Identification Scheme Based on the Binary Syndrome Decoding Problem Using High-Density Parity-Check Matrices

Abstract

Most of cryptosystems, identification and signature schemes rely on the discrete logarithm problem and the prime factorization problem. These problems would be broken through Shor's quantum factorization algorithm in the case that quantum computers would come to exist. Code-based cryptography is one of post-quantum cryptography. There are several cryptography to reduce the key size by using the public matrix with the circulant structure, but some attacks have been proposed with the circulant structure as a weak point. In this paper, we propose a code-based identification scheme using high-density parity-check (HDPC) matrices. The poposed scheme is an improvement of Stern's identification scheme based on the binary syndrome decoding (BSD) problem. In the proposed scheme, we apply HDPC matrices to the BSD problem in order to prevent attacks using iterative decoding algorithm. Also, to prevent attack using circulant structure, we construct HDPC matrices of multiple block-row with circulant submatrices of different size. Furthermore, we evaluate the security level, key size, computational cost and security against existing attacks.