[Resource Topic] 2024/135: A Closer Look at the Belief Propagation Algorithm in Side-Channel-Assisted Chosen-Ciphertext Attacks

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A Closer Look at the Belief Propagation Algorithm in Side-Channel-Assisted Chosen-Ciphertext Attacks

Authors: Kexin Qiao, Siwei Sun, Zhaoyang Wang, Zehan Wu, Junjie Cheng, An Wang, Liehuang Zhu


The implementation security of post-quantum cryptography (PQC) algorithms has emerged as a critical concern with the PQC standardization process reaching its end. In a side-channel-assisted chosen-ciphertext attack, the attacker builds linear inequalities on secret key components and uses the belief propagation (BP) algorithm to solve. The number of inequalities leverages the query complexity of the attack, so the fewer the better. In this paper, we use the PQC standard algorithm Kyber512 as a study case to construct bilateral inequalities on key variables with substantially narrower intervals using a side-channel-assisted oracle. The number of such inequalities required to recover the key with probability 1 utilizing the BP algorithm is reduced relative to previous unilateral inequalities. Furthermore, we introduce strategies aimed at further refining the interval of inequalities. Diving into the BP algorithm, we discover a measure metric named JSD-metric that can gauge the tightness of an inequality. We then develop a heuristic strategy and a machine learning-based strategy to utilize the JSD-metrics to contract boundaries of inequalities even with fewer inequalities given, thus improving the information carried by the system of linear inequalities. This contraction strategy is at the algorithmic level and has the potential to be employed in all attacks endeavoring to establish a system of inequalities concerning key variables.

ePrint: https://eprint.iacr.org/2024/135

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