographic SNARGs for certain hash computations and then applying known/trivial transformations. As an application, we use our holographic SNARGs to weaken the assumption needed for a recent public-coin 3-round zero-knowledge (ZK) argument [Kiyoshima, CRYPTO 2022]. Specifically, we use our holographic SNARGs to show that a public-coin 3-round ZK argument exists under the same assumptions as the state-of-the-art private-coin 3-round ZK argument [Bitansky et al., STOC 2018].

Electronic voting is one of the most interesting application of modern cryptography, as it involves many innovative tools (such as homomorphic public-key encryption, non-interactive zero-knowledge proofs, and distributed cryptography) to guarantee several a priori contradictory security properties: the integrity of the tally and the privacy of the individual votes. While many efficient solutions exist for honest-but-curious voters, that follow the official procedure but try to learn more than just the public result, preventing attacks from malicious voters is much more complex: when voters may have incentive to send biased ballots, the privacy of the ballots is much harder to satisfy, whereas this is the crucial security property for electronic voting. We present a new technique to prove that an ElGamal ciphertext contains a message from a specific subset (quasi-adaptive NIZK of subset membership), using linearly-homomorphic signatures. The proofs are both quite efficient to generate, allowing the use of low-power devices to vote, and randomizable, which is important for the strong receipt-freeness property. They are well-suited to prevent vote-selling and replay attacks, which are the main threats against the privacy in electronic voting, with security proofs in the generic group model and the random oracle model.

The learning with errors problem (LWE) is one of the most important building blocks for post-quantum cryptography. To better understand the quantum hardness of LWE, it is crucial to explore quantum variants of LWE. To this end, Chen, Liu, and Zhandry [Eurocrypt 2022] defined S|LWE> and C|LWE> problems by encoding the error of LWE samples into quantum amplitudes, and showed efficient quantum algorithms for a few interesting amplitudes. However, algorithms or hardness results of the most interesting amplitude, Gaussian, were not addressed before. In this paper, we show new algorithms, hardness results and applications for S|LWE> and C|LWE> with real Gaussian, Gaussian with linear or quadratic phase terms, and other related amplitudes. Let $n$ be the dimension, $q$ be the modulus of LWE samples. Our main results are 1. There is a $2^{\Theta(\sqrt{n \log q})}$-time algorithm for S|LWE> with Gaussian amplitude with known phase, given $2^{\Theta(\sqrt{n \log q})}$ many quantum samples. The algorithm is modified from Kuperberg's sieve, and in fact works for more general amplitudes as long as the amplitudes and phases are completely known. 2. There is a polynomial time quantum algorithm for solving S|LWE> and C|LWE> for Gaussian with quadratic phase amplitudes, where the sample complexity is as small as $\tilde{O}(n)$. As an application, we give a quantum oblivious LWE sampler where the core quantum sampler requires only quasi-linear sample complexity. This improves upon the previous oblivious LWE sampler given by Debris-Alazard, Fallahpour, Stehlé [STOC 2024], whose core quantum sampler requires $\tilde{O}(nr)$ sample complexity, where $r$ is the standard deviation of the error. 3. There exist polynomial time quantum reductions from standard LWE or worst-case GapSVP to S|LWE> with Gaussian amplitude with small unknown phase, and arbitrarily many samples. Compared to the first two items, the appearance of the unknown phase term places a barrier in designing efficient quantum algorithm for solving standard LWE via S|LWE>.

We show that the key agreement scheme [J. Supercomput., 78:12093-12113, 2022] is flawed. (1) It neglects the representation of a point over an elliptic curve and the basic requirement for bit-wise XOR, which results in a trivial equality. By the equality, an adversary can recover a target device's identity, which means the scheme fails to keep anonymity. (2) It falsely requires that the central server should share its master secret key with each dew server. (3) The specified certificate is almost nonsensical.

Central banks around the world are actively exploring the issuance of retail central bank digital currency (rCBDC), which is widely seen as a key upgrade of the monetary system in the 21st century. However, privacy concerns are the main impediment to rCBDC’s development and roll-out. A central bank as the issuer of rCBDC would typically need to keep a digital ledger to record all the balances and transactions of citizens. These data, when combined with other data, could possibly disclose the spending habits of all citizens. On the one hand, the eligible rights of people to keep their transactions private should be protected, including against central bank surveillance. On the other hand, the central bank needs to ensure that no over-issuance of money or other frauds occur, necessarily demanding a certain form of knowledge of rCBDC transactions to safeguard against malicious users who create counterfeit money or spend duplicated money. This work investigates cryptographic tools and privacy-enhancing technology with the aim to craft a scalable solution to strike a balance between user privacy and transaction verifiability. Different from the current mainstream thought among central banks, it assumes that the central bank maintains a ledger to record all balances and transactions of citizens, but in a concealed form. Specifically, this work focuses on rCBDC architectures based on the unspent transaction output (UTXO) data model and tackles the research problem of preserving a sufficient degree of privacy for UTXO transaction records while allowing the central bank to verify their correctness. While UTXO-based rCBDC architectures were widely tested among major central banks, user privacy is not adequately addressed. The adoption of evolving public keys as pseudonyms to hide the real identities of users is the most advanced privacy design for UTXO-based rCBDC, but it only solves the privacy issue partially. Some information could still be leaked out. This work investigates techniques to address the shortcomings of the pseudonym approach. First, a Pedersen commitment scheme is applied to hide the transaction values of a UTXO transaction while allowing the central bank to verify that no over-issuance of rCBDC has occurred in the transaction. Contrary to the conventional approach, which applies a zero knowledge proof to prove no over-issuance, this work uses a Schnorr signature. This not only reduces the overheads but also enables a non-interactive proof. Then, Coinjoin is applied to aggregate UTXO transactions from different users into one larger UTXO transaction to obfuscate the payer-payee relationship while preserving the correctness of the amount of money flow. This work applies a well-developed notion in database research, namely, k-anonymity, to analyse the privacy guarantee of Coinjoin. Through modelling the transaction traffic by a Poisson process, the trade-off between anonymity and transaction confirmation time of Coinjoin is analysed.

Recently, there has been a surge of interest in the security of authenticated encryption with associated data (AEAD) within the context of key commitment frameworks. Security within this framework ensures that a ciphertext chosen by an adversary does not decrypt to two different sets of key, nonce, and associated data. Despite this increasing interest, the security of several widely deployed AEAD schemes has not been thoroughly examined within this framework. In this work, we assess the key committing security of AEGIS, which emerged as a winner in the Competition for Authenticated Encryption: Security, Applicability, and Robustness (CAESAR). A recent assertion has been made suggesting that there are no known attacks on AEGIS in the key committing settings and AEGIS qualifies as a fully committing AEAD scheme in IETF document. However, contrary to this claim, we propose a novel O(1) attack applicable to all variants of AEGIS. This demonstrates the ability to execute a key committing attack within the FROB game setting, which is known to be one of the most stringent key committing frameworks. This implies that our attacks also hold validity in other, more relaxed frameworks, such as CMT-1, CMT-4, and so forth.

Authenticated encryption is a cryptographic mechanism that allows communicating parties to protect the confidentiality and integrity of message exchanged over a public channel, provided they share a secret key. Some applications require committing authenticated encryption schemes, a security notion that is not covered by the classical requirements of confidentiality and integrity given a secret key. An authenticated encryption (AE) scheme is committing in the strongest sense when it is impossible to generate the same ciphertext for different $(K, [N, ]A, P)$ tuples, with $K$ the key, $N$ the nonce, $A$ the associated data and $P$ the plaintext. In this work, we present authenticated encryption schemes for which we provably reduce their confidentiality, integrity and commitment security to the security of an underlying sponge function. In particular, we instantiate them with SHAKE128 and SHAKE256, offering 128 and 256 bits of security strength and based on the security claim in the SHA-3 standard FIPS 202. Cryptanalysis of reduced-round versions of SHA-3 and SHAKE functions suggests that the number of rounds can be divided by two without noticeable security degeneration, and this had lead to the definition of TurboSHAKE128 and TurboSHAKE256; hence we also instantiate our scheme with these functions, offering the same security strength at twice the speed. The AE schemes we propose therefore have the unique advantages that 1) their security is based on a security claim that has received a large amount of public scrutiny and that 2) it makes use of the standard Keccak-p permutation that has dedicated hardware support on more and more CPUs. In more details, we build two online AE modes on top of a sponge function, in multiple layers. At the bottom layer, we use a variant of the duplex construction, referred to as overwrite duplex or OD for short, that uses an overwrite operation leading to a smaller state footprint. Our first AE mode is nonce-based and built using a variant of the SpongeWrap mode on top of OD, and security-equivalent to it. Our second AE mode makes use of the Deck-BO mode published at Asiacrypt 2022, an online version of a Synthetic Initial Value (SIV) authenticated encryption scheme. It requires a deck function that we build on top of the OD, again security-equivalent to it.

Ethereum is undergoing significant changes to its architecture as it evolves. These changes include its switch to PoS consensus and the introduction of significant infrastructural changes that do not require a change to the core protocol, but that fundamentally affect the way users interact with the network. These changes represent an evolution toward a more modular architecture, in which there exists new exogenous vectors for centralization. This paper builds on previous studies of decentralization of Ethereum to reflect these recent significant changes, and Ethereum’s new modular paradigm.

How could quantum cryptography help us achieve what are not achievable in classical cryptography? In this work we study the classical cryptographic problem that two parties would like to perform secure computations with long outputs. As a basic primitive and example, we first consider the following problem which we call secure function sampling with long outputs: suppose $f:\{0,1\}^n\rightarrow \{0,1\}^m$ is a public, efficient classical function, where $m$ is big; Alice would like to sample $x$ from its domain and sends $f(x)$ to Bob; what Bob knows should be no more than $f(x)$ even if it behaves maliciously. Classical cryptography, like FHE and succinct arguments [Gen09,Kil92,HW15], allows us to achieve this task within communication complexity $O(n+m)$; could we achieve this task with communication complexity independent of $m$? In this work, we first design a quantum cryptographic protocol that achieves secure function sampling with approximate security, within $O(n)$ communication (omitting the dependency on the security parameter and error tolerance). We also prove the classical impossibility using techniques in [HW15], which means that our protocol indeed achieves a type of quantum advantage. Building on the secure function sampling protocol, we further construct protocols for general secure two-party computations [Yao86,GB01] with approximate security, with communication complexity only depending on the input length and the targeted security. In terms of the assumptions, we construct protocols for these problems assuming only the existence of collapsing hash functions [Unr16]; what's more, we also construct a classical-channel protocol for these problems additionally assuming the existence of noisy trapdoor claw-free functions [BCMVV,BKVV].

In the aftermath of the Snowden revelations in 2013, concerns about the integrity and security of cryptographic systems have grown significantly. As adversaries with substantial resources might attempt to subvert cryptographic algorithms and undermine their intended security guarantees, the need for subversion-resilient cryptography has become paramount. Security properties are preserved in subversion-resilient schemes, even if the adversary implements the scheme used in the security experiment. This paper addresses this pressing concern by introducing novel constructions of subversion-resilient signatures and hash functions while proving the subversion-resilience of existing cryptographic primitives. Our main contribution is the first construction of subversion-resilient signatures under complete subversion in the offline watchdog model (with trusted amalgamation) without relying on random oracles. We demonstrate that one-way permutations naturally yield subversion-resilient one-way functions, thereby enabling us to establish the subversion-resilience of Lamport signatures, assuming a trusted comparison is available. Additionally, we develop subversion-resilient target-collision-resistant hash functions using a trusted XOR. By leveraging this approach, we expand the arsenal of cryptographic tools that can withstand potential subversion attacks. Our research builds upon previous work in the offline watchdog model with trusted amalgamation (Russell et al. ASIACRYPT'16) and subversion-resilient pseudo-random functions (Bemmann et al. ACNS'23), culminating in the formal proof of subversion-resilience for the classical Naor-Yung signature construction.

Remote state preparation with verifiability (RSPV) is an important quantum cryptographic primitive [GV19,Zha22]. In this primitive, a client would like to prepare a quantum state (sampled or chosen from a state family) on the server side, such that ideally the client knows its full description, while the server holds and only holds the state itself. In this work we make several contributions on its formulations, constructions and applications. In more detail: - We first work on the definitions and abstract properties of the RSPV problem. We select and compare different variants of definitions [GV19,GMP22,Zha22], and study their basic properties (like composability and amplification). - We also study a closely related question of how to certify the server's operations (instead of solely the states). We introduce a new notion named remote operator application with verifiability (ROAV). We compare this notion with related existing definitions [SW87,MY04,MV21,NZ23], study its abstract properties and leave its concrete constructions for further works. - Building on the abstract properties and existing results [BGKPV23], we construct a series of new RSPV protocols. Our constructions not only simplify existing results [GV19] but also cover new state families, for example, states in the form of $\frac{1}{\sqrt{2}}(|0\rangle|x_0\rangle+|1\rangle|x_1\rangle)$. All these constructions rely only on the existence of weak NTCF [BKVV,AMR22], without additional requirements like the adaptive hardcore bit property [BCMVV,AMR22]. - As a further application, we show that the classical verification of quantum computations (CVQC) problem [ABEM,Mah18] could be constructed from assumptions on group actions [ADMP20]. This is achieved by combining our results on RSPV with group-action-based instantiation of weak NTCF [AMR22], and then with the quantum-gadget-assisted quantum verification protocol [FKD18].

Resource efficiency in blockchain systems remains a pivotal concern in their design. While Ethereum often experiences network congestion, leading to rewarding opportunities for miners through transaction inclusions, a significant amount of block space remains underutilized. Remarkably, instances of entirely unutilized blocks contribute to resource wastage within the Ethereum ecosystem. This study delves into the incentives driving miners to produce empty blocks. We ascertain that the immediate rewards of mining empty blocks often lead miners to forego potential benefits from transaction inclusions. Moreover, our investigation reveals a marked reduction in empty blocks after the Ethereum's Merge, highlighting that the Proof-of-Stake (PoS) consensus mechanism enhances block space efficiency in the blockchain sphere.

We present SCALLOP-HD, a novel group action that builds upon the recent SCALLOP group action introduced by De Feo, Fouotsa, Kutas, Leroux, Merz, Panny and Wesolowski in 2023. While our group action uses the same action of the class group $\textnormal{Cl}(\mathfrak{O})$ on $\mathfrak{O}$-oriented curves where $\mathfrak{O} = \mathbb{Z}[f\sqrt{-1}]$ for a large prime $f$ and small $d$ as SCALLOP, we introduce a different orientation representation: The new representation embeds an endomorphism generating $\mathfrak{O}$ in a $2^e$-isogeny between abelian varieties of dimension $2$ with Kani's Lemma, and this representation comes with a simple algorithm to compute the class group action. Our new approach considerably simplifies the SCALLOP framework, potentially surpassing it in efficiency — a claim supported by preliminary implementation results in SageMath. Additionally, our approach streamlines parameter selection. The new representation allows us to select efficiently a class group $\textnormal{Cl}(\mathfrak{O})$ of smooth order, enabling polynomial-time generation of the lattice of relation, hence enhancing scalability in contrast to SCALLOP. To instantiate our SCALLOP-HD group action, we introduce a new technique to apply Kani's Lemma in dimension 2 with an isogeny diamond obtained from commuting endomorphisms. This method allows one to represent arbitrary endomorphisms with isogenies in dimension 2, and may be of independent interest.

Exclusive OR (XOR), a common Boolean logical operation, is an operation on two factors where the result is true if and only if one operand is true and the other is false. A simple way to state this is ``one or the other, but not both''. Using this logical operation, a text string can be encrypted by applying the XOR operator to every character using a ``key''. If you want to decrypt the output, simply reapply the key and the resulting output will be the original message.

In this paper we present an improved version of the classical RC4 stream cipher. The improvements allow to build lightweight high-performance cryptographically strong random number generator suitable for use in IoT and as a corresponding component of operating systems. The criterion for high performance is both a high speed of generating a stream of random numbers and low overhead costs for adding entropy from physical events to the state of the generator.

The rise of virtual currencies has revolutionized the way we conduct financial transactions. These digital assets, governed by intricate online protocols, have rapidly gained prominence as a viable medium of exchange, offering convenience and security. However, as we delve deeper into the digital realm, a challenge persists: How can we bridge the gap between the virtual and the physical? This paper tackles this challenge by proposing a way to materialize virtual coins and make them physically exchangeable offline at the cost of some plausible trust assumptions.

We show how to apply the BZ methodology (Blind signatures from Zero knowledge) to obtain blind signatures in the Kummer varieties defined by Montgomery curves. We also describe specially-tailored arithmetic algorithms to facilitate their efficient implementation. The result can be proved secure under appropriate assumptions, appears to resist even the ROS attack (to which most elliptic-curve blind signature schemes succumb), and is arguably one of the most efficient among those proposals that offer similar security guarantees.

Anonymous transfer, recently introduced by Agrikola, Couteau and Maier [ACM22] (TCC '22), allows a sender to leak a message anonymously by participating in a public non-anonymous discussion where everyone knows who said what. This opens up the intriguing possibility of using cryptography to ensure strong anonymity guarantees in a seemingly non-anonymous environment. The work of [ACM22] presented a lower bound on anonymous transfer, ruling out constructions with strong anonymity guarantees (where the adversary's advantage in identifying the sender is negligible) against arbitrary polynomial-time adversaries. They also provided a (heuristic) upper bound, giving a scheme with weak anonymity guarantees (the adversary's advantage in identifying the sender is inverse in the number of rounds) against fine-grained adversaries whose run-time is bounded by some fixed polynomial that exceeds the run-time of the honest users. This leaves a large gap between the lower bound and the upper bound, raising the intriguing possibility that one may be able to achieve weak anonymity against arbitrary polynomial time adversaries, or strong anonymity against fine grained adversaries. In this work, we present improved lower bounds on anonymous transfer, that rule out both of the above possibilities: - We rule out the existence of anonymous transfer with any non-trivial anonymity guarantees against general polynomial time adversaries. - Even if we restrict ourselves to fine-grained adversaries whose run-time is essentially equivalent to that of the honest parties, we cannot achieve strong anonymity, or even quantitatively improve over the inverse polynomial anonymity guarantees (heuristically) achieved by [ACM22]. Consequently, constructions of anonymous transfer can only provide security against fine-grained adversaries, and even in that case they achieve at most weak quantitative forms of anonymity.

Sparkle is the first threshold signature scheme in the pairing-free discrete logarithm setting (Crites, Komlo, Maller, Crypto 2023) to be proven secure under adaptive corruptions. However, without using the algebraic group model, Sparkle's proof imposes an undesirable restriction on the adversary. Namely, for a signing threshold $t<n$, the adversary is restricted to corrupt at most $t/2$ parties. In addition, Sparkle's proof relies on a strong one-more assumption. In this work, we propose Twinkle, a new threshold signature scheme in the pairing-free setting which overcomes these limitations. Twinkle is the first pairing-free scheme to have a security proof under up to $t$ adaptive corruptions without relying on the algebraic group model. It is also the first such scheme with a security proof under adaptive corruptions from a well-studied non-interactive assumption, namely, the Decisional Diffie-Hellman (DDH) assumption. We achieve our result in two steps. First, we design a generic scheme based on a linear function that satisfies several abstract properties and prove its adaptive security under a suitable one-more assumption related to this function. In the context of this proof, we also identify a gap in the security proof of Sparkle and develop new techniques to overcome this issue. Second, we give a suitable instantiation of the function for which the corresponding one-more assumption follows from DDH.

Recently a completely new post-quantum digital signature scheme was proposed using the so called ``scrap automorphisms''. The structure is inherently multivariate, but differs significantly from most of the multivariate literature in that it relies on sparsity and rings containing zero divisors. In this article, we derive a complete and total break of Scrap, performing a key recovery in not much more time than verifying a signature. We also generalize the result, breaking unrealistic instances of the scheme for which there is no particularly efficient signing algorithm and key sizes are unmanageable.

The Hybrid Public Key Encryption (HPKE) standard was recently published as RFC 9180 by the Crypto Forum Research Group (CFRG) of the Internet Research Task Force (IRTF). The RFC specifies an efficient public key encryption scheme, combining asymmetric and symmetric cryptographic building blocks. Out of HPKE’s four modes, two have already been formally analyzed by Alwen et al. (EUROCRYPT 2021). This work considers the remaining two modes: HPKE_PSK and HPKE_AuthPSK . Both of them are “pre-shared key” modes that assume the sender and receiver hold a symmetric pre-shared key. We capture the schemes with two new primitives which we call pre-shared key public-key encryption (pskPKE) and pre-shared key authenticated public-key encryption (pskAPKE). We provide formal security models for pskPKE and pskAPKE and prove (via general composition theorems) that the two modes HPKE_PSK and HPKE_AuthPSK offer active security (in the sense of insider privacy and outsider authenticity) under the Gap Diffie-Hellman assumption. We furthermore explore possible post-quantum secure instantiations of the HPKE standard and propose new solutions based on lattices and isogenies. Moreover, we show how HPKE’s basic HPKEPSK and HPKEAuthPSK modes can be used black-box in a simple way to build actively secure post-quantum/classic-hybrid (authenticated) encryption schemes. Our hybrid constructions provide a cheap and easy path towards a practical post-quantum secure drop-in replacement for the basic HPKE modes HPKE_Base and HPKE_Auth .

We present a constant-round deterministic broadcast protocol against timid adversaries in the synchronous authenticated setting. A timid adversary is a game-theoretically rational adversary who tries to attack the protocol but prefers the actions to be undetected. Our protocol is secure against such an adversary corrupting t out of n parties for any t < n. The round complexity is 5 for timid adversaries and is at most t + 5 for general malicious adversaries. Our results demonstrate that game-theoretic rationality enables us to circumvent the impossibility of constructing constant-round deterministic broadcast protocols for t = ω(1).

The intuitions behind succinct proof systems are often difficult to separate from some of the deep cryptographic techniques that are used in their construction. In this paper, we show that, using some simple abstractions, a number of commonly-used tools used in the construction of succinct proof systems may be viewed as basic consequences of linear algebra over finite fields. We introduce notation which considerably simplifies these constructions and slowly build a toolkit of useful techniques that can be combined to create different protocols. We also show a simple 'probabilistic calculus' which specifies how to combine these tools and bounds on their resulting security. To show the power of these abstractions and toolkit, we give a short proof of the security of the FRI protocol. Along the way, we discuss some natural generalizations of protocols in the literature and propose a conjecture related to proximity testing using linear error-correcting codes that is of independent interest.

We describe an adaptation of Schnorr's signature to the lattice setting, which relies on Gaussian convolution rather than flooding or rejection sampling as previous approaches. It does not involve any abort, can be proved secure in the ROM and QROM using existing analyses of the Fiat-Shamir transform, and enjoys smaller signature sizes (both asymptotically and for concrete security levels).

We introduce a new variant of malicious obfuscation. Our formalism is incomparable to the existing definitions by Canetti and Varia (TCC 2010), Canetti et al. (EUROCRYPT 2022) and Badrinarayanan et al. (ASIACRYPT 2016). We show that this concept is natural and applicable to obfuscation-as-a-service platforms. We next define a new notion called auditable obfuscation which provides security against malicious obfuscation. Finally, we construct a proof of concept of the developed notions based on well-studied theoretical obfuscation proposals.

We use tropical algebras as platforms for a very efficient digital signature protocol. Security relies on computational hardness of factoring one-variable tropical polynomials; this problem is known to be NP-hard. We also offer countermeasures against recent attacks by Panny and by Brown and Monico.

Recent advancements in post-quantum cryptography have highlighted signature schemes based on the MPC-in-the-Head (MPCitH) framework due to their reliance only on the one-way function of the underlying primitive. This reliance offers a diverse set of assumptions regarding the difficulty of post-quantum cryptographic problems. In this context, Kim et al. proposed $\mathsf{AIM}$, an MPCitH-compatible one-way function. This function is distinguished by its large algebraic S-boxes and parallel architecture, contributing to the reduced size of signatures, as presented at CCS 2023. However, $\mathsf{AIM}$ has faced several cryptanalytic challenges, which have potentially weakened its security by up to 15 bits. This paper provides a comprehensive overview of these cryptanalytic methods and proposes $\mathsf{AIM2}$, an enhanced version that addresses these identified vulnerabilities. We conduct an extensive analysis of its resilience to algebraic attacks and detail the modifications in its efficiency.

Auction and voting schemes play a crucial role in the Web3 ecosystem. Yet currently deployed implementations either lack privacy or require at least two rounds, hindering usability and security. We introduce Cicada, a general framework for using linearly homomorphic time-lock puzzles (HTLPs) to enable provably secure, non-interactive private auction and voting protocols. We instantiate our framework with an efficient new HTLP construction and novel packing techniques that enable succinct ballot correctness proofs independent of the number of candidates. We demonstrate the practicality of our approach by implementing our protocols for the Ethereum Virtual Machine (EVM).

This work introduces the notion of naysayer proofs. We observe that in numerous (zero-knowledge) proof systems, it is significantly more efficient for the verifier to be convinced by a so-called naysayer that a false proof is invalid than it is to check that a genuine proof is valid. We show that every NP language has constant-size and constant-time naysayer proofs. We also show practical constructions for several example proof systems, including FRI polynomial commitments, post-quantum secure digital signatures, and verifiable shuffles. Naysayer proofs enable an interesting new optimistic verification mode potentially suitable for resource-constrained verifiers, such as smart contracts.

The NTRU assumption provides one of the most prominent problems on which to base post-quantum cryptography. Because of the efficiency and security of NTRU-style schemes, structured variants have been proposed, using modules. In this work, we create a structured form of NTRU using lattices obtained from orders in cyclic division algebras of index 2, that is, from quaternion algebras. We present a public-key encryption scheme, and show that its public keys are statistically close to uniform. We then prove IND-CPA security of a variant of our scheme when the discriminant of the quaternion algebra is not too large, assuming the hardness of Learning with Errors in cyclic division algebras.

Zero-knowledge proof or argument systems for generic NP statements (such as circuit satisfiability) have typically been instantiated with cryptographic commitment schemes; this implies that the security of the proof system (e.g., computational or statistical) depends on that of the chosen commitment scheme. The MPC-in-the-Head paradigm (Ishai et al., JoC 2009) uses the same approach to construct zero-knowledge systems from the simulated execution of secure multiparty computation protocols. This paper presents a novel method to construct zero-knowledge protocols which takes advantage of the unique properties of MPC-in-the-Head and replaces commitments with an oblivious transfer protocol. The security of the new construction is proven in the Universal Composability framework of security and suitable choices of oblivious transfer protocols are discussed together with their implications on the security properties and computational efficiency of the zero-knowledge system.

Recent works on lattice-based extractable polynomial commitments can be grouped into two classes: (i) non-interactive constructions that stem from the functional commitment by Albrecht, Cini, Lai, Malavolta and Thyagarajan (CRYPTO 2022), and (ii) lattice adaptations of the Bulletproofs protocol (S&P 2018). The former class enjoys security in the standard model, albeit a knowledge assumption is desired. In contrast, Bulletproof-like protocols can be made secure under falsifiable assumptions, but due to technical limitations regarding subtractive sets, they only offer inverse-polynomial soundness error. This issue becomes particularly problematic when transforming these protocols to the non-interactive setting using the Fiat-Shamir paradigm. In this work, we propose the first lattice-based non-interactive extractable polynomial commitment scheme which achieves polylogarithmic proof size and verifier runtime (in the length of the committed message) under standard assumptions. At the core of our work lies a new tree-based commitment scheme, along with an efficient proof of polynomial evaluation inspired by FRI (ICALP 2018). Natively, the construction is secure under a “multi-instance version” of the Power-Ring BASIS assumption (Eprint 2023/846). We then fully reduce security to the Module-SIS assumption by introducing several re-randomisation techniques which can be of independent interest.

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

Fully homomorphic encryption (FHE) can perform computations on encrypted data, allowing us to analyze sensitive data without losing its security. The main issue for FHE is its lower performance, especially for high-precision computations, compared to calculations on plaintext data. Making FHE viable for practical use requires both algorithmic improvements and hardware acceleration. Recently, Klemsa and Önen (CODASPY'22) presented fast homomorphic algorithms for high-precision integers, including addition, multiplication and some fundamental functions, by utilizing a technique called redundant representation. Their algorithms were applied on TFHE, which was proposed by Chillotti et al. (Asiacrypt'16). In this paper, we further accelerate this method by extending their algorithms to multithreaded environments. The experimental results show that our approach performs 128-bit addition in 0.41 seconds, 32-bit multiplication in 4.3 seconds, and 128-bit Max and ReLU functions in 1.4 seconds using a Tesla V100S server.

We study verifiable outsourcing of computation in a model where the verifier has black-box access to the function being computed. We introduce the problem of oracle-aided batch verification of computation (OBVC) for a function class $\mathcal{F}$. This allows a verifier to efficiently verify the correctness of any $f \in \mathcal{F}$ evaluated on a batch of $n$ instances $x_1, \ldots, x_n$, while only making $\lambda$ calls to an oracle for $f$ (along with $O(n \lambda)$ calls to low-complexity helper oracles), for security parameter $\lambda$. We obtain the following positive and negative results: 1.) We build OBVC protocols for the class of all functions that admit random-self-reductions. Some of our protocols rely on homomorphic encryption schemes. 2.) We show that there cannot exist OBVC schemes for the class of all functions mapping $\lambda$-bit inputs to $\lambda$-bit outputs, for any $n = \mathsf{poly}(\lambda)$.

The well-defined information leakage of Encrypted Search Algorithms (ESAs) is predominantly analyzed by crafting so-called leakage attacks. These attacks utilize adversarially known auxiliary data and the observed leakage to attack an ESA instance built on a user's data. Known-data attacks require the auxiliary data to be a subset of the user's data. In contrast, sampled-data attacks merely rely on auxiliary data that is, in some sense, statistically close to the user's data and hence reflect a much more realistic attack scenario where the auxiliary data stems from a publicly available data source instead of the private user's data. Unfortunately, it is unclear what "statistically close" means in the context of sampled-data attacks. This leaves open how to measure whether data is close enough for attacks to become a considerable threat. Furthermore, sampled-data attacks have so far not been evaluated in the more realistic attack scenario where the auxiliary data stems from a source different to the one emulating the user's data. Instead, auxiliary and user data have been emulated with data from one source being split into distinct training and testing sets. This leaves open whether and how well attacks work in the mentioned attack scenario with data from different sources. In this work, we address these open questions by providing a measurable metric for statistical closeness in encrypted keyword search. Using real-world data, we show a clear exponential relation between our metric and attack performance. We uncover new data that are intuitively similar yet stem from different sources. We discover that said data are not "close enough" for sampled-data attacks to perform well. Furthermore, we provide a re-evaluation of sampled-data keyword attacks with varying evaluation parameters and uncover that some evaluation choices can significantly affect evaluation results.

An hard homogeneous space (HHS) is a finite group acting on a set with the group action being hard to invert and the set lacking any algebraic structure. As such HHS could potentially replace finite groups where the discrete logarithm is hard for building cryptographic primitives and protocols in a post-quantum world. Threshold HHS-based primitives typically require parties to compute the group action of a secret-shared input on a public set element. On one hand this could be done through generic MPC techniques, although they incur in prohibitive costs due to the high complexity of circuits evaluating group actions known to date. On the other hand round-robin protocols only require black box usage of the HHS. However these are highly sequential procedures, taking as many rounds as parties involved. The high round complexity appears to be inherent due the lack of homomorphic properties in HHS, yet no lower bounds were known so far. In this work we formally show that round-robin protocols are optimal. In other words, any at least passively secure distributed computation of a group action making black-box use of an HHS must take a number of rounds greater or equal to the threshold parameter. We furthermore study fair protocols in which all users receive the output in the same round (unlike plain round-robin), and prove communication and computation lower bounds of $\Omega(n \log_2 n)$ for $n$ parties. Our results are proven in Shoup's Generic Action Model (GAM), and hold regardless of the underlying computational assumptions.

State-machine replication (SMR) allows a {deterministic} state machine to be replicated across a set of replicas and handle clients' requests as a single machine. Most existing SMR protocols are leader-based requiring a leader to order requests and coordinate the protocol. This design places a disproportionately high load on the leader, inevitably impairing the scalability. If the leader fails, a complex and bug-prone fail-over protocol is needed to switch to a new leader. An adversary can also exploit the fail-over protocol to slow down the protocol. In this paper, we propose a crash-fault tolerant SMR named Aurora, with the following properties: • Leaderless: it does not require a leader, hence completely get rid of the fail-over protocol. • Scalable: it can scale up to 11 replicas. • Robust: it behaves well even under a poor network connection. We provide a full-fledged implementation of Aurora and systematically evaluate its performance. Our benchmark results show that Aurora achieves a throughput of around two million Transactions Per Second (TPS), up to 8.7X higher than the state-of-the-art leaderless SMR.

A prevalent issue in the residue number system (RNS) variant of the Cheon-Kim-Kim-Song (CKKS) homomorphic encryption (HE) scheme is the challenge of efficiently achieving high precision on hardware architectures with a fixed, yet smaller, word-size of bit-length $W$, especially when the scaling factor satisfies $\log\Delta > W$. In this work, we introduce an efficient solution termed composite scaling. In this approach, we group multiple RNS primes as $q_\ell:= \prod_{j=0}^{t-1} q_{\ell,j}$ such that $\log q_{\ell,j} < W$ for $0\le j < t$, and use each composite $q_\ell$ in the rescaling procedure as $\mathsf{ct}\mapsto \lfloor \mathsf{ct} / q_\ell\rceil$. Here, the number of primes, denoted by $t$, is termed the composition degree. This strategy contrasts the traditional rescaling method in RNS-CKKS, where each $q_\ell$ is chosen as a single $\log\Delta$-bit prime, a method we designate as single scaling. To achieve higher precision in single scaling, where $\log\Delta > W$, one would either need a novel hardware architecture with word size $W' > \log\Delta$ or would have to resort to relatively inefficient solutions rooted in multi-precision arithmetic. This problem, however, doesn't arise in composite scaling. In the composite scaling approach, the larger the composition degree $t$, the greater the precision attainable with RNS-CKKS across an extensive range of secure parameters tailored for workload deployment. We have integrated composite scaling RNS-CKKS into both OpenFHE and Lattigo libraries. This integration was achieved via a concrete implementation of the method and its application to the most up-to-date workloads, specifically, logistic regression training and convolutional neural network inference. Our experiments demonstrate that single and composite scaling approaches are functionally equivalent, both theoretically and practically.

Blockchain users who submit transactions through private pools are guaranteed pre-trade privacy but face execution risk. We argue that private pools serve the intended purpose of eliminating frontrunning risk, only if such risk is high. Otherwise, some validators may decide to avoid monitoring private pools to preserve rents extracted from frontrunning bots. Private pools intensify the execution arms race for bots, thus decreasing their payoffs {and increasing validators' rents}. The private pool option reduces blockspace allocative inefficiencies and raises aggregate welfare.

Dual attacks aiming at decoding generic linear codes have been found recently to outperform for certain parameters information set decoding techniques which have been for $60$ years the dominant tool for solving this problem and choosing the parameters of code-based cryptosystems. However, the analysis of the complexity of these dual attacks relies on some unproven assumptions that are not even fully backed up with experimental evidence. These dual attacks can actually be viewed as the code-based analogue of dual attacks in lattice based cryptography. Here too, dual attacks have been found out those past years to be strong competitors to primal attacks and a controversy has emerged whether similar heuristics made for instance on the independence of certain random variables really hold. We will show that the dual attacks in coding theory can be studied by providing in a first step a simple alternative expression of the fundamental quantity used in these dual attacks. We then show that this expression can be studied without relying on independence assumptions whatsoever. This study leads us to discover that there is indeed a problem with the latest and most powerful dual attack introduced in the recent Asiacrypt 2022 paper "Statistical decoding 2.0: Reducing Decoding to LPN" (RLPN) and that for the parameters chosen in this algorithm there are indeed false candidates which are produced and which are not predicted by the analysis provided there which relies on independence assumptions. We then suggest a slight modification of this algorithm consisting in a further verification step, analyze it thoroughly, provide experimental evidence that our analysis is accurate and show that the complexity claims made in RLPN are indeed valid for this modified algorithm. This approach provides a simple methodology for studying rigorously dual attacks which could turn out to be useful for further developing the subject.

The identity-based signature, initially introduced by Shamir [Sha84], plays a fundamental role in the domain of identity-based cryptography. It offers the capability to generate a signature on a message, allowing any user to verify the authenticity of the signature using the signer's identifier information (e.g., an email address), instead of relying on a public key stored in a digital certificate. Another significant concept in practical applications is the threshold signature, which serves as a valuable tool for distributing the signing authority. The notion of an identity-based threshold signature scheme pertains to the distribution of a secret key associated with a specific identity among multiple entities, rather than depending on a master secret key generated by a public key generator. This approach enables a qualified group of participants to jointly engage in the signing process. In this paper, we present two identity-based threshold signature schemes based on isogenies, each of which addresses a different aspect of security. The first scheme prioritizes efficiency but offers security with abort, while the second scheme focuses on robustness. Both schemes ensure active security in the quantum random oracle model. To build these identity-based threshold signatures, we begin by modifying the identity-based signature scheme proposed by Shaw and Dutta [SD21], to accommodate the CSI-SharK signature scheme. Subsequently, we leverage the resulting identity-based signature and build two threshold schemes within the CSIDH (Commutative Supersingular Isogeny Diffie-Hellman) framework. Our proposed identity-based threshold signatures are designed based on CSI-SharK and can be easily adapted with minimal adjustments to function with CSI-FiSh.

Vectorial dual-bent functions have recently attracted some researchers' interest as they play a significant role in constructing partial difference sets, association schemes, bent partitions and linear codes. In this paper, we further study vectorial dual-bent functions $F: V_{n}^{(p)}\rightarrow V_{m}^{(p)}$, where $2\leq m \leq \frac{n}{2}$, $V_{n}^{(p)}$ denotes an $n$-dimensional vector space over the prime field $\mathbb{F}_{p}$. We give new characterizations of certain vectorial dual-bent functions (called vectorial dual-bent functions with Condition A) in terms of amorphic association schemes, linear codes and generalized Hadamard matrices, respectively. When $p=2$, we characterize vectorial dual-bent functions with Condition A in terms of bent partitions. Furthermore, we characterize certain bent partitions in terms of amorphic association schemes, linear codes and generalized Hadamard matrices, respectively. For general vectorial dual-bent functions $F: V_{n}^{(p)}\rightarrow V_{m}^{(p)}$ with $F(0)=0, F(x)=F(-x)$ and $2\leq m \leq \frac{n}{2}$, we give a necessary and sufficient condition on constructing association schemes. Based on such a result, more association schemes are constructed from vectorial dual-bent functions.

This paper analyses the Secure Remote Password Protocol (SRP) in the context of provable security. SRP is an asymmetric Password-Authenticated Key Exchange (aPAKE) protocol introduced in 1998. It allows a client to establish a shared cryptographic key with a server based on a password of potentially low entropy. Although the protocol was part of several standardization efforts, and is deployed in numerous commercial applications such as Apple Homekit, 1Password or Telegram, it still lacks a formal proof of security. This is mainly due to some of the protocol's design choices which were implemented to circumvent patent issues. Our paper gives the first security analysis of SRP in the universal composability (UC) framework. We show that SRP is UC-secure against passive eavesdropping attacks under the standard CDH assumption in the random oracle model. We then highlight a major protocol change designed to thwart active attacks and propose a new assumption -- the additive Simultaneous Diffie Hellman (aSDH) assumption -- under which we can guarantee security in the presence of an active attacker. Using this new assumption as well as the Gap CDH assumption, we prove security of the SRP protocol against active attacks. Our proof is in the "Angel-based UC framework", a relaxation of the UC framework which gives all parties access to an oracle with super-polynomial power. In our proof, we assume that all parties have access to a DDH oracle (limited to finite fields). We further discuss the plausibility of this assumption and which level of security can be shown without it.

The support minors method has become indispensable to cryptanalysts in attacking various post-quantum cryptosystems in the areas of multivariate cryptography and rank-based cryptography. The complexity analysis for support minors minrank calculations is a bit messy, with no closed form for the Hilbert series of the ideal generated by the support minors equations (or, more correctly, for the quotient of the polynomial ring by this ideal). In this article, we provide a generating series whose coefficients are the Hilbert Series of related MinRank ideals. This simple series therefore reflects and relates the structure of all support minors ideals. Its simplicity also makes it practically useful in computing the complexity of support minors instances.

Distributing the Elliptic Curve Digital Signature Algorithm (ECDSA) has received increased attention in past years due to the wide range of applications that can benefit from this, particularly after the popularity that the blockchain technology has gained. Many schemes have been proposed in the literature to improve the efficiency of multi- party ECDSA. Most of these schemes either require heavy homomorphic encryption computation or multiple executions of a functionality that transforms Multiplicative shares to Additive shares (MtA). Xue et al. (CCS 2021) proposed a 2-party ECDSA protocol secure against mali- cious adversaries and only requires one execution of MtA, with an online phase that consists of only one party sending one field element to the other party with a computational overhead dominated by the verifica- tion step of the signature scheme. We propose a novel protocol, based on the assumption that the Computational Diffie-Hellman problem is hard, that offers the same online phase performance as the protocol of Xue et al., but improves the offline phase by reducing the computational cost by one elliptic curve multiplication and the communication cost by two field elements. To the best of our knowledge, our protocol offers the most efficient offline phase for a two-party ECDSA protocol with such an efficient online phase.

Blockchain auction plays an important role in the price discovery of digital assets (e.g. NFTs). However, despite their importance, implementing auctions directly on blockchains such as Ethereum incurs scalability issues. In particular, the on-chain transactions scale poorly with the number of bidders, leading to network congestion, increased transaction fees, and slower transaction confirmation time. This lack of scalability significantly hampers the ability of the system to handle large-scale, high-speed auctions that are common in today's economy. In this work, we build a protocol where an auctioneer can conduct sealed bid auctions that run entirely off-chain when parties behave honestly, and in the event that $k$ bidders deviate (e.g., do not open their sealed bid) from an $n$-party auction protocol, then the on-chain complexity is only $O(k)$. This improves over existing solutions that require $O(n)$ on-chain complexity, even if a single bidder deviates from the protocol. In the event of a malicious auctioneer, our protocol still guarantees that the auction will successfully terminate. We implement our protocol and show that it offers significant efficiency improvements compared to existing on-chain solutions. Our use of zkSnark to achieve scalability also ensures that the on-chain contract and other participants do not acquire any information about the bidders' identities and their respective bids, except for the winner and the winning bid amount.

Ascon, a family of algorithms that supports hashing and authenticated encryption, is the winner of the NIST Lightweight Cryptography Project. In this paper, we propose an improved preimage attack against 2-round Ascon-XOF-64 with a complexity of $2^{32}$ via a better guessing strategy. Furthermore, in order to find a good guessing strategy efficiently, we build a MILP model and successfully extend the attack to 3 rounds. The time complexity is $2^{53}$ when $IV=0$, while for the real $IV$, the attack still works and the time complexity is $2^{51}$. Additionally, we also investigate the resistance of Ascon-HASH against collision attacks. We introduce the linearization of the inverse of S-boxes and then propose a practical free-start collision attack on 3-round Ascon-HASH using a differential trail searched dedicatedly. Furthermore, We construct different 2-round connectors using the linearization of the inverse of S-boxes and successfully extend the collision attack to 4 rounds and 5 rounds of Ascon-HASH with complexities of $2^{21}$ and $2^{41}$ respectively. Although our attacks do not compromise the security of the full 12-round Ascon-XOF and Ascon-HASH, they provide some insights into Ascon's security.

We present a cryptographic string commitment scheme that is computationally hiding and binding based on (modular) subset sum problems. It is believed that these NP-complete problems provide post-quantum security contrary to the number theory assumptions currently used in cryptography. Using techniques recently introduced by Feneuil, Maire, Rivain and Vergnaud, this simple commitment scheme enables an efficient zero-knowledge proof of knowledge for committed values as well as proofs showing Boolean relations amongst the committed bits. In particular, one can prove that committed bits $m_0, m_1, ..., m_\ell$ satisfy $m_0 = C(m_1, ..., m_\ell)$ for any Boolean circuit $C$ (without revealing any information on those bits). The proof system achieves good communication and computational complexity since for a security parameter $\lambda$, the protocol's communication complexity is $\tilde{O}(|C| \lambda + \lambda^2)$ (compared to $\tilde{O}(|C| \lambda^2)$ for the best code-based protocol due to Jain, Krenn, Pietrzak and Tentes).

A central result in the theory of Cryptography, by Hastad, Imagliazzo, Luby and Levin [SICOMP’99], demonstrates that the existence one-way functions (OWF) implies the existence of pseudo-random generators (PRGs). Despite the fundamental importance of this result, and several elegant improvements/simplifications, analyses of constructions of PRGs from OWFs remain complex (both conceptually and technically). Our goal is to provide a construction of a PRG from OWFs with a simple proof of security; we thus focus on the setting of non-uniform security (i.e., we start off with a OWF secure against non-uniform PPT, and we aim to get a PRG secure against non-uniform PPT). Our main result is a construction of a PRG from OWFs with a self-contained, simple, proof of security, relying only on the Goldreich-Levin Theorem (and the Chernoff bound). Although our main goal is simplicity, the construction, and a variant there-of, also improves the efficiency—in terms of invocations and seed lengths—of the state-of-the-art constructions due to [Haitner-Reingold-Vadhan, STOC’10] and [Vadhan-Zheng, STOC’12], by a factor $O(\log^2 n)$. The key novelty in our analysis is a generalization of the Blum-Micali [FOCS’82] notion of unpredictabilty—rather than requiring that every bit in the output of a function is unpredictable, we count how many unpredictable bits a function has, and we show that any OWF on $n$ input bits (after hashing the input and the output) has $n + O(\log n)$ unpredictable output bits. Such unpredictable bits can next be “extracted” into a pseudorandom string using standard techniques.

Gentry's groundbreaking work showed that a fully homomorphic, provably secure scheme is possible via bootstrapping a somewhat homomorphic scheme. However, a major drawback of bootstrapping is its high computational cost. One alternative is to use a different metric for noise so that homomorphic operations do not accumulate noise, eliminating the need for boostrapping altogether. Leonardi and Ruiz-Lopez present a group-theoretic framework for such a ``noise non-accumulating'' multiplicative homomorphic scheme, but Agathocleous et al. expose weaknesses in this framework when working over finite abelian groups. Tangentially, Li and Wang present a ``noise non-accumulating'' fully homomorphic scheme by performing Ostrovsky and Skeith's transform on a multiplicative homomorphic scheme of non-abelian group rings. Unfortunately, the security of Li and Wang's scheme relies on the Factoring Large Numbers assumption, which is false given an adversary with a quantum computer. In this work, we seek to modify Li and Wang's scheme to be post-quantum secure by fitting it into the Leonardi and Ruiz-Lopez framework for non-abelian rings. We discuss improved security assumptions for Li and Wang encryption and assess the shortcomings of working in a non-abelian setting. Finally, we show that a large class of semisimple rings is incompatible with the Leonardi and Ruiz-Lopez framework.

Truncated differential cryptanalyses were introduced by Knudsen in 1994. They are a well-known family of attacks that has arguably received less attention than some other variants of differential attacks. This paper gives some new insights into the theory of truncated differential attacks, specifically the provable security of SPN ciphers with MDS diffusion matrices against this type of attack. Furthermore, our study extends to various versions within the QARMA family of block ciphers, unveiling the only valid instances of single-tweak attacks on 10-round QARMAv1-64, 10-round QARMAv1-128, and 10- and 11-round QARMAv2-64. These attacks benefit from the optimal truncated differential distinguishers as well as some evolved key-recovery techniques.

Given a supersingular elliptic curve $E$ and a non-scalar endomorphism $\alpha$ of $E$, we prove that the endomorphism ring of $E$ can be computed in classical time about $\text{disc}(\mathbb{Z}[\alpha])^{1/4}$ , and in quantum subexponential time, assuming the generalised Riemann hypothesis. Previous results either had higher complexities, or relied on heuristic assumptions. Along the way, we prove that the Primitivisation problem can be solved in polynomial time (a problem previously believed to be hard), and we prove that the action of smooth ideals on oriented elliptic curves can be computed in polynomial time (previous results of this form required the ideal to be powersmooth, i.e., not divisible by any large prime power). Following the attacks on SIDH, isogenies in high dimension are a central ingredient of our results.

Blind signatures serve as a foundational tool for privacy-preserving applications and have recently seen renewed interest due to new applications in blockchains and privacy-authentication tokens. With this, constructing practical round-optimal (i.e., signing consists of the minimum two rounds) blind signatures in the random oracle model (ROM) has been an active area of research, where several impossibility results indicate that either the ROM or a trusted setup is inherent. In this work, we present two round-optimal blind signatures under standard assumptions in the ROM with different approaches: one achieves the smallest sum of the signature and communication sizes, while the other achieves the smallest signature size. Both of our instantiations are based on standard assumptions over asymmetric pairing groups, i.e., CDH, DDH, and/or SXDH. Our first construction is a highly optimized variant of the generic blind signature construction by Fischlin (CRYPTO'06) and has signature and communication sizes 447 B and 303 B, respectively. We progressively weaken the building blocks required by Fischlin and we result in the first blind signature where the sum of the signature and communication sizes fit below 1 KB based on standard assumptions. Our second construction is a semi-generic construction from a specific class of randomizable signature schemes that admits an all-but-one reduction. The signature size is only 96 B while the communication size is 2.2 KB. This matches the previously known smallest signature size while improving the communication size by several orders of magnitude. Finally, both of our constructions rely on a (non-black box) fine-grained analysis of the forking lemma that may be of independent interest.

As concerns are increasingly raised about data privacy, encrypted database management system (DBMS) based on fully homomorphic encryption (FHE) attracts increasing research attention, as FHE permits DBMS to be directly outsourced to cloud servers without revealing any plaintext data. However, the real-world deployment of FHE-based DBMS faces two main challenges: i) high computational latency, and ii) lack of elastic query processing capability, both of which stem from the inherent limitations of the underlying FHE operators. Here, we introduce HE$^3$DB, a fully homomorphically encrypted, efficient and elastic DBMS framework based on a new FHE infrastructure. By proposing and integrating new arithmetic and logic homomorphic operators, we devise fast and high-precision homomorphic comparison and aggregation algorithms that enable a variety of SQL queries to be applied over FHE ciphertexts, e.g., compound filter-aggregation, sorting, grouping, and joining. In addition, in contrast to existing encrypted DBMS that only support aggregated information retrieval, our framework permits further server-side analytical processing over the queried FHE ciphertexts, such as private decision tree evaluation. In the experiment, we rigorously study the efficiency and flexibility of HE$^3$DB. We show that, compared to the state-of-the-art techniques,HE$^3$DB can homomorphically evaluate end-to-end SQL queries as much as $41\times$ -$299\times$ faster than the state-of-the-art solution, completing a TPC-H query over a 16-bit 10K-row database within 241 seconds.

We propose a new compiler framework that automates code generation over multiple fully homomorphic encryption (FHE) schemes. While it was recently shown that algorithms combining multiple FHE schemes (e.g., CKKS and TFHE) achieve high execution efficiency and task utility at the same time, developing fast cross-scheme FHE algorithms for real-world applications generally require heavy hand-tuned optimizations by cryptographic experts, resulting in either high usability costs or low computational efficiency. To solve the usability and efficiency dilemma, we design and implement HEIR, a compiler framework based on multi-level intermediate representation (IR). To achieve cross-scheme compilation of efficient FHE circuits, we develop a two-stage code-lowering structure based on our custom IR dialects. First, the plaintext program along with the associated data types are converted into FHE-friendly dialects in the transformation stage. Then, in the optimization stage, we apply FHE-specific optimizations to lower the transformed dialect into our bottom-level FHE library operators. In the experiment, we implement the entire software stack for HEIR, and demonstrate that complex end-to-end programs, such as homomorphic K-Means clustering and homomorphic data aggregation in databases, can easily be compiled to run $72$--$179\times$ faster than the program generated by the state-of-the-art FHE compilers.

Sponge paradigm, used in the design of SHA-3, is an alternative hashing technique to the popular Merkle-Damgård paradigm. We revisit the problem of finding $B$-block-long collisions in sponge hash functions in the auxiliary-input random permutation model, in which an attacker gets a piece of $S$-bit advice about the random permutation and makes $T$ (forward or inverse) oracle queries to the random permutation. Recently, significant progress has been made in the Merkle-Damgård setting and optimal bounds are known for a large range of parameters, including all constant values of $B$. However, the sponge setting is widely open: there exist significant gaps between known attacks and security bounds even for $B=1$. Freitag, Ghoshal and Komargodski (CRYPTO 2022) showed a novel attack for $B=1$ that takes advantage of the inverse queries and achieves advantage $\tilde{\Omega}(\min(S^2T^2/2^{2c}$, $ (S^2T/2^{2c})^{2/3})+T^2/2^r)$, where $r$ is bit-rate and $c$ is the capacity of the random permutation. However, they only showed an $\tilde{O}(ST/2^c+T^2/2^r)$ security bound, leaving open an intriguing quadratic gap. For $B=2$, they beat the general security bound by Coretti, Dodis, Guo (CRYPTO 2018) for arbitrary values of $B$. However, their highly non-trivial argument is quite laborious, and no better (than the general) bounds are known for $B\geq 3$. In this work, we study the possibility of proving better security bounds in the sponge setting. To this end, - For $B=1$, we prove an improved $\tilde{O}(S^2T^2/2^{2c}+S/2^c+T/2^c+T^2/2^r)$ bound. Our bound strictly improves the bound by Freitag et al., and is optimal for $ST^2\leq 2^c$. - For $B=2$, we give a considerably simpler and more modular proof, recovering the bound obtained by Freitag et al. - We obtain our bounds by adapting the recent multi-instance technique of Akshima, Guo and Liu (CRYPTO 2022) which bypasses the limitations of prior techniques in the Merkle-Damgård setting. To complement our results, we provably show that the recent multi-instance technique cannot further improve our bounds for $B=1,2$, and the general bound by Correti et al., for $B\geq 3$. Overall, our results yield state-of-the-art security bounds for finding short collisions and fully characterize the power of the multi-instance technique in the sponge setting.

The notion of functional re-encryption security (funcCPA) for public-key encryption schemes was recently introduced by Akavia et al. (TCC'22), in the context of homomorphic encryption. This notion lies in between CPA security and CCA security: we give the attacker a functional re-encryption oracle instead of the decryption oracle of CCA security. This oracle takes a ciphertext $c$ and a function $f$, and returns fresh encryption of the output of $f$ applied to the decryption of $c$; in symbols, $c'=Enc(f(Dec(c)))$. More generally, we even allow for a multi-input version, where the oracle takes an arbitrary number of ciphetexts $c_1,\ldots,c_\ell$ and outputs $c' = Enc(f(Dec(c_1), \ldots, Dec(c_\ell)))$. In this work we observe that funcCPA security may have applications beyond homomorphic encryption, and set out to study its properties. As our main contribution, we prove that funcCPA is ``closer to CPA than to CCA''; that is, funcCPA secure encryption can be constructed in a black-box manner from CPA-secure encryption. We stress that, prior to our work, this was not known even for basic re-encryption queries corresponding to the identity function $f$. At the core of our result is a new technique, showing how to handle adaptive functional re-encryption queries using tools previously developed in the context of non-malleable encryption, which roughly corresponds to a single non-adaptive parallel decryption query.

In this paper we show that Bleichenbacher-style attacks on RSA decryption are not only still possible, but also that vulnerable implementations are common. We have successfully attacked multiple implementations using only timing of decryption operation and shown that many others are vulnerable. To perform the attack we used more statistically rigorous techniques like the sign test, Wilcoxon signed-rank test, and bootstrapping of median of pairwise differences. We publish a set of tools for testing libraries that perform RSA decryption against timing side-channel attacks, including one that can test arbitrary TLS servers with no need to write a test harnesses. Finally, we propose a set of workarounds that implementations can employ if they can't avoid the use of RSA.

In this paper we analyse typical timing data that can be collected over loopback interface, in local, and in metropolitan area networks. We evaluate performance of few statistical test for detecting differences in timing of server responses. The evaluated tests include the popular Box test, as well as sign test, Wilcoxon signed-rank test, and paired sample t-test. We found that the Box test offers poor performance, as it's an incorrect test to use for the measurements we collected. Use of appropriate tests also allows for robust differentiation between much smaller differences than the existing literature would suggest. We were able to detect side channels of single-digit CPU cycles over regular gigabit Ethernet. Those alternative tests were also found to be robust against noise in production networks, allowing detection of side channel of just few nanoseconds with 6 network hops between test systems.

Thangavel and Varalakshmi proposed an enhanced DNA and ElGamal cryptosystem for secure data storage and retrieval in cloud. They modified ElGamal algorithm which it calls enhanced ElGamal cryptosystem. We prove that their enhanced ElGamal scheme, which does not require two random numbers by data owner. Although the attacker is unable to find out what message the data owner gave to the data user. However, the attackers can still confuse the issue of sending messages to data users. On the other hand, this scheme can not against insider attack, therefore it is insecure.

An anonymous communication network (ACN) is designed to protect the identities of two parties communicating through it, even if an adversary controls or observes parts of the network. Among the ACNs, Tor represents a practical trade-off between offering a reasonable level of anonymity and, simultaneously, an acceptable transmission delay. Due to its practical impact, there is abundant literature on the performance of Tor concerning both communication and security aspects. Recently, a static framework was suggested for evaluating and comparing, in a quantifiable way, the effect of different scenarios (attacks, defence mechanisms, and other protocol changes). Although a static model is useful, many scenarios involve parameters and stochastic variables that change or evolve over time, or that may be influenced by active and malicious adversaries. In this paper, we propose a dynamic framework for evaluating such scenarios. We identify several scenarios where this framework is applicable, and illustrate our framework by considering the guard node mechanism in Tor. We evaluate and compare variations on the guard node concept suggested in the literature with respect to relevant performance metrics and, using the framework, support our evaluation with a theoretical analysis.

Tiptoe is a private web search engine that allows clients to search over hundreds of millions of documents, while revealing no information about their search query to the search engine’s servers. Tiptoe’s privacy guarantee is based on cryptography alone; it does not require hardware enclaves or non-colluding servers. Tiptoe uses semantic embeddings to reduce the problem of private full-text search to private nearest-neighbor search. Then, Tiptoe implements private nearest-neighbor search with a new, high-throughput protocol based on linearly homomorphic encryption. Running on a 45-server cluster, Tiptoe can privately search over 360 million web pages with 145 core-seconds of server compute, 56.9 MiB of client-server communication (74% of which occurs before the client enters its search query), and 2.7 seconds of end-to-end latency. Tiptoe’s search works best on conceptual queries (“knee pain”) and less well on exact string matches (“123 Main Street, New York”). On the MS MARCO search-quality benchmark, Tiptoe ranks the best-matching result in position 7.7 on average. This is worse than a state-of-the-art, non-private neural search algorithm (average rank: 2.3), but is close to the classical tf-idf algorithm (average rank: 6.7). Finally, Tiptoe is extensible: it also supports private text-to-image search and, with minor modifications, it can search over audio, code, and more.

As the global migration to post-quantum cryptography (PQC) continues to progress actively, in Korea, the Post-Quantum Cryptography Research Center has been established to acquire PQC technology, leading the KpqC Competition. In February 2022, the KpqC Competition issued a call for proposals for PQC algorithms. By November 2022, 16 candidates were selected for the first round (7 KEMs and 9 DSAs). Currently, Round 1 submissions are being evaluated with respect to security, efficiency, and scalability in various environments. At the current stage, evaluating the software through an analysis to improve the software quality of the first-round submissions is judged appropriately. In this paper, we present analysis results regarding performance and implementation security on based dependency-free approach of external libraries. Namely, we configure extensive tests for an analysis with no dependencies by replacing external libraries that can complicate the build process with hard coding. From the performance perspective, we provide analysis results of performance profiling, execution time, and memory usage for each of the KpqC candidates. From the implementation security perspective, we examine bugs and errors in the actual implementations using Valgrind software, a metamorphic testing methodology that can include wide test coverage and constant-time implementation against the timing attack. Until the KpqC standard algorithm is announced, we argue that continuous integration of extensive tests will lead to higher-level software quality of KpqC candidates.

Elisabeth-4 is a stream cipher tailored for usage in hybrid homomorphic encryption applications that has been introduced by Cosseron et al. at ASIACRYPT 2022. In this paper, we present several variants of a key-recovery attack on the full Elisabeth-4 that break the 128-bit security claim of that cipher. Our most optimized attack is a chosen-IV attack with a time complexity of $2^{88}$ elementary operations, a memory complexity of $2^{54}$ bits and a data complexity of $2^{41}$ bits. Our attack applies the linearization technique to a nonlinear system of equations relating some keystream bits to the key bits and exploits specificities of the cipher to solve the resulting linear system efficiently. First, due to the structure of the cipher, the system to solve happens to be very sparse, which enables to rely on sparse linear algebra and most notably on the Block Wiedemann algorithm. Secondly, the algebraic properties of the two nonlinear ingredients of the filtering function cause rank defects which can be leveraged to solve the linearized system more efficiently with a decreased data and time complexity. We have implemented our attack on a toy version of Elisabeth-4 to verify its correctness. It uses the efficient implementation of the Block Wiedemann algorithm of CADO-NFS for the sparse linear algebra.

Identity-based matchmaking encryption (IB-ME) proposed by Ateniese et al. [CRYPTO 2019; Journal of Cryptology 2021] enables users to communicate privately, anonymously, and authentically. Following the seminal work of Ateniese et al., considerable research has been conducted on the security and construction of IB-ME schemes, but no scheme with enhanced privacy against chosen-ciphertext attacks is known. In this paper, we propose two IB-ME schemes that simultaneously achieve enhanced privacy against chosen-ciphertext attacks. The first scheme is built on the bilinear Diffie–Hellman assumption in the random oracle model. Inspired by the scheme of Ateniese et al., our construction attains stronger security guarantees while providing more compact decryption keys and ciphertexts than the scheme of Ateniese et al. The second scheme is a generic construction built upon anonymous identity-based encryption, digital signatures, NIZK systems, and reusable extractors. This scheme is obtained by generalizing the specific scheme of Francati et al. [INDOCRYPT 2021] with several technique to solve CCA-related issues. It constitutes the first IB-ME scheme achieving the stronger security notions in the standard model. As an additional contribution, we classify existing authenticity notions for IB-ME into four categories—no message attacks (NMA) and chosen message attacks (CMA), each considered against both insiders and outsiders. This taxonomy enables a precise comparison among existing IB-ME schemes.

Password-authenticated key exchange (PAKE) is a class of protocols enabling two parties to convert a shared (possibly low-entropy) password into a high-entropy joint session key. Strong asymmetric PAKE (saPAKE), an extension that models the client-server setting where servers may store a client's password for repeated authentication, was the subject of standardization efforts by the IETF in 2019-20. In this work, we present the most computationally efficient saPAKE protocol so far: a compiler from PAKE to saPAKE which costs only 2 messages and 7 group exponentiations in total (3 for client and 4 for server) when instantiated with suitable underlying PAKE protocols. In addition to being efficient, our saPAKE protocol is conceptually simple and achieves the strongest notion of universally composable (UC) security. In addition to classical assumptions and classical PAKE, we may instantiate our PAKE-to-saPAKE compiler with cryptographic group actions, such as the isogeny-based CSIDH, and post-quantum PAKE. This yields the first saPAKE protocol from post-quantum assumptions as all previous constructions rely on cryptographic assumptions weak to Shor's algorithm.

The recent devastating attacks on SIDH rely on the fact that the protocol reveals the images $\varphi(P)$ and $\varphi(Q)$ of the secret isogeny $\varphi : E_0 \rightarrow E$ on a basis $\{P, Q\}$ of the $N$-torsion subgroup $E_0[N]$ where $N^2 > \deg(\varphi)$. To thwart this attack, two recent proposals, M-SIDH and FESTA, proceed by only revealing the images upto unknown scalars $\lambda_1, \lambda_2 \in \mathbb{Z}_N^\times$, i.e., only $\lambda_1 \varphi(P)$ and $\lambda_2 \varphi(Q)$ are revealed, where $\lambda_1 = \lambda_2$ for M-SIDH and $\lambda_1 = \lambda_2^{-1}$ for FESTA. Similar information is leaked in CSIDH since $\varphi$ maps the eigenspaces of Frobenius on $E_0$ to the corresponding eigenspaces on $E$. In this paper, we introduce a new polynomial time attack that generalizes the well known "lollipop" attack and analyze how it applies to M-SIDH, FESTA and CSIDH. We show that M-SIDH can be broken in polynomial time whenever $E_0$ or $E$ is $\mathbb{F}_p$-rational, even when the endomorphism rings of $E_0$ and $E$ are unknown. This can be generalized to the case where the starting (or end) curve is not $\mathbb{F}_p$-rational, but is connected to its Frobenius conjugate by an isogeny of small degree. For FESTA, where the curve $E_0$ is already $\mathbb{F}_p$-rational, we obtain a polynomial time attack under the added requirement that at least one of the basis points $P, Q$ spans an eigenspace of Frobenius, of an endomorphism of low degree, or of a composition of both. We note that the current implementation of FESTA does not choose such a basis. Since it is always possible to construct an endomorphism, typically of large degree, with either $P, Q$ an eigenvector, we conclude that FESTA with overstretched parameters is insecure. Although the information leaked in CSIDH is very similar to FESTA, we show that our attack does not reveal any new information about the secret isogeny, i.e., we only learn that it is $\mathbb{F}_p$-rational, which is a priori knowledge. Finally, we analyze if and how it would be possible to backdoor M-SIDH and FESTA by choosing system parameters that look inconspicuous, but in fact reduce to the special cases above via a secret isogeny chosen by the adversary.

A Rugged Pseudorandom Permutation (RPRP) is a variable-input-length tweakable cipher satisfying a security notion that is intermediate between tweakable PRP and tweakable SPRP. It was introduced at CRYPTO 2022 by Degabriele and Karadžić, who additionally showed how to generically convert such a primitive into nonce-based and nonce-hiding AEAD schemes satisfying either misuse-resistance or release-of-unverified-plaintext security as well as Nonce-Set AEAD which has applications in protocols like QUIC and DTLS. Their work shows that RPRPs are powerful and versatile cryptographic primitives. However, the RPRP security notion itself can seem rather contrived, and the motivation behind it is not immediately clear. Moreover, they only provided a single RPRP construction, called UIV, which puts into question the generality of their modular approach and whether other instantiations are even possible. In this work, we address this question positively by presenting new RPRP constructions, thereby validating their modular approach and providing further justification in support of the RPRP security definition. Furthermore, we present a more refined view of their results by showing that strictly weaker RPRP variants, which we introduce, suffice for many of their transformations. From a theoretical perspective, our results show that the well-known three-round Feistel structure achieves stronger security as a permutation than a mere pseudorandom permutation---as was established in the seminal result by Luby and Rackoff. We conclude on a more practical note by showing how to extend the left domain of one RPRP construction for applications that require larger values in order to meet the desired level of security.

At CRYPTO'18, Datta et al. proposed nPolyMAC and proved the security up to 2^{2n/3} authentication queries and 2^{n} verification queries. At EUROCRYPT'19, Dutta et al. proposed CWC+ and showed the security up to 2^{2n/3} queries. At FSE'19, Datta et al. proposed PolyMAC and its key-reduced variant 2k-PolyMAC, and showed the security up to 2^{2n/3} queries. This security bound was then improved by Kim et al. (EUROCRYPT'20) and Datta et al (FSE'23) respectively to 2^{3n/4} and in the multi-user setting. At FSE'20, Chakraborti et al. proposed PDM*MAC and 1k-PDM*MAC and showed the security up to 2^{2n/3} queries. Recently, Chen et al. proposed nEHtM_p^+ and showed the security up to 2^{2n/3} queries. In this paper, we show forgery attacks on nPolyMAC, CWC+, PolyMAC, 2k-PolyMAC, PDM*MAC, 1k-PDM*MAC and nEHtM_p^+. Our attacks exploit some vulnerability in the underlying polynomial hash function Poly, and (i) require only one authentication query and one verification query; (ii) are nonce-respecting; (iii) succeed with probability 1. Thus, our attacks disprove the provable high security claims of these schemes. We then revisit their security analyses and identify what went wrong. Finally, we propose two solutions that can restore the beyond-birthday-bound security.

We show that the key agreement scheme [J. Syst. Archit., 131:102698, 2022] fails to keep user anonymity and service provider anonymity, not as claimed. The scheme simply thinks that user anonymity is equivalent to protecting the target user's identity against exposure, while its long-term pseudo-identity can be exposed. We want to clarify that the true anonymity means that an adversary cannot attribute different sessions to different target users, even if the true identifier cannot be retrieved from the exposed pseudo-identifier.

Homomorphic Encryption (HE) enhances data security by facilitating computations on encrypted data, opening new paths for privacy-focused computations. The Brakerski-Fan-Vercauteren (BFV) scheme, a promising HE scheme, raises considerable performance challenges. Graphics Processing Units (GPUs), with considerable parallel processing abilities, have emerged as an effective solution. In this work, we present an in-depth study focusing on accelerating and comparing BFV variants on GPUs, including Bajard-Eynard-Hasan-Zucca (BEHZ), Halevi-Polyakov-Shoup (HPS), and other recent variants. We introduce a universal framework accommodating all variants, propose optimized BEHZ implementation, and first support HPS variants with large parameter sets on GPUs. Moreover, we devise several optimizations for both low-level arithmetic and high-level operations, including minimizing instructions for modular operations, enhancing hardware utilization for base conversion, implementing efficient reuse strategies, and introducing intra-arithmetic and inner-conversion fusion methods, thus decreasing the overall computational and memory consumption. Leveraging our framework, we offer comprehensive comparative analyses. Our performance evaluation showcases a marked speed improvement, achieving 31.9× over OpenFHE running on a multi-threaded CPU and 39.7% and 29.9% improvement, respectively, over the state-of-the-art GPU BEHZ implementation. Our implementation of the leveled HPS variant records up to 4× speedup over other variants, positioning it as a highly promising alternative for specific applications.

Homomorphic Encryption (HE) presents a promising solution to securing neural networks for Machine Learning as a Service (MLaaS). Despite its potential, the real-time applicability of current HE-based solutions remains a challenge, and the diversity in network structures often results in inefficient implementations and maintenance. To address these issues, we introduce a unified and compact network structure for real-time inference in convolutional neural networks based on HE. We further propose several optimization strategies, including an innovative compression and encoding technique and rearrangement in the pixel encoding sequence, enabling a highly efficient batched computation and reducing the demand for time-consuming HE operations. To further expedite computation, we propose a GPU acceleration engine to leverage the massive thread-level parallelism to speed up computations. We test our framework with the MNIST, Fashion-MNIST, and CIFAR-10 datasets, demonstrating accuracies of 99.14%, 90.8%, and 61.09%, respectively. Furthermore, our framework maintains a steady processing speed of 0.46 seconds on a single-thread CPU, and a brisk 31.862 milliseconds on an A100 GPU for all datasets. This represents an enhancement in speed more than 3000 times compared to pervious work, paving the way for future explorations in the realm of secure and real-time machine learning applications.

The recently announced National Institute of Standards and Technology (NIST) Post-quantum cryptography (PQC) third-round standardization process has released its candidates to be standardized and Falcon is one of them. On the other hand, however, very few hardware implementation works for Falcon have been released due to its very complicated computation procedure and intensive complexity. With this background, in this paper, we propose an efficient hardware structure to implement residue numeral system (RNS) decomposition within NTRUSolve (a key arithmetic component for key generation of Falcon). In total, we have proposed three stages of coherent interdependent efforts to finish the proposed work. First, we have identified the necessary algorithmic operation related to RNS decomposition. Then, we have innovatively designed a hardware structure to realize these algorithms. Finally, field-programmable gate array (FPGA)-based implementation has been carried out to verify the superior performance of the proposed hardware structure. For instance, the proposed hardware design involves at least 3.91x faster operational time than the software implementation. To the authors' best knowledge, this is the first paper about the hardware acceleration of RNS decomposition for Falcon, and we hope the outcome of this work will facilitate the research in this area.

Secure multi-party computation (MPC) enables multiple distrusting parties to compute a function while keeping their respective inputs private. In a threshold implementation of a symmetric primitive, e.g., of a block cipher, each party holds a share of the secret key or of the input block. The output block is computed without reconstructing the secret key. This enables the construction of distributed TPMs or transciphering for secure data transmission in/out of the MPC context. This paper investigates implementation approaches for the lightweight primitives SKINNY and PHOTON in arithmetic circuits. For these primitives, we identify arithmetic expressions for the S-box that result in smaller arithmetic circuits compared to the Boolean expressions from the literature. We validate the optimization using a generic actively secure MPC protocol and obtain 18% faster execution time with 49% less communication data for SKINNY-64-128 and 27% to 74% faster execution time with 49% to 81% less data for PHOTON $P_{100}$ and $P_{288}$. Furthermore, we find a new set of parameters for the heuristic method of polynomial decomposition, introduced by Coron, Roy and Vivek, specialized for SKINNY's 8-bit S-box. We reduce the multiplicative depth from 9 to 5.