Paper 2026/071 Original: eprint.iacr.org/2026/071 ↗

Codeword Masking Can Be Harmful Under Replay Attacks on HQC

Abstract

HQC, selected by NIST for standardization in 2025, was recently shown vulnerable to a replay attack recovering $\mathbf{v} - \mathbf{u}\cdot \mathbf{y}$, from which the long-term secret $\mathbf{y}$ was shown to be recoverable, and against which \emph{codeword masking} was proposed as the countermeasure. We revisit both and demonstrate that the countermeasure yields an opposite effect: on the target build, the unmasked replay attack is ineffective, whereas introducing codeword masking paradoxically enables its success. We present a new leakage venue in HQC, in the Reed--Muller encoder, and apply to it the post-decoding idea of recent work, turning HQC's own error correction into a side-channel budget that recovers the message: a single trace suffices, with only ${\sim}80$ profiling traces, and we confirm the same across the official implementations (the NIST reference and optimized code, and PQClean) at both \texttt{-O3} and \texttt{-Os}. We then improve the replay attack on $\mathbf{v} - \mathbf{u}\cdot \mathbf{y}$, raising its per-bit recovery probability; at the optimization level we study, that is still not enough for a practical attack. Codeword masking, adopted as the defense, supplies what replay could not: the random share erases the ambiguity that identical replays leave behind, and the extrapolated probability of recovering the whole $\mathbf{v} - \mathbf{u}\cdot \mathbf{y}$ rises from $10^{-555}$ to $1.0$. Increasing the masking order fails to mitigate the attack: we demonstrate identical recovery against a three-share implementation, without incurring additional profiling overhead for the adversary. Masking must therefore be designed against the optimization level and the device it is deployed on.