A Signature Scheme Based on the Syndrome Decoding Problem Using LDPC Codes

The security of widely used authentication and signature schemes is based on the difficulty of the discrete logarithm problem and the prime factorization problem. A quantum computer might solve these problems in probabilistic polynomial time. In other words, if a quantum computer is realized, these schemes are expected to eventually become vulnerable. In preparation for the development of a quantum computer, research on post-quantum cryptography is in progress. In addition, authentication and signature schemes using the post-quantum cryptography are also studied. Generally, authentication and signature schemes based on the public key cryptography have the large computational complexity. A zero-knowledge authentication scheme based on the syndrome decoding problem was proposed as a post-quantum authentication scheme. We have proposed the smaller computational complexity authentication scheme by using LDPC codes. This paper presents a post-quantum signature scheme which is constructed from the authentication scheme by Fiat-Shamir transformation.