Rank Metric Code-based Signature

We propose a rank metric code-based signature scheme based on the rank syndrome decoding problem, and analyze its security. We also provide necessary conditions for being MRD codes. Then, we provide parameters for the constructed signature scheme based on random linear codes constructed from Cauchy matrix. We also compare the signature scheme with those code-based signature schemes submitted to the NIST call for Post-Quantum Cryptography Standardization. The comparison shows that our signature scheme performs better than those schemes in terms of public key size and secret key size. The public key size and secret key size of our signature scheme are more than 3 times and 40 times smaller than those of the signature schemes submitted to the NIST call for Post-Quantum Cryptography Standardization.