Secret and shared keys recovery on hamming quasi-cyclic with SASCA

Abstract

Soft Analytical Side Channel Attacks (SASCA) are a powerful family of Side Channel Attacks (SCA) that allows the recovery of secret values with only a small number of traces. Their effectiveness lies in the Belief Propagation (BP) algorithm, which enables efficient computation of the marginal distributions of intermediate values. Post-quantum schemes such as Kyber, and more recently, Hamming Quasi-Cyclic (HQC), have been targets of SASCA. Previous SASCA on HQC focused on Reed–Solomon (RS) codes and successfully retrieved the shared key with a high success rate for high noise levels using a single trace. In this work, we present new SASCA on HQC, where both the shared key and the secret key are targeted. Our attacks are realized on simulations. Unlike the previous SASCA, we take a closer look at the Reed–Muller (RM) code. The advantage of this choice is that the RM decoder is applied before the RS decoder, enabling attacks targeting both the secret key and shared key. We build a factor graph of the Fast Hadamard Transform (FHT) function from the HQC reference implementation of April 2023. The information recovered from BP allows us to retrieve the shared key with a single trace. In addition to the previous SASCA targeting HQC, we also manage to recover the secret key with two different chosen ciphertext attacks. One of them requires a single trace and is successful until high noise levels.