International Association
for Cryptologic Research

Recently, there has been a lot of interest in improving the understanding of the practical hardness of the 3-Tensor Isomorphism (3-TI) problem, which, given two 3-tensors, asks for an isometry between the two. The current state-of-the-art for solving this problem is the algebraic algorithm of Ran et al. '23 and the graph-theoretic algorithm of Narayanan et al. '24 that have both slightly reduced the security of the signature schemes MEDS and ALTEQ, based on variants of the 3-TI problem (Matrix Code Equivalence (MCE) and Alternating Trilinear Form Equivalence (ATFE) respectively). In this paper, we propose a new combined technique for solving the 3-TI problem. Our algorithm, as typically done in graph-based algorithms, looks for an invariant in the graphs of the isomorphic tensors that can be used to recover the secret isometry. However, contrary to usual combinatorial approaches, our approach is purely algebraic. We model the invariant as a system of non-linear equations and solve it. Using this modelling we are able to find very rare invariant objects in the graphs of the tensors — cycles of length 3 (triangles) — that exist with probability approximately 1/q. For solving the system of non-linear equations we use Gröbner-basis techniques adapted to tri-graded polynomial rings. We analyze the algorithm theoretically, and we provide lower and upper bounds on its complexity. We further provide experimental support for our complexity claims. Finally, we describe two dedicated versions of our algorithm tailored to the specifics of the MCE and the ATFE problems. The implications of our algorithm are improved cryptanalysis of both MEDS and ALTEQ for the cases when a triangle exists, i.e. in approximately 1/q of the cases. While for MEDS, we only marginally reduce the security compared to previous work, for ALTEQ our results are much more significant with at least 60 bits improvement compared to previous work for all security levels. For Level I parameters, our attack is practical, and we are able to recover the secret key in only 1501 seconds. The code is available for testing and verification of our results.

Due to recent cryptanalytical breakthroughs, the multivariate signature schemes that seemed to be most promising in the past years are no longer in the focus of the research community. Hence, the cryptographically mature UOV scheme is of great interest again. Since it has not been part of the NIST process for standardizing post-quantum cryptography so far, it has not been studied intensively for its physical security.In this work, we present a side-channel attack on the latest implementation of UOV. In the first part of the attack, a single side-channel trace of the signing process is used to learn all vinegar variables used in the computation. Then, we employ a combination of the Kipnis-Shamir attack and the reconciliation attack to reveal the complete secret key. Our attack, unlike previous work, targets the inversion of the central map and not the subsequent linear transformation. It further does not require the attacker to control the message to be signed.We have verified the practicality of our attack on a ChipWhisperer-Lite board with a 32-bit STM32F3 ARM Cortex-M4 target mounted on a CW308 UFO board. We publicly provide the code and both reference and target traces. Additionally, we discuss several countermeasures that can at least make our attack less efficient.

In LWE-based KEMs, observed decryption errors leak information about the secret key in the form of equations or inequalities. Several practical fault attacks have already exploited such leakage by either directly applying a fault or enabling a chosen-ciphertext attack using a fault. When the leaked information is in the form of inequalities, the recovery of the secret key is not trivial. Recent methods use either statistical or algebraic methods (but not both), with some being able to handle incorrect information. Having in mind that integration of the side-channel information is a crucial part of several classes of implementation attacks on LWEbased schemes, it is an important question whether statistically processed information can be successfully integrated in lattice reduction algorithms.We answer this question positively by proposing an error-tolerant combination of statistical and algebraic methods that make use of the advantages of both approaches. The combination enables us to improve upon existing methods – we use both fewer inequalities and are more resistant to errors. We further provide precise security estimates based on the number of available inequalities.Our recovery method applies to several types of implementation attacks in which decryption errors are used in a chosen-ciphertext attack. We practically demonstrate the improved performance of our approach in a key-recovery attack against Kyber with fault-induced decryption errors.

Single-trace attacks are a considerable threat to implementations of classic public-key schemes, and their implications on newer lattice-based schemes are still not well understood. Two recent works have presented successful single-trace attacks targeting the Number Theoretic Transform (NTT), which is at the heart of many lattice-based schemes. However, these attacks either require a quite powerful side-channel adversary or are restricted to specific scenarios such as the encryption of ephemeral secrets. It is still an open question if such attacks can be performed by simpler adversaries while targeting more common public-key scenarios. In this paper, we answer this question positively. First, we present a method for crafting ring/module-LWE ciphertexts that result in sparse polynomials at the input of inverse NTT computations, independent of the used private key. We then demonstrate how this sparseness can be incorporated into a side-channel attack, thereby significantly improving noise resistance of the attack compared to previous works. The effectiveness of our attack is shown on the use-case of CCA2 secure Kyber k-module-LWE, where k ∈ {2, 3, 4}. Our k-trace attack on the long-term secret can handle noise up to a σ ≤ 1.2 in the noisy Hamming weight leakage model, also for masked implementations. A 2k-trace variant for Kyber1024 even allows noise σ ≤ 2.2 also in the masked case, with more traces allowing us to recover keys up to σ ≤ 2.7. Single-trace attack variants have a noise tolerance depending on the Kyber parameter set, ranging from σ ≤ 0.5 to σ ≤ 0.7. As a comparison, similar previous attacks in the masked setting were only successful with σ ≤ 0.5.

This paper presents an attack based on side-channel information and information set decoding (ISD) on the code-based Niederreiter cryptosystem and an evaluation of the practicality of the attack using an electromagnetic side channel. We start by directly adapting the timing side-channel plaintext-recovery attack by Shoufan et al. from 2010 to the constant-time implementation of the Niederreiter cryptosystem as used in the official FPGA-implementation of the NIST finalist “Classic McEliece”. We then enhance our attack using ISD and a new technique that we call iterative chunking to further significantly reduce the number of required side-channel measurements. We theoretically show that our attack improvements have a significant impact on reducing the number of required side-channel measurements. For example, for the 256-bit security parameter set kem/mceliece6960119 of “Classic McEliece”, we improve the basic attack that requires 5415 measurements to less than 562 measurements on average to mount a successful plaintext-recovery attack. Further reductions can be achieved at the price of increasing the cost of the ISD computations. We confirm our findings by practically mounting the attack on the official FPGA-implementation of “Classic McEliece” for all proposed parameter sets.

We propose SOFIA, the first $$\mathcal {MQ}$$MQ-based signature scheme provably secure in the quantum-accessible random oracle model (QROM). Our construction relies on an extended version of Unruh’s transform for 5-pass identification schemes that we describe and prove secure both in the ROM and QROM.Based on a detailed security analysis, we provide concrete parameters for SOFIA that achieve 128-bit post-quantum security. The result is SOFIA-4-128 with parameters carefully optimized to minimize signature size and maximize performance. SOFIA-4-128 comes with an implementation targeting recent Intel processors with the AVX2 vector-instruction set; the implementation is fully protected against timing attacks.