A Horizontal Attack on the Codes and Restricted Objects Signature Scheme (CROSS)

CROSS is a post-quantum secure digital signature scheme submitted to NIST’s Call for Additional Signatures which was recently selected for round 2. It features signature and key sizes in the range of SLH-DSA while providing a substantially faster signing operation. Within this work, we provide the first passive side-channel attack on the scheme. The attack recovers the secret key from all except one parameter sets and security levels from a single power trace while requiring at maximum two power traces for the R-SDP(G) 1 Fast instance. To successfully mount the attack, we show how to recover the secret key from side-channel information gained from the syndrome computation in CROSS’ identification protocol. We furthermore show how the hypothesis space for the attack can be restricted using information from the published signature.