A code-based signature scheme from the Lyubashevsky framework

Abstract

We propose a new method to construct code-based signature scheme following the Lyubashevsky's lattice-based framework. Our technique ensures that the Hamming weight of each row of the private key matrix is below the GV bound instead of fixed weight. Our scheme can generate signatures whose maximum Hamming weight is below the GV bound of random linear codes with the public key matrix as parity-check matrix. We argue that our scheme can resist existing attacks on code-based signatures. We provide a detailed security analysis and prove that our scheme is existentially unforgeable under adaptive chosen-message attacks (EUF-CMA) in the random oracle model through exploiting and expanding code-based complex problems. Our scheme enjoys the shorter signature size than the Durandal signature scheme (EUROCRYPT 2019) and the Wave signature scheme (ASIACRYPT 2019) for security level of 128 bits. We also show that there is a generic method to construct Weight Restricted Hash (WRH) functions which can produce hash value with a given Hamming weight.