The privacy pass protocol allows users to redeem anonymously issued cryptographic tokens instead of solving annoying CAPTCHAs. The issuing authority verifies the credibility of the user, who can later use the pass while browsing the web using an anonymous or virtual private network. Hendrickson et al. proposed an IETF draft (privacypass-rate-limit-tokens-00) for a rate-limiting version of the privacy pass protocol, also called rate-limited Privacy Pass (RlP). Introducing a new actor called a mediator makes both versions inherently different. The mediator applies access policies to rate-limit users’ access to the service while, at the same time, should be oblivious to the website/origin the user is trying to access. In this paper, we formally define the rate-limited Privacy Pass protocol and propose a game-based security model to capture the informal security notions introduced by Hendrickson et al.. We show a construction from simple building blocks that fulfills our security definitions and even allows for a post-quantum secure instantiation. Interestingly, the instantiation proposed in the IETF draft is a specific case of our construction. Thus, we can reuse the security arguments for the generic construction and show that the version used in practice is secure.

The evolution of quantum algorithms threatens to break public key cryptography in polynomial time. The development of quantum-resistant algorithms for the post-quantum era has seen a significant growth in the field of post quantum cryptography (PQC). Polynomial multiplication is the core of Ring Learning with Error (RLWE) lattice based cryptography (LBC) which is one of the most promising PQC candidates. In this work, we present the design of fast and energy-efficient pipelined Number Theoretic Transform (NTT) based polynomial multipliers and present synthesis results on a Field Programmable Gate Array (FPGA) to evaluate their efficacy. NTT is performed using the pipelined R2SDF and R22SDF Fast Fourier Transform (FFT) architectures. In addition, we propose an energy efficient modified architecture (Modr2). The NTT-based designed polynomial multipliers employs the Modr2 architecture that achieve on average 2× better performance over the R2SDF FFT and 2.4× over the R22SDF FFT with similar levels of energy consumption. The proposed polynomial multiplier with Modr2 architecture reaches 12.5× energy efficiency over the state-ofthe-art convolution-based polynomial multiplier and 4× speedup over the systolic array NTT based polynomial multiplier for polynomial degrees of 1024, demonstrating its potential for practical deployment in future designs.

Guillou-Quisquater (GQ) signature is an efficient RSA-based digital signature scheme amongst the most famous Fiat-Shamir follow-ons owing to its good simplicity. However, there exist two bottlenecks for GQ hindering its application in industry or academia: the RSA trapdoor $n=pq$ in the key generation phase and its high bandwidth caused by the storage-consuming representation of RSA group elements (3072 bits per one element in 128-bit security). In this paper, we first formalize the definition and security proof of class group based GQ signature (CL-GQ), which eliminates the trapdoor in key generation phase and improves the bandwidth efficiency from the RSA-based GQ signature. Then, we construct a trustless GQ multi-signature scheme by applying non-malleable equivocable commitments and our well-designed compact non-interactive zero-knowledge proofs (NIZK). Our scheme has a well-rounded performance compared to existing multiparty GQ, Schnorr and ECDSA schemes, in the aspects of bandwidth (no range proof or multiplication-to-addition protocol required), rather few interactions (only 4 rounds in signing), provable security in \textit{dishonest majority model} and identifiable abort property. Another interesting finding is that, our NIZK is highly efficient (only one round required) by using the Bezout formula, and this trick can also optimize the ZK proof of Paillier ciphertext which greatly improves the speed of Yi's Blind ECDSA (AsiaCCS 2019).

The LowMC family of SPN block cipher proposed by Albrecht et al. was designed specifically for MPC-/FHE-/ZKP-friendly use cases. It is especially used as the underlying block cipher of PICNIC, one of the alternate third-round candidate digital signature algorithms for NIST post-quantum cryptography standardization. The security of PICNIC is highly related to the difficulty of recovering the secret key of LowMC from a given plaintext/ciphertext pair, which raises new challenges for security evaluation under extremely low data complexity. In this paper, we improve the attacks on LowMC under low data complexity, i.e. 1 or 2 chosen plaintext/ciphertext pairs. For the difference enumeration attack with 2 chosen plaintexts, we propose new algebraic methods to better exploit the nonlinear relation inside the introduced variables based on the attack framework proposed by Liu et al. at ASIACRYPT 2022. With this technique, we significantly extend the number of attack rounds for LowMC with partial nonlinear layers and improve the success probability from around 0.5 to over 0.9. The security margin of some instances can be reduced to only 3/4 rounds. For the key-recovery attack using a single plaintext, we adopt a different linearization strategy to reduce the huge memory consumption caused by the polynomial methods for solving multivariate equation systems. The memory complexity reduces drastically for all 5-/6-round LowMC instances with full nonlinear layers at the sacrifice of a small factor of time complexity. For 5-round LowMC instances with a block size of 129, the memory complexity decreases from $2^{86.46}$ bits to $2^{48.18}$ bits while the time complexity even slightly reduces. Our results indicate that the security for different instances of LowMC under extremely low data complexity still needs further exploration.

Quantum computing is considered among the next big leaps in computer science. While a fully functional quantum computer is still in the future, there is an ever-growing need to evaluate the security of the symmetric key ciphers against a potent quantum adversary. Keeping this in mind, our work explores the key recovery attack using the Grover's search on the three variants of AES (-128, -192, -256). In total, we develop a pool of 20 implementations per AES variant (thus totaling in 60), by taking the state-of-the-art advancements in the relevant fields into account. In a nutshell, we present the least Toffoli depth and full depth implementations of AES, thereby improving from Zou et al.'s Asiacrypt'20 paper by more than 97 percent for each variant of AES. We show that the qubit count - Toffoli depth product is reduced from theirs by more than 86 percent. Furthermore, we analyze the Jaques et al.'s Eurocrypt'20 implementations in details, fix the bugs (arising from some problem of the quantum computing tool used and not related to their coding) and report corrected benchmarks. To the best of our finding, our work improves from all the previous works (including the Asiacrypt'22 paper by Huang and Sun and the Asiacrypt'23 paper by Liu et al.) in terms of various quantum circuit complexity metrics (Toffoli depth, full depth, Toffoli/full depth - qubit count product, full depth - gate count product, etc.). Also, our bug-fixing of Jaques et al.'s Eurocrypt'20 implementations seem to improve from the authors' own bug-fixing, thanks to our architecture consideration. Equipped with the basic AES implementations, we further investigate the prospect of the Grover's search. We also propose three new implementations of the S-box, one new implementation of the MixColumn; as well as five new architecture (one is motivated by the architecture by Jaques et al. in Eurocrypt’20, and the rest four are entirely our innovation). Under the MAXDEPTH constraint (specified by NIST), the circuit depth metrics (Toffoli depth, T-depth and full depth) become crucial factors and parallelization for often becomes necessary. We provide the least depth implementation in this respect, that offers the best performance in terms of metrics for circuit complexity (like, depth-squared - qubit count product, depth - gate count product).

The Number Theoretic Transform (NTT) plays a central role in efficient implementations of cryptographic primitives selected for Post Quantum Cryptography. Although it certainly exists, academic papers that cite the NTT omit the connection between the NTT and residues of a polynomial modulo factors of $X^{2^d} + 1$ and mention only the final expressions of what the NTT computes. This short paper establishes that connection and, in doing so, elucidates key aspects of computing the NTT. Based on this, the specific instantiations of the NTT function used in CRYSTALS-Kyber and CRYSTALS-Dilithium are derived.

The Algorand consensus protocol is interesting both in theory and in practice. On the theoretical side, to achieve adaptive security, it introduces the novel idea of player replaceability, where each step of the protocol is executed by a different randomly selected committee whose members remain secret until they send their first and only message. The protocol provides consistency under arbitrary network conditions and liveness under intermittent network partitions. On the practical side, the protocol is used to secure the Algorand cryptocurrency, whose total value is approximately $850M at the time of writing. The Algorand protocol in use differs substantially from the protocols described in the published literature on Algorand. Despite its significance, it lacks a formal analysis. In this work, we describe and analyze the Algorand consensus protocol as deployed today in Algorand’s ecosystem. We show that the overall protocol framework is sound by characterizing network conditions and parameter settings under which the protocol can be proven secure.

The Fujisaki-Okamoto (FO) transformation is used in most proposals for post-quantum secure key encapsulation mechanisms (KEMs) like, e.g., Kyber [BDK+18]. The security analysis of FO in the presence of quantum attackers has made huge progress over the last years. Recently, [HHM22] made a particular improvement by giving a security proof that is agnostic towards how invalid ciphertexts are being treated: in contrast to previous proofs, it works regardless whether invalid ciphertexts are rejected by reporting decryption failure explicitly or implicitly (by returning pseudorandom values). The proof in [HHM22] involves a new correctness notion for the encryption scheme that is used to encapsulate the keys. This allows in principle for a smaller additive security related to decryption failures, but requires to analyze this new notion for the encryption scheme on which a concrete KEM at hand is based. This note offers a trade-off between [HHM22] and its predecessors: it offers a bound for both rejection variants, being mostly based on [HHM22], but uses a more established correctness notion.

Blind Signatures are a useful primitive for privacy preserving applications such as electronic payments, e-voting, anonymous credentials, and more. However, existing practical blind signature schemes based on standard assumptions require either pairings or lattices. We present the first construction of a round-optimal blind signature in the random oracle model based on standard assumptions without resorting to pairings or lattices. In particular, our construction is secure under the strong RSA assumption and DDH (in pairing-free groups). For our construction, we provide a NIZK-friendly signature based on strong RSA, and efficiently instantiate Fischlin's generic framework (CRYPTO'06). Our Blind Signature scheme has signatures of size 4.28 KB and communication cost 62.19 KB. On the way, we develop techniques that might be of independent interest. In particular, we provide efficient relaxed range-proofs with subversion zero-knowledge and compact commitments to elements of arbitrary groups.

Micciancio and Sorrel (ICALP 2018) proposed a bootstrapping algorithm that can refresh many messages at once with sublinearly many homomorphic operations per message. However, despite the attractive asymptotic cost, it is unclear if their algorithm could ever be practical, which reduces the impact of their results. In this work, we follow their general framework, but propose an amortized bootstrapping that is conceptually simpler and asymptotically cheaper. We reduce the number of homomorphic operations per refreshed message from $O(3^\rho \cdot n^{1/\rho} \cdot \log n)$ to $O(\rho \cdot n^{1/\rho})$, and the noise overhead from $\tilde{O}(n^{2 + 3 \cdot \rho})$ to $\tilde{O}(n^{1 + \rho})$. We also make it more general, by handling non-binary messages and applying programmable bootstrapping. To obtain a concrete instantiation of our bootstrapping algorithm, we propose a double-CRT (aka RNS) version of the GSW scheme, including a new operation, called shrinking, used to speed-up homomorphic operations by reducing the dimension and ciphertext modulus of the ciphertexts. We also provide a C++ implementation of our algorithm, thus showing for the first time the practicability of the amortized bootstrapping. Moreover, it is competitive with existing bootstrapping algorithms, being even around 3.4 times faster than an equivalent non-amortized version of our bootstrapping.

Algorithm hardness can be described by 5 categories: hardness in computation, in sequential computation, in memory, in energy consumption (or bandwidth), in code size. Similarly, hardness can be a concern for solving or for verifying, depending on the context, and can depend on a secret trapdoor or be universally hard. Two main lines of research investigated such problems: cryptographic puzzles, that gained popularity thanks to blockchain consensus systems (where solving must be moderately hard, and verification either public or private), and white box cryptography (where solving must be hard without knowledge of the secret key). In this work, we improve upon the classification framework proposed by Biryukov and Perrin in Asiacypt 2017 and offer a united hardness framework, PURED, that can be used for measuring all these kinds of hardness, both in solving and verifying. We also propose three new constructions that fill gaps previously uncovered by the literature (namely, trapdoor proof of CMC, trapdoor proof of code, and a hard challenge in sequential time trapdoored in verification), and analyse their hardness in the PURED framework.

Graph convolutional networks (GCNs) are gaining popularity due to their powerful modelling capabilities. However, guaranteeing privacy is an issue when evaluating on inputs that contain users’ sensitive information such as financial transactions, medical records, etc. To address such privacy concerns, we design Entrada, a framework for securely evaluating GCNs that relies on the technique of secure multiparty computation (MPC). For efficiency and accuracy reasons, Entrada builds over the MPC framework of Tetrad (NDSS’22) and enhances the same by providing the necessary primitives. Moreover, Entrada leverages the GraphSC paradigm of Araki et al. (CCS’21) to further enhance efficiency. This entails designing a secure and efficient shuffle protocol specifically in the 4-party setting, which to the best of our knowledge, is done for the first time and may be of independent interest. Through extensive experiments, we showcase that the accuracy of secure GCN evaluated via Entrada is on par with its cleartext counterpart. We also benchmark efficiency of Entrada with respect to the included primitives as well as the framework as a whole. Finally, we showcase Entrada’s practicality by benchmarking GCN-based fraud detection application.

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.

The linear layer of block ciphers plays an important role in their security. In particular, ciphers designed following the wide-trail strategy use the branch number of the linear layer to derive bounds on the probability of linear and differential trails. At FSE 2014, the LS-design construction was introduced as a simple and regular structure to design bitsliced block ciphers. It considers the internal state as a bit matrix, and applies alternatively an identical S-Box on all the columns, and an identical L-Box on all the lines. Security bounds are derived from the branch number of the L-Box. In this paper, we focus on bitsliced linear layers inspired by the LS-design construction and the Spook AEAD algorithm. We study the construction of bitsliced linear transformations with efficient implementations using XORs and rotations (optimized for bitsliced ciphers implemented on 32-bit processors), and a high branch number. In order to increase the density of the activity patterns, the linear layer is designed on the whole state, rather than using multiple parallel copies of an L-Box. Our main result is a linear layer for 128-bit ciphers with branch number 21, improving upon the best 32-bit transformation with branch number 12, and the one of Spook with branch number 16.

Secure computation enables mutually distrusting parties to jointly compute a function on their secret inputs, while revealing nothing beyond the function output. A long-running challenge is understanding the required communication complexity of such protocols---in particular, when communication can be sublinear in the circuit representation size of the desired function. Significant advances have been made affirmatively answering this question within the two-party setting, based on a variety of structures and hardness assumptions. In contrast, in the multi-party setting, only one general approach is known: using Fully Homomorphic Encryption (FHE). This remains the state of affairs even for just three parties, with two corruptions. We present a framework for achieving secure sublinear-communication $(N+1)$-party computation, building from a particular form of Function Secret Sharing for only $N$ parties. In turn, we demonstrate implications to sublinear secure computation for various function classes in the 3-party and 5-party settings based on an assortment of assumptions not known to imply FHE.

This work describes an existential signature forgery vulnerability of the current CMS and PKCS#7 signature standards. The vulnerability results from an ambiguity of how to process the signed message in the signature verification process. Specifically, the absence or presence of the so called SignedAttributes field determines whether the signature message digest receives as input the message directly or the SignedAttributes, a DER-encoded structure which contains a digest of the message. If an attacker takes a CMS or PKCS#7 signed message M which was originally signed with SignedAttributes present, then he can craft a new message M 0 that was never signed by the signer and has the DER-encoded SignedAttributes of the original message as its content and verifies correctly against the original signature of M . Due to the limited flexibility of the forged message and the limited control the attacker has over it, the fraction of vulnerable systems must be assumed to be small but due to the wide deployment of the affected protocols, such instances cannot be excluded. We propose a countermeasure based on attack-detection that prevents the attack reliably.

Proof-of-Stake (PoS) algorithms, implemented as foundational components of the consensus mechanism of distributed ledgers, are defective cryptosystems by nature. This paper presents intuitive arguments for why PoS, by trying to improve the energy efficiency of Proof-of-Work (PoW) when implemented as a Sybil control mechanism in distributed ledgers, introduces a set of significant new flaws. Such systems are plutocratic, oligopolistic, and permissioned.

Payment Channel Hub (PCH) is a promising solution to the scalability issue of first-generation blockchains or cryptocurrencies such as Bitcoin. It supports off-chain payments between a sender and a receiver through an intermediary (called the tumbler). Relationship anonymity and value privacy are desirable features of privacy-preserving PCHs, which prevent the tumbler from identifying the sender and receiver pairs as well as the payment amounts. To our knowledge, all existing Bitcoin-compatible PCH constructions that guarantee relationship anonymity allow only a (predefined) fixed payment amount. Thus, to achieve payments with different amounts, they would require either multiple PCH systems or running one PCH system multiple times. Neither of these solutions would be deemed practical. In this paper, we propose the first Bitcoin-compatible PCH that achieves relationship anonymity and supports variable amounts for payment. To achieve this, we have several layers of technical constructions, each of which could be of independent interest to the community. First, we propose $\textit{BlindChannel}$, a novel bi-directional payment channel protocol for privacy-preserving payments, where {one of the channel parties} is unable to see the channel balances. Then, we further propose $\textit{BlindHub}$, a three-party (sender, tumbler, receiver) protocol for private conditional payments, where the tumbler pays to the receiver only if the sender pays to the tumbler. The appealing additional feature of BlindHub is that the tumbler cannot link the sender and the receiver while supporting a variable payment amount. To construct BlindHub, we also introduce two new cryptographic primitives as building blocks, namely $\textit{Blind Adaptor Signature}$(BAS), and $\textit{Flexible Blind Conditional Signature}$. BAS is an adaptor signature protocol built on top of a blind signature scheme. Flexible Blind Conditional Signature is a new cryptographic notion enabling us to provide an atomic and privacy-preserving PCH. Lastly, we instantiate both BlindChannel and BlindHub protocols and present implementation results to show their practicality.

Designing novel symmetric-key primitives for advanced protocols like secure multiparty computation (MPC), fully homomorphic encryption (FHE) and zero-knowledge proof systems (ZK), has been an important research topic in recent years. Many such existing primitives adopt quite different design strategies from conventional block ciphers. Notable features include that many of these ciphers are defined over a large finite field, and that a power map is commonly used to construct the nonlinear component due to its efficiency in these applications as well as its strong resistance against the differential and linear cryptanalysis. In this paper, we target the MPC-friendly ciphers AIM and RAIN used for the post-quantum signature schemes AIMer (CCS 2023 and NIST PQC Round 1 Additional Signatures) and Rainier (CCS 2022), respectively. Specifically, we can find equivalent representations of 2-round RAIN and full-round AIM, respectively, which make them vulnerable to either the polynomial method, or the crossbred algorithm, or the fast exhaustive search attack. Consequently, we can break 2-round RAIN with the 128/192/256-bit key in only $2^{111}/2^{170}/2^{224}$ bit operations. For full-round AIM with the 128/192/256-bit key, we could break them in $2^{136.2}/2^{200.7}/2^{265}$ bit operations, which are equivalent to about $2^{115}/2^{178}/2^{241}$ calls of the underlying primitives. In particular, our analysis indicates that AIM does not reach the required security levels by the NIST competition.

In the recent work of (Cheon & Lee, Eurocrypt'22), the concept of a degree-$D$ packing method was formally introduced, which captures the idea of embedding multiple elements of a smaller ring into a larger ring, so that element-wise multiplication in the former is somewhat "compatible" with the product in the latter. Then, several optimal bounds and results are presented, and furthermore, the concept is generalized from one multiplication to degrees larger than two. These packing methods encompass several constructions seen in the literature in contexts like secure multiparty computation and fully homomorphic encryption. One such construction is the concept of reverse multiplication-friendly embeddings (RMFEs), which are essentially degree-2 packing methods. In this work we generalize the notion of RMFEs to \emph{degree-$D$ RMFEs} which, in spite of being "more algebraic" than packing methods, turn out to be essentially equivalent. Then, we present a general construction of degree-$D$ RMFEs by generalizing the ideas on algebraic geometry used to construct traditional degree-$2$ RMFEs which, by the aforementioned equivalence, leads to explicit constructions of packing methods. Furthermore, our theory is given in an unified manner for general Galois rings, which include both rings of the form $\mathbb{Z}_{p^k}$ and fields like $\mathbb{F}_{p^k}$, which have been treated separately in prior works. We present multiple concrete sets of parameters for degree-$D$ RMFEs (including $D=2$), which can be useful for future works. Finally, we apply our RMFEs to the task of non-interactively generating high degree correlations for secure multiparty computation protocols. This requires the use of Shamir secret sharing for a large number of parties, which is known to require large-degree Galois ring extensions. Our RMFE enables the generation of such preprocessing data over small rings, without paying for the multiplicative overhead incurred by using Galois ring extensions of large degree. For our application we also construct along the way, as a side contribution of potential independent interest, a pseudo-random secret-sharing solution for non-interactive generation of packed Shamir-sharings over Galois rings with structured secrets, inspired by the PRSS solutions from (Benhamouda et al, TCC 2021).

Lasso (Setty, Thaler, Wahby, ePrint 2023/1216) is a recent lookup argument that ensures that the prover cryptographically commits to only "small" values. This note describes BabySpartan, a SNARK for a large class of constraint systems that achieves the same property. The SNARK is a simple combination of SuperSpartan and Lasso. The specific class of constraint systems supported is a generalization of so-called Plonkish constraint systems (and a special case of customizable constraint systems (CCS)). Whereas a recent work called Jolt (Arun, Setty, and Thaler, ePrint 2023/1217) can be viewed as an application of Lasso to uniform computation, BabySpartan can be viewed as applying Lasso to non-uniform computation.

Updatable encryption (UE) enables a cloud server to update ciphertexts using client-generated tokens. There are two types of UE: ciphertext-independent (c-i) and ciphertext-dependent (c-d). In terms of construction and efficiency, c-i UE utilizes a single token to update all ciphertexts. The update mechanism relies mainly on the homomorphic properties of exponentiation, which limits the efficiency of encryption and updating. Although c-d UE may seem inconvenient as it requires downloading parts of the ciphertexts during token generation, it allows for easy implementation of the Dec-then-Enc structure. This methodology significantly simplifies the construction of the update mechanism. Notably, the c-d UE scheme proposed by Boneh et al. (ASIACRYPT’20) has been reported to be 200 times faster than prior UE schemes based on DDH hardness, which is the case for most existing c-i UE schemes. Furthermore, c-d UE ensures a high level of security as the token does not reveal any information about the key, which is difficult for c-i UE to achieve. However, previous security studies on c-d UE only addressed selective security; the studies for adaptive security remain an open problem. In this study, we make three significant contributions to ciphertextdependent updatable encryption (c-d UE). Firstly, we provide stronger security notions compared to previous work, which capture adaptive security and also consider the adversary’s decryption capabilities under the adaptive corruption setting. Secondly, we propose a new c-d UE scheme that achieves the proposed security notions. The token generation technique significantly differs from the previous Dec-then-Enc structure, while still preventing key leakages. At last, we introduce a packing technique that enables the simultaneous encryption and updating of multiple messages within a single ciphertext. This technique helps alleviate the cost of c-d UE by reducing the need to download partial ciphertexts during token generation.

We present a secret-key encryption scheme based on random rank metric ideal linear codes with a simple decryption circuit. It supports unlimited homomorphic additions and plaintext absorptions as well as a fixed arbitrary number of homomorphic multiplications. We study a candidate bootstrapping algorithm that requires no multiplication but additions and plaintext absorptions only. This latter operation is therefore very efficient in our scheme, whereas bootstrapping is usually the main reason which penalizes the performance of other fully homomorphic encryption schemes. However, the security reduction of our scheme restricts the number of independent ciphertexts that can be published. In particular, this prevents to securely evaluate the bootstrapping algorithm as the number of ciphertexts in the key switching material is too large. Our scheme is nonetheless the first somewhat homomorphic encryption scheme based on random ideal codes and a first step towards full homomorphism. Random ideal codes give stronger security guarantees as opposed to existing constructions based on highly structured codes. We give concrete parameters for our scheme that shows that it achieves competitive sizes and performance, with a key size of 3.7 kB and a ciphertext size of 0.9 kB when a single multiplication is allowed.

Arithmetization-Oriented primitives are the building block of advanced cryptographic protocols such as Zero-Knowledge proof systems. One approach to designing such primitives is the HADES design strategy which aims to provide an efficient way to instantiate generalizing substitution-permutation networks to include partial S-box rounds. A notable instance of HADES, introduced by Grassi \emph{et al.} at USENIX Security '21, is Poseidon. Because of its impressive efficiency and low arithmetic complexity, Poseidon is a popular choice among the designers of integrity-proof systems. An updated version of Poseidon, namely, Poseidon2 was published at AfricaCrypt '23 aiming to improve the efficiency of Poseidon by optimizing its linear operations. In this work, we show some caveats in the security argument of HADES against algebraic attacks and quantify the complexity of Gr\"{o}bner basis attacks. We show that the complexity of the attack is lower than claimed with the direct implication that there are cases where the recommended number of rounds is insufficient for meeting the claimed security. Concretely, the complexity of a Gr\"{o}bner basis attack for an instance of Poseidon with 1024 bits of security is 731.77 bits and the original security argument starts failing already at the 384-bit security level. Since the security of Poseidon2 is derived from the security of Poseidon, the same analysis applies to the instances of Poseidon2. The results were shared with the designers and the security arguments were updated accordingly.

This paper presents a comprehensive analysis of the verification algorithm of the CRYSTALS-Dilithium, focusing on a C reference implementation. Limited research has been conducted on its susceptibility to fault attacks, despite its critical role in ensuring the scheme’s security. To fill this gap, we investigate three distinct fault models - randomizing faults, zeroizing faults, and skipping faults - to identify vulnerabilities within the verification process. Based on our analysis, we propose a methodology for forging CRYSTALS-Dilithium signatures without knowledge of the secret key. Instead, we leverage specific types of faults during the verification phase and some properties about public parameters to make these signatures accepted. Additionally, we compared different attack scenarios after identifying sensitive operations within the verification algorithm. The most effective requires potentially fewer fault injections than targeting the verification check itself. Finally, we introduce a set of countermeasures designed to thwart all the identified scenarios rendering the verification algorithm intrinsically resistant to the presented attacks.

This paper examines the vulnerabilities inherent in prevailing Public Key Infrastructure (PKI) systems reliant on centralized Certificate Authorities (CAs), wherein a compromise of the CA introduces risks to the integrity of public key management. We present PKChain, a decentralized and compromise-tolerant public key management system built on blockchain technology, offering transparent, tamper-resistant, and verifiable services for key operations such as registration, update, query, validation, and revocation. Our innovative approach involves a novel threshold block validation scheme that combines a novel threshold cryptographic scheme with blockchain consensus. This scheme allows each validator to validate each public key record partially and proactively secures it before inclusion in a block. Additionally, to further validate and verify each block and to facilitate public verification of the public key records, we introduce an aggregate commitment signature scheme. Our contribution extends to the development of a new, efficient, and practical Byzantine Compromise-Tolerant and Verifiable (pBCTV) consensus model, integrating the proposed validation and signature schemes with practical Byzantine Fault Tolerance (pBFT). Through a comprehensive examination encompassing security analysis, performance evaluation, and a prototype implementation, we substantiate that PKChain is a secure, efficient, and robust solution for public key management.

Since its introduction at Asiacrypt 2017, the CKKS approximate homomorphic encryption scheme has become one of the most widely used and implemented homomorphic encryption schemes. Due to the approximate nature of the scheme, application developers using CKKS must ensure that the evaluation output is within a tolerable error of the corresponding plaintext computation. Choosing appropriate parameters requires a good understanding of how the noise will grow through the computation. A strong understanding of the noise growth is also necessary to limit the performance impact of mitigations to the attacks on CKKS presented by Li and Micciancio (Eurocrypt 2021). In this work we present a comprehensive noise analysis of CKKS, that considers noise coming both from the encoding and homomorphic operations. Our main contribution is the first average-case analysis for CKKS noise, and we also introduce refinements to prior worst-case noise analyses. We develop noise heuristics both for the original CKKS scheme and the RNS variant presented at SAC 2018. We then evaluate these heuristics by comparing the predicted noise growth with experiments in the HEAAN and FullRNS-HEAAN libraries, and by comparing with a worst-case noise analysis as done in prior work. Our findings show mixed results: while our new analyses lead to heuristic estimates that more closely model the observed noise growth than prior approaches, the new heuristics sometimes slightly underestimate the observed noise growth. This evidences the need for implementation-specific noise analyses for CKKS, which recent work has shown to be effective for implementations of similar schemes.

Post-compromise security (PCS) has been a core goal of end-to-end encrypted messaging applications for many years, both in one-to-one continuous key agreement (CKA) and for groups (CGKA). At its essence, PCS relies on a compromised party to perform a key update in order to `self-heal'. However, due to bandwidth constraints, receive-only mode, and various other environmental demands of the growing number of use cases for such CGKA protocols, a group member may not be able to issue such updates. In this work, we address the issue of devices functioning in limited mode through the introduction of guardianship, where a designated guardian can perform key updates on the behalf of its paired edge device. We introduce a Guardianship PCS (GPCS) security, and provide an associated security experiment. We investigate various architectural designs in the pursuit of GPCS, provide constructions and security analyses, and describe trade-offs.

Deploying cryptography on embedded systems requires security against physical attacks. At CHES 2019, M&M was proposed as a combined countermeasure applying masking against SCAs and information-theoretic MAC tags against FAs. In this paper, we show that one of the protected AES implementations in the M&M paper is vulnerable to a zero-value SIFA2-like attack. A practical attack is demonstrated on an ASIC board. We propose two versions of the attack: the first follows the SIFA approach to inject faults in the last round, while the second one is an extension of SIFA and FTA but applied to the first round with chosen plaintext. The two versions work at the byte level, but the latter version considerably improves the efficiency of the attack. Moreover, we show that this zero-value SIFA2 attack is specific to the AES tower-field decomposed S-box design. Hence, such attacks are applicable to any implementation featuring this AES S-box architecture. Then, we propose a countermeasure that prevents these attacks. We extend M&M with a fine-grained detection-based feature capable of detecting the zero-value glitch attacks. In this effort, we also solve the problem of a combined attack on the ciphertext output check of M&M scheme by using Kronecker's delta function. We deploy the countermeasure on FPGA and verify its security against both fault and side-channel analysis with practical experiments.

Let's consider a scenario where the server encrypts data using AES-CBC without authentication and then sends only the encrypted ciphertext through TLS (without IV). Then, having a padding oracle, we managed to recover the initialization vector and the sensitive data, doing a cybersecurity audit for a Chilean company.

The classic stable matching algorithm of Gale and Shapley (American Mathematical Monthly '69) and subsequent variants such as those by Roth (Mathematics of Operations Research '82) and Abdulkadiroglu et al. (American Economic Review '05) have been used successfully in a number of real-world scenarios, including the assignment of medical-school graduates to residency programs, New York City teenagers to high schools, and Norwegian and Singaporean students to schools and universities. However, all of these suffer from one shortcoming: in order to avoid strategic manipulation, they require all participants to submit their preferences to a trusted third party who performs the computation. In some sensitive application scenarios, there is no appropriate (or cost-effective) trusted party. This makes stable matching a natural candidate for secure computation. Several approaches have been proposed to overcome this, based on secure multiparty computation (MPC), fully homomorphic encryption, etc.; many of these protocols are slow and impractical for real-world use. We propose a novel primitive for privacy-preserving stable matching using MPC (i.e., arithmetic circuits, for any number of parties). Specifically, we discuss two variants of oblivious stable matching and describe an improved oblivious stable matching on the random memory access model based on lookup tables. To explore and showcase the practicality of our proposed primitive, we present detailed benchmarks (at various problem sizes) of our constructions using two popular frameworks: SCALE-MAMBA and MP-SPDZ.

Homomorphic Encryption (HE) schemes such as BGV, BFV, and CKKS consume some ciphertext modulus for each multiplication. Bootstrapping (BTS) restores the modulus and allows homomorphic computation to continue, but it is time-consuming and requires a significant amount of modulus. For these reasons, decreasing modulus consumption is crucial topic for BGV, BFV and CKKS, on which numerous studies have been conducted. We propose a novel method, called $\mathsf{mult}^2$, to perform ciphertext multiplication in the CKKS scheme with lower modulus consumption. $\mathsf{mult}^2$ relies an a new decomposition of a ciphertext into a pair of ciphertexts that homomorphically performs a weak form of Euclidean division. It multiplies two ciphertexts in decomposed formats with homomorphic double precision multiplication, and its result approximately decrypts to the same value as does the ordinary CKKS multiplication. $\mathsf{mult}^2$ can perform homomorphic multiplication by consuming almost half of the modulus. We extend it to $\mathsf{mult}^t$ for any $t\geq 2$, which relies on the decomposition of a ciphertext into $t$ components. All other CKKS operations can be equally performed on pair/tuple formats, leading to the double-CKKS (resp. tuple-CKKS) scheme enabling homomorphic double (resp. multiple) precision arithmetic. As a result, when the ciphertext modulus and dimension are fixed, the proposed algorithms enable the evaluation of deeper circuits without bootstrapping, or allow to reduce the number of bootstrappings required for the evaluation of the same circuits. Furthermore, they can be used to increase the precision without increasing the parameters. For example, $\mathsf{mult}^2$ enables 8 sequential multiplications with 100 bit scaling factor with a ciphertext modulus of only 680 bits, which is impossible with the ordinary CKKS multiplication algorithm.

We show how to obfuscate pseudo-deterministic quantum circuits in the classical oracle model, assuming the quantum hardness of learning with errors. Given the classical description of a quantum circuit $Q$, our obfuscator outputs a quantum state $\ket{\widetilde{Q}}$ that can be used to evaluate $Q$ repeatedly on arbitrary inputs. Instantiating the classical oracle using any candidate post-quantum indistinguishability obfuscator gives us the first candidate construction of indistinguishability obfuscation for all polynomial-size pseudo-deterministic quantum circuits. In particular, our scheme is the first candidate obfuscator for a class of circuits that is powerful enough to implement Shor's algorithm (SICOMP 1997). Our approach follows Bartusek and Malavolta (ITCS 2022), who obfuscate \emph{null} quantum circuits by obfuscating the verifier of an appropriate classical verification of quantum computation (CVQC) scheme. We go beyond null circuits by constructing a publicly-verifiable CVQC scheme for quantum \emph{partitioning} circuits, which can be used to verify the evaluation procedure of Mahadev's quantum fully-homomorphic encryption scheme (FOCS 2018). We achieve this by upgrading the one-time secure scheme of Bartusek (TCC 2021) to a fully reusable scheme, via a publicly-decodable \emph{Pauli functional commitment}, which we formally define and construct in this work. This commitment scheme, which satisfies a notion of binding against committers that can access the receiver's standard and Hadamard basis decoding functionalities, is constructed by building on techniques of Amos, Georgiou, Kiayias, and Zhandry (STOC 2020) introduced in the context of equivocal but collision-resistant hash functions.

In this paper we revise the idea of our previous work ‘Lin2-Xor lemma and Log-size Linkable Threshold Ring Signature’ and introduce another lemma, called Lin2-Choice, which extends the Lin2-Xor lemma. Using an novel zero-knowledge membership proof argument defined in the Lin2-Choice lemma, we create a compact general-purpose trusted-setup-free log-size linkable threshold ring signature called EFLRSL. The signature size is 2log(n+1)+3l+1, where n is the ring size and l is the threshold. By extending the membership argument of the Lin2-Choice lemma, we create a multifunctional version of the EFLRSL signature aliased as Multratug, of size 2log(n+l+1)+7l+4. In addition to signing a message, Multratug simultaneously proves balance and allows for easy multiparty signing. We use an arbitrary vector commitment argument in the role of the pivotal building block for both versions of our signature, considering it as a black box. Only the black-boxed pivot contributes components that depend on the ring size n into the signature sizes. This makes both of EFLRSL and Multratug combinable with other proofs, with overall size reduction. All this takes place in a prime-order group without bilinear parings under the decisional Diffie-Hellman assumption in the random oracle model. Both versions of our signature are proved unforgeable w.r.t. insider corruption and existentially unforgeable under chosen message attack. They remain anonymous even for non-uniformly distributed and malformed keys, which makes it possible to use them as a log-size drop-in replacement for LSAG-based schemes.

We consider the mainstream model in secure computation known as the bare PKI setup, also as the {bulletin-board PKI}. It allows players to broadcast once and non-interactively before they receive their inputs and start the execution. A bulletin-board PKI is essentially the minimum setup known so far to implement the model known as {messages-authentication}, i.e., when $P$ is forwarded a signed message, it considers it to be issued by $R$ if and only if $R$ signed it. It is known since [Lamport et al, 82] that BA under honest majority (let alone secure computation) would not be possible without messages-authentication. But as further highlighted by [Borcherding, 96], messages-authentication cannot not simply be implemented with digital signatures, without a bulletin-board of public keys. So the bulletin-board PKI setup and the messages-authentication model seem very close: this raizes the question whether there is a separation between them. In the bulletin-board PKI setup, the most communication-efficient synchronous BA is the one of [Boyle-Cohen-Goel, Podc'21 \& J. Cryptol.'24], which has $O(n.\text{polylog}(n))$ bit complexity, $f<n(1/3-\epsilon)$ resilience and tolerates an adversary which cannot adaptively corrupt after the setup. Our main upper-bound is a BA (and also a VBA) in this same model with strictly better parameters: {quasi-optimal} resilience $f<n(1/2-\epsilon)$, with an expected bit complexity of communications which is {linear} in $n$, and tolerance to an {adaptive} rushing adversary (but which unavoidably cannot remove messages sent). As [BCG'21], they have constant expected latency. All previous BAs or VBAs achieving the same metrics as our upper bound, are either in the static adversary model: Sleepy [Pass-Shi, Asiacrypt'17], Snow White [Daian-Pass-Shi, FC'19], or assume more than a bare PKI setup: (i) The model of Thunderella [Pass-Shi, EC'17], Algorand [Gilad et al, SOSP'17], Praos [David et al, EC'18], [Goyal et al, FC'21] and [Momose et al, CCS'22 and CCS'23] assumes a public random seed which is unpredictable until strictly after all players published on the bulletin board; (ii) [Abraham et al, Podc'19] assume a trusted entity which honestly samples the keys of all players; (iii) All known implementations of the setups (i) and (ii), as well as the setup of [Blum et al, TCC'20], require interactions, furthermore in the form of BAs. (iv) [Garay-Kiayas-Shen '23] assume that honest players work more than the adversary, or, [Eckey-Faust-Loss et al '17 '22] at least as fast. Of independent interest, our tool is a very simple non-interactive mechanism which {sets-up a self-sortition function from non-interactive publications on the bulletin board}, and still, guarantees an honest majority in every committee up to probability exponentially small in both $\epsilon$ and in the multicast complexity. We provide the following further results: {- Optimality.} We show that resilience up to a tight honest majority $f<n/2$ is impossible for any multicast-based adaptively secure BA with subquadratic communication, whatever the setup. {- Separation.} We show impossibility of subquadratic multicast-based BA in the messages-authentication model. Our model for this lower bound is even stronger, since it onboards other assumptions at least as strong as all popular implications of a bulletin-board PKI setup: {secure channels}, {a (possibly structured) random string}, {NIZK}. {- Partial synchrony.} Given that the multicast lower-bound holds a fortiori, and that the upper-bound adapts seamlessly (for $f<n(1/3-\epsilon)$), the separation also holds. We show a second separation, which holds for general BAs, non-necessarily multicast-based: any partially-synchronous BA in the messages-authentication model, if it has linear message complexity, then it has latency at least {logarithmic in $f$}. {- Extension to VBA.} We extend to VBA the logarithmic latency lower bound. This is the first communication lower bound for randomized VBA to our knowledge. It shows that the separation under partial synchrony also holds for VBA. Along the way, we close the characterization of [Civit et al, Podc'23] of validity conditions in authenticated consensus, by apparently new results on VBA: both BA and VBA are infeasible under partial synchrony beyond $f<n/3$, whatever the setup; whereas synchronous VBA is feasible up to $f=n-1$ (contrary to BA).

Privacy-preserving blueprints enable users to create escrows using the auditor's public key. An escrow encrypts the evaluation of a function $P(t,x)$, where $t$ is a secret input used to generate the auditor's key and $x$ is the user's private input to escrow generation. Nothing but $P(t,x)$ is revealed even to a fully corrupted auditor. The original definition and construction (Kohlweiss et al., EUROCRYPT'23) only support the evaluation of functions on an input $x$ provided by a single user. We address this limitation by introducing updatable privacy-preserving blueprint schemes (UPPB), which enhance the original notion with the ability for multiple parties to non-interactively update the private value $x$ in a blueprint. Moreover, a UPPB scheme allows for verifying that a blueprint is the result of a sequence of valid updates while revealing nothing else. We present uBlu, an efficient instantiation of UPPB for computing a comparison between private user values and a private threshold $t$ set by the auditor, where the current value $x$ is the cumulative sum of private inputs, which enables applications such as privacy-preserving anti-money laundering and location tracking. Additionally, we show the feasibility of the notion generically for all value update functions and (binary) predicates from FHE and NIZKs. Our main technical contribution is a technique to keep the size of primary blueprint components independent of the number of updates and reasonable for practical applications. This is achieved by elegantly extending an algebraic NIZK by Couteau and Hartmann (CRYPTO'20) with an update function and making it compatible with our additive updates. This result is of independent interest and may find additional applications thanks to the concise size of our proofs.

The Crossbred algorithm is one of the algorithms for solving a system of polynomial equations, proposed by Joux and Vitse in 2017. It has been implemented in Fukuoka MQ challenge, which is related to the security of multivariate crytography, and holds several records. A framework for estimating the complexity has already been provided by Chen et al. in 2017. However, it is generally unknown which parameters are actually available. This paper investigates how to select available parameters for the Crossbred algorithm. As a result, we provide formulae that give an available parameter set and estimate the complexity of the Crossbred algorithm.

In this paper, we perform a systematic study of functions $f: \mathbb{Z}_{p^e} \to \mathbb{Z}_{p^e}$ and categorize those functions that can be represented by a polynomial with integer coefficients. More specifically, we cover the following properties: necessary and sufficient conditions for the existence of an integer polynomial representation; computation of such a representation; and the complete set of equivalent polynomials that represent a given function. As an application, we use the newly developed theory to speed up bootstrapping for the BGV and BFV homomorphic encryption schemes. The crucial ingredient underlying our improvements is the existence of null polynomials, i.e. non-zero polynomials that evaluate to zero in every point. We exploit the rich algebraic structure of these null polynomials to find better representations of the digit extraction function, which is the main bottleneck in bootstrapping. As such, we obtain sparse polynomials that have 50% fewer coefficients than the original ones. In addition, we propose a new method to decompose digit extraction as a series of polynomial evaluations. This lowers the time complexity from $\mathcal{O}(\sqrt{pe})$ to $\mathcal{O}(\sqrt{p}\sqrt[^4]{e})$ for digit extraction modulo $p^e$, at the cost of a slight increase in multiplicative depth. Overall, our implementation in HElib shows a significant speedup of a factor up to 2.6 over the state-of-the-art.

We unify the state-of-the-art bootstrapping algorithms for BGV and BFV in a single framework, and show that both schemes can be bootstrapped with identical complexity. This result corrects a claim by Chen and Han (Eurocrypt 2018) that BFV is more efficient to bootstrap than BGV. We also fix an error in their optimized procedure for power-of-two cyclotomics, which occurs for some parameter sets. Our analysis is simpler, yet more general than earlier work, in that it simultaneously covers both BGV and BFV. Furthermore, we also design and implement a high-level open source software library for bootstrapping in the Magma Computer Algebra System. It is the first library to support both BGV and BFV bootstrapping in full generality, with all recent techniques (including the above fixes) and trade-offs.

Optimization of finite field arithmetic is important for the deployment of public key cryptography, particularly in the context of elliptic curve cryptography. Until now the primary concern has been operations over the prime field $\F_p$, where $p$ is a prime. With the advent of pairing-based cryptography there arises a need to also look at optimal arithmetic over extension fields $\F_{p^n}$ for small values of $n$. Here we focus on the determination of quadratic residuosity and the calculation of inverses and square roots over these fields, operations often carried out in conjunction with one another. We demonstrate with a minor improvement in a hash-to-curve algorithm, and a major speed-up in the calculation of square roots in quadratic extensions.

In their 2022 study, Kuang et al. introduced the Multivariable Polynomial Public Key (MPPK) cryptography, a quantum-safe public key cryptosystem leveraging the mutual inversion relationship between multiplication and division. MPPK employs multiplication for key pair construction and division for decryption, generating public multivariate polynomials. Kuang and Perepechaenko expanded the cryptosystem into the Homomorphic Polynomial Public Key (HPPK), transforming product polynomials over large hidden rings using homomorphic encryption through modular multiplications. Initially designed for key encapsulation mechanism (KEM), HPPK ensures security through homomorphic encryption of public polynomials over concealed rings. This paper extends its application to a digital signature scheme. The framework of HPPK KEM can not be directly applied to the digital signatures dues to the different nature of verification procedure compared to decryption procedure. Thus, in order to use the core ideas of the HPPK KEM scheme in the framework of digital signatures, the authors introduce an extension of the Barrett reduction algorithm. This extension transforms modular multiplications over hidden rings into divisions in the verification equation, conducted over a prime field. The extended algorithm non-linearly embeds the signature into public polynomial coefficients, employing the floor function of big integer divisions. This innovative approach overcomes vulnerabilities associated with linear relationships of earlier MPPK DS schemes. The security analysis reveals exponential complexity for both private key recovery and forged signature attacks, taking into account that the bit length of the rings is twice that of the prime field size. The effectiveness of the proposed Homomorphic Polynomial Public Key Digital Signature (HPPK DS) scheme is illustrated through a practical toy example, showcasing its intricate functionality and enhanced security features.

Recent private information retrieval (PIR) schemes preprocess the database with a query-independent offline phase in order to achieve sublinear computation during a query-specific online phase. These offline/online protocols expand the set of applications that can profitably use PIR, but they make a critical assumption: that the database is immutable. In the presence of changes such as additions, deletions, or updates, existing schemes must preprocess the database from scratch, wasting prior effort. To address this, we introduce incremental preprocessing for offline/online PIR schemes, allowing the original preprocessing to continue to be used after database changes, while incurring an update cost proportional to the number of changes rather than the size of the database. We adapt two offline/online PIR schemes to use incremental preprocessing and show how it significantly improves the throughput and reduces the latency of applications where the database changes over time.