A Practical Attack on a Certain Braid Group Based Shifted Conjugacy Authentication Protocol

In recent years, Artin’s braid groups have undergone intense scrutiny as a possible cryptographic platform, due mainly to the key-exchange protocols proposed in [1] and [12]. The security of both of these protocols relies on the difficulty of variants of the conjugacy search problem in braid groups, a well-studied problem (see [9], [6], [10]). More recently, Dehornoy has proposed a zero-knowledge authentication protocol based on group operations satisfying the left self-distributivity law [5]. Conjugacy is an example of a left self-distributive operation. Another example is the so-called shifted conjugacy operation of braids. This operation and its properties form the main object of study in this paper.