IACR Communications in Cryptology
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Attacking trapdoors from matrix products
Get PDF Recently, Geraud-Stewart and Naccache proposed two trapdoors based on matrix products. In this paper, we answer the call for cryptanalysis. We explore how using the trace and determinant of a matrix can be used to attack their constructions. We fully break their first construction in a polynomial-time attack. We show an information leak in the second construction using characteristic polynomials, and provide two attacks that decrease the bit security by about half. </p
Almost pairwise independence and resilience to deep learning attacks
Get PDFAlmost pairwise independence (API) is a quantitative property of a class of functions that is desirable in many cryptographic applications. This property is satisfied by Learning with errors (LWE)-mappings and by special Substitution-Permutation Networks (SPN). API block ciphers are known to be resilient to differential and linear cryptanalysis attacks. Recently, security of protocols against neural network-based attacks became a major trend in cryptographic studies. Therefore, it is relevant to study the hardness of learning a target function from an API class of functions by gradient-based methods.We propose a theoretical analysis based on the study of the variance of the gradient of a general machine learning objective with respect to a random choice of target function from a class. We prove an upper bound and verify that, indeed, such a variance is extremely small for API classes of functions. This implies the resilience of actual LWE-based primitives against deep learning attacks, and to some extent, the security of SPNs. The hardness of learning reveals itself in the form of the barren plateau phenomenon during the training process, or in other words, in a low information content of the gradient about the target function. Yet, we emphasize that our bounds hold for the case of a regular parameterization of a neural network and the gradient may become informative if a class is mildly pairwise independent and a parameterization is non-regular. We demonstrate our theory in experiments on the learnability of LWE mappings. </p
The Uber-Knowledge Assumption: A Bridge to the AGM
Get PDFThe generic-group model (GGM) and the algebraic-group model (AGM) have been exceptionally successful in proving the security of many classical and modern cryptosystems. These models, however, come with standard-model uninstantiability results, raising the question of whether the schemes analyzed under them can be based on firmer standard-model footing.We formulate the uber-knowledge (UK) assumption, a standard-model assumption that naturally extends the uber-assumption family to knowledge-type problems. We justify the soundness of UK in both the bilinear GGM and the bilinear AGM. Along the way we extend these models to account for hashing into groups, an adversarial capability that is available in many concrete groups—In contrast to standard assumptions, hashing may affect the validity of knowledge assumptions. These results, in turn, enable a modular approach to security in the GGM and the AGM.As example applications, we use the UK assumption to prove knowledge soundness of Groth\u27s zero-knowledge SNARK (EUROCRYPT 2016) and of KZG polynomial commitments (ASIACRYPT 2010) in the standard model, where for the former we reuse the existing proof in the AGM without hashing. </p
A short-list of pairing-friendly curves resistant to the Special TNFS algorithm at the 192-bit security level
Get PDFFor more than two decades, pairings have been a fundamental tool for designing elegant cryptosystems, varying from digital signature schemes to more complex privacy-preserving constructions. However, the advancement of quantum computing threatens to undermine public-key cryptography. Concretely, it is widely accepted that a future large-scale quantum computer would be capable to break any public-key cryptosystem used today, rendering today\u27s public-key cryptography obsolete and mandating the transition to quantum-safe cryptographic solutions. This necessity is enforced by numerous recognized government bodies around the world, including NIST which initiated the first open competition in standardizing post-quantum (PQ) cryptographic schemes, focusing primarily on digital signatures and key encapsulation/public-key encryption schemes. Despite the current efforts in standardizing PQ primitives, the landscape of complex, privacy-preserving cryptographic protocols, e.g., zkSNARKs/zkSTARKs, is at an early stage. Existing solutions suffer from various disadvantages in terms of efficiency and compactness and in addition, they need to undergo the required scrutiny to gain the necessary trust in the academic and industrial domains. Therefore, it is believed that the migration to purely quantum-safe cryptography would require an intermediate step where current classically secure protocols and quantum-safe solutions will co-exist. This is enforced by the report of the Commercial National Security Algorithm Suite version 2.0, mandating transition to quantum-safe cryptographic algorithms by 2033 and suggesting to incorporate ECC at 192-bit security in the meantime. To this end, the present paper aims at providing a comprehensive study on pairings at 192-bit security level. We start with an exhaustive review in the literature to search for all possible recommendations of such pairing constructions, from which we extract the most promising candidates in terms of efficiency and security, with respect to the advanced Special TNFS attacks. Our analysis is focused, not only on the pairing computation itself, but on additional operations that are relevant in pairing-based applications, such as hashing to pairing groups, cofactor clearing and subgroup membership testing. We implement all functionalities of the most promising candidates within the RELIC cryptographic toolkit in order to identify the most efficient pairing implementation at 192-bit security and provide extensive experimental results. </p
Cryptanalysis of TS-Hash
Get PDF This note presents attacks on the lightweight hash function TS-Hash proposed by Tsaban, including a polynomial-time preimage attack for short messages (at most bits), high-probability differentials, a general subexponential-time preimage attack, and linearization techniques. </p
Unforgeability of Blind Schnorr in the Limited Concurrency Setting
Get PDFBlind signature schemes enable a user to obtain a digital signature on a message from a signer without revealing the message itself. Among the most fundamental examples of such a scheme is blind Schnorr, but recent results show that it does not satisfy the standard notion of security against malicious users, One-More Unforgeability (OMUF), as it is vulnerable to the ROS attack. However, blind Schnorr does satisfy the weaker notion of sequential OMUF, in which only one signing session is open at a time, in the Algebraic Group Model (AGM) + Random Oracle Model (ROM), assuming the hardness of the Discrete Logarithm (DL) problem.This paper serves as a first step towards characterizing the security of blind Schnorr in the limited concurrency setting. Specifically, we show that blind Schnorr satisfies OMUF when at most two signing sessions can be concurrently open (in the AGM+ROM, assuming DL). Our argument suggests that it is plausible that blind Schnorr satisfies OMUF for up to polylogarithmically many concurrent signing sessions. Our security proof involves interesting techniques from linear algebra and combinatorics. </p
Improving Differential-Neural Cryptanalysis
Get PDF Our first objective is to enhance the capabilities of differential-neural distinguishers by applying more deep-learning techniques, focusing on handling more rounds and improving accuracy. Inspired by the Inception Block in GoogLeNet, we adopted a design that uses multiple parallel convolutional layers with varying kernel sizes before the residual block to capture multi-dimensional information. Additionally, we expanded the convolutional kernels in the residual blocks, enlarging the network\u27s receptive field. In the case of Speck32/64, our efforts yield accuracy improvements in rounds 6, 7, and 8, enabling the successful training of a 9-round differential-neural distinguisher. As for Simon32/64, we developed a differential-neural distinguisher capable of effectively handling 12 rounds while achieving noteworthy accuracy enhancements in rounds 9, 10, and 11. Additionally, we utilized neutral bits to ensure the required data distribution for launching a successful key recovery attack when using multiple-ciphertext pairs as input for the neural network. Meanwhile, we redefined the formula for time complexity based on the differences in prediction speeds of the distinguisher between a single-core CPU and a GPU. Combining these various advancements allows us to considerably reduce the time and data complexity of key recovery attacks on 13-round Speck32/64. Furthermore, we used knowledge distillation techniques to reduce the model size, accelerating the distinguisher\u27s prediction speed and reducing the time complexity. In particular, we achieved a successful 14-round key recovery attack by exhaustively guessing a 1-round subkey. For Simon32/64, we accomplished a 17-round key recovery attack for the first time and reduced the time complexity of the 16-round key recovery attack. </p
Unpacking Needs Protection A Single-Trace Secret Key Recovery Attack on Dilithium
Get PDFMost of the previous attacks on Dilithium exploit side-channel information which is leaked during the computation of the polynomial multiplication cs1, where s1 is a small-norm secret and c is a verifier\u27s challenge. In this paper, we present a new attack utilizing leakage during secret key unpacking in the signing algorithm. The unpacking is also used in other post-quantum cryptographic algorithms, including Kyber, because inputs and outputs of their API functions are byte arrays. Exploiting leakage during unpacking is more challenging than exploiting leakage during the computation of cs1 since c varies for each signing, while the unpacked secret key remains constant. Therefore, post-processing is required in the latter case to recover a full secret key. We present two variants of post-processing. In the first one, a half of the coefficients of the secret s1 and the error s2 is recovered by profiled deep learning-assisted power analysis and the rest is derived by solving linear equations based on t = As1 + s2, where A and t are parts of the public key. This case assumes knowledge of the least significant bits of t, t0. The second variant uses lattice reduction to derive s1 without the knowledge of t0. However, it needs a larger portion of s1 to be recovered by power analysis. We evaluate both variants on an ARM Cortex-M4 implementation of Dilithium-2. The experiments show that the attack assuming the knowledge of t0 can recover s1 from a single trace captured from a different from profiling device with a non-negligible probability. </p
A Central Limit Approach for Ring-LWE Noise Analysis
Get PDFThis paper develops Central Limit arguments for analysing the noise in ciphertexts in two homomorphic encryption schemes that are based on Ring-LWE. The first main contribution of this paper is to present and evaluate an average-case noise analysis for the BGV scheme. Our approach relies on the recent work of Costache et al.(SAC 2023) that gives the approximation of a polynomial product as a multivariate Normal distribution. We show how this result can be applied in the BGV context and evaluate its efficacy. We find this average-case approach can much more closely model the noise growth in BGV implementations than prior approaches, but in some cases it can also underestimate the practical noise growth. Our second main contribution is to develop a Central Limit framework to analyse the noise growth in the homomorphic Ring-LWE cryptosystem of Lyubashevsky, Peikert and Regev (Eurocrypt 2013, full version). Our approach is very general: apart from finite variance, no assumption on the distribution of the noise is required (in particular, the noise need not be subgaussian). We show that our approach leads to tighter bounds for the probability of decryption failure than those of prior work. </p
Public-Key Authenticated Encryption with Keyword Search Made Easy
Get PDF Public-key searchable encryption allows keyword-associated tokens to be used to test if a ciphertext contains specific keywords. Due to the low entropies of keywords, the token holder can create ciphertexts from candidate keywords and test them using the token in hand to recover the keywords, known as inside keyword guessing attacks (IKGA). Public-key authenticated encryption with keyword search is a searchable encryption proposed to defend against such attacks. It ensures the sender\u27s private key protects the ciphertexts from the IKGA. PAEKS schemes with reasonable security and practical efficiency remain elusive despite many proposals. This work provides a simple generic PAEKS scheme from non-interactive key exchange (NIKE) and symmetric-key equality-predicate encryption with three new constructions for the latter, respectively from pseudorandom functions (PRFs), the decision bilinear Diffie-Hellman assumption, and the learning-with-errors assumption. Instantiating our generic scheme, we derive several PAEKS schemes from the most well-known assumptions, with some of them achieving full cipher-keyword indistinguishability and full token indistinguishability in the standard model, for the first time. Our instantiated schemes allow practical implementations and outperform the existing PAEKS schemes under the same assumptions. </p