A security analysis of uniformly-layered rainbow defined over non-commutative rings

Abstract Hashimoto and Sakurai proposed a signature scheme (HS scheme), whose security is based on the difficulty of integer factorization. In this paper, we redefine HS scheme as a signature scheme in Multivariate Public Key Cryptosystems (MPKC). MPKC are public key cryptosystems whose security is based on the difficulty of solving multivariate quadratic equations, and candidates for post-quantum cryptography. In this paper, we analyze the security of the extended HS scheme using technique of security analysis for MPKC. Furthermore, based on the security analysis of the extended HS scheme, we estimate secure parameters of the extended HS scheme.

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