Improving Key Size and Bit-Security of Modified pqsigRM

Abstract

The importance of post-quantum cryptography (PQC), which is secure against quantum algorithms, is growing larger. The pqsigRM is a code-based PQC digital signature scheme which was accepted in round 1 of the NIST's PQC standardization process. This scheme was revised as the modified pqsigRM by removing all known vulnerabilities during the standardization process. Its advantages include an efficient decoding process, proven security, and small signature sizes. Small signature sizes are very useful in signature schemes because we should send signatures in every signing process. However, it has a problem with large public key sizes. In this paper, we propose a method to reduce the public key size of modified pqsigRM. We change the public key into a systematic form, improve its parameters, and fine-tune the bit-security for each parameter. Thus, we can reduce to 0.20, 0.40, and 0.23 times smaller public key sizes compared to the modified pqsigRM parameters for 80, 128, and 256 security levels, respectively. Also, we are able to obtain a larger exact bit-security for these parameters.