Conjugacy decision algorithm for braid signature scheme

Abstract

We proposed recently new signature schemes using the braid groups. Our schemes are based on a gap between the decision version and the computational version of the conjugacy problem in the braid groups. In order to construct our schemes, we need an algorithm for deciding whether any two braids are conjugate each other or not, which must be efficient and cryptographically secure. In this thesis, we construct this algorithm, called the conjugacy decision algorithm. In Chapter 1, we introduce the braid group and the digital signature scheme briefly. In Chapter 2, we introduce invariants of a conjugacy class of a braid, which are used to construct this algorithm. In Chapter 3, we describe the conjugacy problem and the braid signature scheme using it in brief. In Chapter 4, we explain the efficiency and cryptographical security of this algorithm. Then we design the conjugacy decision algorithm and describe subalgorithms of it in concrete forms.