First-Order Masked Kyber on ARM Cortex-M4

In this work, we present a fast and first-order secure Kyber implementation optimized for ARM Cortex-M4. Most notably, to our knowledge this is the first liberally-licensed open-source Cortex-M4 implementation of masked Kyber. The ongoing NIST standardization process for post-quantum cryptography and newly proposed side-channel attacks have increased the demand for side-channel analysis and countermeasures for the finalists. On the foundation of the commonly used PQM4 project, we make use of the previously presented optimizations for Kyber on a Cortex-M4 and further combine different ideas from various recent works to achieve a better performance and improve the security in comparison to the original implementations. We show our performance results for first-order secure implementations. Our masked Kyber768 decapsulation on the ARM Cortex-M4 requires only 2 978 441 cycles, including randomness generation from the internal RNG. We then practically verify our implementation by using the t-test methodology with 100 000 traces

An update on Keccak performance on ARMv7-M

This note provides an update on Keccak performance on the ARMv7-M processors. Starting from the XKCP implementation, we have applied architecture-specific optimizations that have yielded a performance gain of up to 21% for the largest permutation instance

A Novel Power Analysis Attack against CRYSTALS-Dilithium Implementation

Post-Quantum Cryptography (PQC) was proposed due to the potential threats quantum computer attacks against conventional public key cryptosystems, and four PQC algorithms besides CRYSTALS-Dilithium (Dilithium for short) have so far been selected for NIST standardization. However, the selected algorithms are still vulnerable to side-channel attacks in practice, and their physical security need to be further evaluated. This study introduces two efficient power analysis attacks, the optimized fast two-stage approach and the single-bit approach, aimed at reducing the key guess space in NTT polynomial multiplication on an STM32F405 device (ARM Cortex-M4 core). Our findings reveal that the optimized approach outperforms the conservative approach and the fast two-stage approach proposed in ICCD 2021 by factors of 519 and 88, respectively. Similarly, the single-bit approach demonstrates speedups of 365 and 62 times compared to these two approaches, respectively

Safe-Error Attacks on SIKE and CSIDH

The isogeny-based post-quantum schemes SIKE (NIST PQC round 3 alternate candidate) and CSIDH (Asiacrypt 2018) have received only little attention with respect to their fault attack resilience so far. We aim to fill this gap and provide a better understanding of their vulnerability by analyzing their resistance towards safe-error attacks. We present four safe-error attacks, two against SIKE and two against a constant-time implementation of CSIDH that uses dummy isogenies. The attacks use targeted bitflips during the respective isogeny-graph traversals. All four attacks lead to full key recovery. By using voltage and clock glitching, we physically carried out two of the attacks - one against each scheme -, thus demonstrate that full key recovery is also possible in practice

To Infect Or Not To Infect: A Critical Analysis Of Infective Countermeasures In Fault Attacks

As fault based cryptanalysis is becoming more and more of a practical threat, it is imperative to make efforts to devise suitable countermeasures. In this regard, the so-called ``infective countermeasures\u27\u27 have garnered particular attention from the community due to its ability in inhibiting differential fault attacks without explicitly detecting the fault. We observe that despite being adopted over a decade ago, a systematic study of infective countermeasures is missing from the literature. Moreover, there seems to be a lack of proper security analysis of the schemes proposed, as quite a few of them have been broken promptly. Our first contribution comes in the form of a generalization of infective schemes which aids us with a better insight into the vulnerabilities, scopes for cost reduction and possible improvements. This way, we are able to propose lightweight alternatives of two existing schemes. Further we analyze shortcomings of LatinCrypt\u2712 and CHES\u2714 schemes and propose a simple patch for the former

Analogue of Vélu\u27s Formulas for Computing Isogenies over Hessian Model of Elliptic Curves

Vélu\u27s formulas for computing isogenies over Weierstrass model of elliptic curves has been extended to other models of elliptic curves such as the Huff model, the Edwards model and the Jacobi model of elliptic curves. This work continues this line of research by providing efficient formulas for computing isogenies over elliptic curves of Hessian form. We provide explicit formulas for computing isogenies of degree 3 and isogenies of degree l not divisible by 3. The theoretical cost of computing these maps in this case is slightly faster than the case with other curves. We also extend the formulas to obtain isogenies over twisted and generalized Hessian forms of elliptic curves. The formulas in this work have been verified with the Sage software and are faster than previous results on the same curve

Exploiting Decryption Failures in Mersenne Number Cryptosystems

Mersenne number schemes are a new strain of potentially quantum-safe cryptosystems that use sparse integer arithmetic modulo a Mersenne prime to encrypt messages. Two Mersenne number based schemes were submitted to the NIST post-quantum standardization process: Ramstake and Mersenne-756839. Typically, these schemes admit a low but non-zero probability that ciphertexts fail to decrypt correctly. In this work we show that the information leaked from failing ciphertexts can be used to gain information about the secret key. We present an attack exploiting this information to break the IND-CCA security of Ramstake. First, we introduce an estimator for the bits of the secret key using decryption failures. Then, our estimates can be used to apply the Slice-and-Dice attack due to Beunardeau et al. at significantly reduced complexity to recover the full secret. We implemented our attack on a simplified version of the code submitted to the NIST competition. Our attack is able to extract a good estimate of the secrets using $2^{12}$ decryption failures, corresponding to $2^{74}$~failing ciphertexts in the original scheme. Subsequently the exact secrets can be extracted in $O(2^{46})$ quantum computational steps

A Novel Duplication Based Countermeasure To Statistical Ineffective Fault Analysis

The Statistical Ineffective Fault Analysis, SIFA, is a recent addition to the family of fault based cryptanalysis techniques. SIFA based attack is shown to be formidable and is able to bypass virtually all the conventional fault attack countermeasures. Reported countermeasures to SIFA incur overheads of the order of at least thrice the unprotected cipher. We propose a novel countermeasure that reduces the overhead (compared to all existing countermeasures) as we rely on a simple duplication based technique. In essence, our countermeasure eliminates the observation that enables the attacker to perform SIFA. The core idea we use here is to choose the encoding for the state bits randomly. In this way, each bit of the state is free from statistical bias, which renders SIFA unusable. Our approach protects against stuck-at faults and also does not rely on any side channel countermeasure. We show the effectiveness of the countermeasure through an open source gate-level fault attack simulation tool. Our approach is probably the simplest and the most cost effective

STAMP-Single Trace Attack on M-LWE Pointwise Multiplication in Kyber

In this work, we propose a novel single-trace key recovery attack targeting side-channel leakage from the key-generation procedure of Kyber KEM. Our attack exploits the inherent nature of the Module-Learning With Errors (Module-LWE) problem used in Kyber KEM. We demonstrate that the inherent reliance of Kyber KEM on the Module-LWE problem results in a higher number of repeated computations with the secret key, compared to the Ring-LWE problem of similar security level. We exploit leakage from the pointwise multiplication operation in the key-generation procedure, and take advantage of the properties of the Module-LWE instance to enable a potential single trace key recovery attack. We validated the efficacy of our attack on both simulated and real traces, and we performed experiments on both the reference and assembly optimized implementation of Kyber KEM, taken from the pqm4 library, a well-known benchmarking and testing framework for PQC schemes on the ARM Cortex-M4 microcontroller. We also analyze the applicability of our attack on the countermeasures against traditional SCA such as masking and shuffling. We believe our work motivates more research towards SCA resistant implementation of key-generation procedure for Kyber KEM