A Reaction Attack against Cryptosystems based on LRPC Codes

Abstract

Rank metric is a very promising research direction for code-based cryptography. In fact, thanks to the high complexity of generic decoding attacks against codes in this metric, it is possible to easily select parameters that yield very small data sizes. In this paper we analyze cryptosystems based on Low-Rank Parity-Check (LRPC) codes, one of the classes of codes that are efficiently decodable in the rank metric. We show how to exploit the decoding failure rate, which is an inherent feature of these codes, to devise a reaction attack aimed at recovering the private key. As a case study, we cryptanalyze the recent McNie submission to NIST’s Post-Quantum Standardization process. Additionally, we provide details of a simple implementation to validate our approach.