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Title:
Optimizing Key Recovery in Classic McEliece: Advanced Error Correction for Noisy Side-Channel Measurements
Authors: Nicolas Vallet, Pierre-Louis Cayrel, Brice Colombier, Vlad-Florin Dragoi, Vincent Grosso
Abstract:Classic McEliece is one of the code-based Key Encapsulation Mechanism finalists in the ongoing NIST post-quantum cryptography standardization process. Several key-recovery side-channel attacks on the decapsulation algorithm have already been published. However none of them discusses the feasibility and/or efficiency of the attack in the case of noisy side-channel acquisitions. In this paper, we address this issue by proposing two improvements on the recent key-recovery attack published by Drăgoi et al… First, we introduce an error correction algorithm for the lists of Hamming weights obtained by side-channel measurements, based on the assumption, validated experimentally, that the error on a recovered Hamming weight is bounded to \pm1. We then offer a comparison between two decoding efficiency metrics, the theoretical minimal error correction capability and an empirical average correction probability. We show that the minimal error correction capability, widely used for linear codes, is not suitable for the (non-linear) code formed by the lists of Hamming weights. Conversely, experimental results show that out of 1 million random erroneous lists of 2t=128 Hamming weights, only 2 could not be corrected by the proposed algorithm. This shows that the probability of successfully decoding a list of erroneous Hamming weights is very high, regardless of the error weight. In addition to this algorithm, we describe how the secret Goppa polynomial g, recovered during the first step of the attack, can be exploited to reduce both the time and space complexity of recovering the secret permuted support \mathcal{L}.
ePrint: https://eprint.iacr.org/2025/802
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