Cryptanalysis of the birational permutation signature scheme over a non-commutative ring

Abstract

In 2008, Hashimoto and Sakurai proposed a new efficient signature scheme, which is a noncommutative version of Shamir's birational permutation signature scheme. Shamir's scheme is a generalization of the Ong-Schnorr-Shamir scheme and was broken by Coppersmith et al. using its linearity and commutativity. The HS (Hashimoto-Sakurai) scheme is expected to be secure against the attack from its non-commutative structure. In this paper, we propose an attack against the HS scheme, which is practical under the condition that its step size and the number of steps are small. We discuss its efficiency by using some experimental results.

A ring signature scheme over braid groups

“…In order to resist the quantum attacks, cryptographers have trying to design public key schemes not based on number theory or based on non-commutative algebraic systems, such as signature schemes based on non-commutative rings [3,4] . Braid groups were first introduced by Artin [5] .…”