##### 12 results sorted by publication date

We generalize and abstract the problem of extracting a witness from a prover of a special sound protocol into a combinatorial problem induced by a sequence of matroids and a predicate, and present a parametrized algorithm for solving this problem.

The parametrization provides a tight tradeoff between the running time and the extraction error of the algorithm, which allows optimizing the parameters to minimize: the soundness error for interactive proofs, or the extraction time for proofs of knowledge.

In contrast to previous work we bound the distribution of the running time and not only the expected running time. Tail bounds give a tighter analysis when applied recursively and a concentrated running time.

Mixed-Integer Linear Programming (MILP) modeling has become an important tool for both the analysis and the design of symmetric cryptographic primitives. The bit-wise modeling of their nonlinear components, especially the S-boxes, is of particular interest since it allows more informative analysis compared to word-oriented models focusing on counting active S-boxes. At the same time, the size of these models, especially in terms of the number of required inequalities, tends to significantly influence and ultimately limit the applicability of this method to real-world ciphers, especially for larger number of rounds.

It is therefore of great cryptographic significance to study optimal linear inequality descriptions for Boolean functions. The pioneering works of Abdelkhalek et al. (FSE 2017), Boura and Coggia (FSE 2020) and Li and Sun (FSE 2023) provided various heuristic techniques for this computationally hard problem, decomposing it into two algorithmic steps, coined Problem 1 and Problem 2, with the latter being identical to the well-known NP-hard set cover problem, for which there are many heuristic and exact algorithms in the literature.

In this paper, we introduce a novel and efficient branch-and-bound algorithm for generating all minimal, non-redundant candidate inequalities that satisfy a given Boolean function, therefore solving Problem 1 in an optimal manner without relying on heuristics. We furthermore prove that our algorithm correctly computes optimal solutions. Using a number of dedicated optimizations, it provides significantly improved runtimes compared to previous approaches and allows the optimal modeling of the difference distribution tables (DDT) and linear approximation tables (LAT) of many practically used S-boxes. The source code for our algorithm is publicly available as a tool for researchers and practitioners in symmetric cryptography.

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's 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's 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.

New proposals for scalable key rank estimation methods have appeared recently, in particular the sampling based approach MCRank. The idea is that one can consistently estimate the key rank by sampling only a small portion of the key space as a “proxy”, leading to both an accurate and scalable approach, at least in comparison with another approach based on histograms. We show that the (earlier) GEEA algorithm is in fact a sampling based algorithm, and provide an in-depth comparison between GEEA (when adapted to produce rank estimates rather than guessing entropy estimates), GM bounds, MCRank and the currently most performant counting based rank estimation as implemented in the Labynkyr library. We find that although MCRank does live up to the promised accuracy and scalability for probability-based distinguishers, it fails to handle cases with unusual distinguisher distributions.

Furthermore, we put forward a novel proposal for a highly scalable key rank estimation method by introducing the notion of an “attacker budget”. Our proposal is based on the idea that, in particular for very long keys, the exact key rank is less important than the knowledge whether a key is within a certain bound. Thus our “budget approach” is based on efficiently checking if the result of an attack is such that the attacker's budget suffices for successful enumeration. Our budget approach scales linearly with the key size and thus enables security estimations even for post-quantum key lengths.

Raccoon is a lattice-based scheme submitted to the NIST 2022 call for additional post-quantum signatures. One of its main selling points is that its design is intrinsically easy to mask against side-channel attacks. So far, Raccoon's physical security guarantees were only stated in the abstract probing model. In this paper, we discuss how these probing security results translate into guarantees in more realistic leakage models. We also highlight that this translation differs from what is usually observed (e.g., in symmetric cryptography), due to the algebraic structure of Raccoon's operations. For this purpose, we perform an in-depth information theoretic evaluation of Raccoon's most innovative part, namely the AddRepNoise function which allows generating its arithmetic shares on-the-fly. Our results are twofold. First, we show that the resulting shares do not enforce a statistical security order (i.e., the need for the side-channel adversary to estimate higher-order moments of the leakage distribution), as usually expected when masking. Second, we observe that the first-order leakage on the (large) random coefficients manipulated by Raccoon cannot be efficiently turned into leakage on the (smaller) coefficients of its long-term secret. Concretely, our information theoretic evaluations for relevant leakage functions also suggest that Raccoon's masked implementations can ensure high security with less shares than suggested by a conservative analysis in the probing model.

Masking is a prominent strategy to protect cryptographic implementations against side-channel analysis. Its popularity arises from the exponential security gains that can be achieved for (approximately) quadratic resource utilization. Many variants of the countermeasure tailored for different optimization goals have been proposed. The common denominator among all of them is the implicit demand for robust and high entropy randomness. Simply assuming that uniformly distributed random bits are available, without taking the cost of their generation into account, leads to a poor understanding of the efficiency vs. security tradeoff of masked implementations. This is especially relevant in case of hardware masking schemes which are known to consume large amounts of random bits per cycle due to parallelism. Currently, there seems to be no consensus on how to most efficiently derive many pseudo-random bits per clock cycle from an initial seed and with properties suitable for masked hardware implementations. In this work, we evaluate a number of building blocks for this purpose and find that hardware-oriented stream ciphers like Trivium and its reduced-security variant Bivium B outperform most competitors when implemented in an unrolled fashion. Unrolled implementations of these primitives enable the flexible generation of many bits per cycle, which is crucial for satisfying the large randomness demands of state-of-the-art masking schemes. According to our analysis, only Linear Feedback Shift Registers (LFSRs), when also unrolled, are capable of producing long non-repetitive sequences of random-looking bits at a higher rate per cycle for the same or lower cost as Trivium and Bivium B. Yet, these instances do not provide black-box security as they generate only linear outputs. We experimentally demonstrate that using multiple output bits from an LFSR in the same masked implementation can violate probing security and even lead to harmful randomness cancellations. Circumventing these problems, and enabling an independent analysis of randomness generation and masking, requires the use of cryptographically stronger primitives like stream ciphers. As a result of our studies, we provide an evidence-based estimate for the cost of securely generating $n$ fresh random bits per cycle. Depending on the desired level of black-box security and operating frequency, this cost can be as low as $20n$ to $30n$ ASIC gate equivalents (GE) or $3n$ to $4n$ FPGA look-up tables (LUTs), where $n$ is the number of random bits required. Our results demonstrate that the cost per bit is (sometimes significantly) lower than estimated in previous works, incentivizing parallelism whenever exploitable. This provides further motivation to potentially move low randomness usage from a primary to a secondary design goal in hardware masking research.

Traitor tracing schemes [Chor–Fiat–Naor, Crypto ’94] help content distributors fight against piracy and are defined with the content distributor as a trusted authority having access to the secret keys of all users. While the traditional model caters well to its original motivation, its centralized nature makes it unsuitable for many scenarios. For usage among mutually untrusted parties, a notion of *ad hoc* traitor tracing (naturally with the capability of broadcast and revocation) is proposed and studied in this work. Such a scheme allows users in the system to generate their own public/secret key pairs, without trusting any other entity. To encrypt, a list of public keys is used to identify the set of recipients, and decryption is possible with a secret key for any of the public keys in the list. In addition, there is a tracing algorithm that given a list of recipients’ public keys and a pirate decoder capable of decrypting ciphertexts encrypted to them, identifies at least one recipient whose secret key must have been used to construct the said decoder.

Two constructions are presented. The first is based on functional encryption for circuits (conceptually, obfuscation) and has constant-size ciphertext, yet its decryption time is linear in the number of recipients. The second is a generic transformation that reduces decryption time at the cost of increased ciphertext size. A matching lower bound on the trade-off between ciphertext size and decryption time is shown, indicating that the two constructions achieve all possible optimal trade-offs, i.e., they fully demonstrate the Pareto front of efficiency. The lower bound also applies to broadcast encryption (hence all mildly expressive attribute-based encryption schemes) and is of independent interest.

Distributed key generation (DKG) is a key building block in developing many efficient threshold cryptosystems. This work initiates the study of communication complexity and round complexity of DKG protocols over a point-to-point (bounded) synchronous network. Our key result is the first synchronous DKG protocol for discrete log-based cryptosystems with $O(\kappa n^3)$ communication complexity ($\kappa$ denotes a security parameter) that tolerates any $t < n/2$ Byzantine faults among $n$ parties. We present two variants of the protocol: (i) a protocol with worst-case $O(\kappa n^3)$ communication and $O(t)$ rounds, and (ii) a protocol with expected $O(\kappa n^3)$ communication and expected constant rounds. In the process of achieving our results, we design (1) a novel weak gradecast protocol with a communication complexity of $O(\kappa n^2)$ for linear-sized inputs and constant rounds, (2) a protocol called “recoverable-set-of-shares” for ensuring recovery of shared secrets, (3) an oblivious leader election protocol with $O(\kappa n^3)$ communication and constant rounds, and (4) a multi-valued validated Byzantine agreement (MVBA) protocol with $O(\kappa n^3)$ communication complexity for linear-sized inputs and expected constant rounds. Each of these primitives is of independent interest.

This 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.

One of the central questions in cryptology is how efficient generic constructions of cryptographic primitives can be. Gennaro, Gertner, Katz, and Trevisan [SIAM J. of Compt., 2005] studied the lower bounds of the number of invocations of a (trapdoor) one-way permutation in order to construct cryptographic schemes, e.g., pseudorandom number generators, digital signatures, and public-key and symmetric-key encryption.

Recently, quantum machines have been explored to _construct_ cryptographic primitives other than quantum key distribution. This paper studies the efficiency of _quantum_ black-box constructions of cryptographic primitives when the communications are _classical_. Following Gennaro et al., we give the lower bounds of the number of invocations of an underlying quantumly-computable quantum-one-way permutation when the _quantum_ construction of pseudorandom number generator and symmetric-key encryption is weakly black-box. Our results show that the quantum black-box constructions of pseudorandom number generator and symmetric-key encryption do not improve the number of invocations of an underlying quantumly-computable quantum-one-way permutation.

In the permutation inversion problem, the task is to find the preimage of some challenge value, given oracle access to the permutation. This fundamental problem in query complexity appears in many contexts, particularly cryptography. In this work, we examine the setting in which the oracle allows for quantum queries to both the forward and the inverse direction of the permutation—except that the challenge value cannot be submitted to the latter. Within that setting, we consider three options for the inversion algorithm: whether it can get quantum advice about the permutation, whether the query algorithm can restrict the distribution with which the challenge input is sampled, and whether it must produce the entire preimage (search) or only the first bit (decision). We prove several theorems connecting the hardness of the resulting variations of the permutation inversion problem and establish lower bounds for them. Our results show that, perhaps surprisingly, the permutation inversion problem does not become significantly easier when the adversary is granted oracle access to the inverse—provided it cannot query the challenge itself.

There has been a recent interest in proposing quantum protocols whose security relies on weaker computational assumptions than their classical counterparts. Importantly to our work, it has been recently shown that public-key encryption (PKE) from one-way functions (OWF) is possible if we consider quantum public keys. Notice that we do not expect classical PKE from OWF given the impossibility results of Impagliazzo and Rudich (STOC'89).

However, the distribution of quantum public keys is a challenging task. Therefore, the main question that motivates our work is if quantum PKE from OWF is possible if we have classical public keys. Such protocols are impossible if ciphertexts are also classical, given the impossibility result of Austrin et al.(CRYPTO'22) of quantum enhanced key-agreement (KA) with classical communication.

In this paper, we focus on black-box separation for PKE with classical public key and quantum ciphertext from OWF under the polynomial compatibility conjecture, first introduced in Austrin et al.. More precisely, we show the separation when the decryption algorithm of the PKE does not query the OWF. We prove our result by extending the techniques of Austrin et al. and we show an attack for KA in an extended classical communication model where the last message in the protocol can be a quantum state.