A New Key Recovery Side-Channel Attack on HQC with Chosen Ciphertext

Abstract

Hamming Quasi-Cyclic (HQC) is a code-based candidate of NIST post-quantum standardization procedure. The decoding steps of code-based cryptosystems are known to be vulnerable to side-channel attacks and HQC is no exception to this rule. In this paper, we present a new key recovery side-channel attack on HQC with chosen ciphertext. Our attack takes advantage of the reuse of a static secret key on a micro-controller with a physical access. The goal is to retrieve the static secret key by targeting the Reed-Muller decoding step of the decapsulation and more precisely the Hadamard transform. This function is known for its diffusion property, a property that we exploit through side-channel analysis. The side-channel information is used to build an Oracle that distinguishes between several decoding patterns of the Reed-Muller codes. We show how to query the Oracle such that the responses give a full information about the static secret key. Experiments show that less than 20.000 electromagnetic attack traces are sufficient to retrieve the whole static secret key used for the decapsulation. Finally, we present a masking-based countermeasure to thwart our attack.