Paper 2022/1493

Enhanced pqsigRM: Code-Based Digital Signature Scheme with Short Signature and Fast Verification for Post-Quantum Cryptography

Abstract

We present a novel code-based digital signature scheme, called Enhanced pqsigRM for post-quantum cryptography (PQC). This scheme is based on modified Reed–Muller (RM) codes, which modified RM codes with several security problems. Enhanced pqsigRM is a strengthened version of pqsigRM, which was submitted to NIST PQC standardization in round 1. The proposed scheme has the advantage of short signature size, fast verification cycles. For 128 bits of classical security, the signature size of the proposed scheme is 1032 bytes, which corresponds to 0.42 times that of Crystals-Dilithium, and the number of median verification cycles is 235,656, which is smaller than that of Crystals-Dilithium. Also, we use public codes, called modified RM codes, that are more difficult to distinguish from random codes. We use (U,U + V )-codes with high-dimensional hull to make these. Using modified RM codes, the proposed signature scheme resists various known attacks on RM-code-based cryptography. The proposed decoder samples from coset elements with small Hamming weight for any given syndrome and efficiently finds such elements.