Adapting Belief Propagation to Counter Shuffling of NTTs

The Number Theoretic Transform (NTT) is a major building block in recently introduced lattice based post-quantum (PQ) cryptography. The NTT was target of a number of recently proposed Belief Propagation (BP)-based Side Channel Attacks (SCAs). Ravi et al. have recently proposed a number of countermeasures mitigating these attacks. In 2021, Hamburg et al. presented a chosen-ciphertext enabled SCA improving noise-resistance, which we use as a starting point to state our findings. We introduce a pre-processing step as well as a new factor node which we call shuffle node. Shuffle nodes allow for a modified version of BP when included into a factor graph. The node iteratively learns the shuffling permutation of fine shuffling within a BP run. We further expand our attacker model and describe several matching algorithms to find inter-layer connections based on shuffled measurements. Our matching algorithm allows for either mixing prior distributions according to a doubly stochastic mix matrix or to extract permutations and perform an exact un-matching of layers. We additionally discuss the usage of sub-graph inference to reduce uncertainty and improve un-shuffling of butterflies. Based on our results, we conclude that the proposed countermeasures of Ravi et al. are powerful and counter Hamburg et al., yet could lead to a false security perception – a powerful adversary could still launch successful attacks. We discuss on the capabilities needed to defeat shuffling in the setting of Hamburg et al. using our expanded attacker model. Our methods are not limited to the presented case but provide a toolkit to analyze and evaluate shuffling countermeasures in BP-based attack scenarios

Bitslicing Arithmetic/Boolean Masking Conversions for Fun and Profit

The performance of higher-order masked implementations of lattice-based based key encapsulation mechanisms (KEM) is currently limited by the costly conversions between arithmetic and Boolean masking. While bitslicing has been shown to strongly speed up masked implementations of symmetric primitives, its use in arithmetic-to-Boolean and Boolean-to-arithmetic masking conversion gadgets has never been thoroughly investigated. In this paper, we first show that bitslicing can indeed accelerate existing conversion gadgets. We then optimize these gadgets, exploiting the degrees of freedom offered by bitsliced implementations. As a result, we introduce new arbitrary-order Boolean masked addition, arithmetic-to-Boolean and Boolean-to-arithmetic masking conversion gadgets, each in two variants: modulo 2k and modulo p (for any integers k and p). Practically, our new gadgets achieve a speedup of up to 25x over the state of the art. Turning to the KEM application, we develop the first open-source embedded (Cortex-M4) implementations of Kyber768 and Saber masked at arbitrary order. The implementations based on the new bitsliced gadgets achieve a speedup of 1.8x for Kyber and 3x for Saber, compared to the implementation based on state-of-the-art gadgets. The bottleneck of the bitslice implementations is the masked Keccak-f[1600] permutation