A Zero-knowledge Undeniable Signature Scheme in Non-abelian Group Setting

Abstract

Recently non-abelian groups have attracted the atten- tion of cryptographers for constructing public-key cryp- tographic protocols. In this paper we use the conju- gacy problem in non-abelian groups to construct a zero- knowledge undeniable signature scheme. a more efficient alternative to well established numeric computations in abelian groups. Where as the secu- rity of cryptographic protocols based on number-theoretic abelian groups are based on the hardness of problems like integer factorization and discrete logarithm, the se- curity of cryptographic protocols based on non-abelian groups are based on the hardness of problems like conju- gacy search, decomposition and root problem. Almost all the undeniable signature schemes constructed so far have been based on the hardness of integer factorization (10) and discrete logarithm problems (6, 7). In this paper, we present a zero-knowledge undeniable signature scheme based on the hardness of the conjugacy problem in non- abelian groups. The outline of the paper is as follows. In Section 2, we describe the preliminaries needed for this paper. A zero-knowledge undeniable signature scheme is given in Section 3. We prove the completeness, soundness and zero-knowledgeness of the protocols also. In Section 4, we suggest some non-abelian groups for the implementation of the above signature scheme. The paper concludes with some general remarks in Section 5.