A New Authentication and Signature Scheme Based on the Conjugacy Search Problem

The conjugacy search problem in a group G is the problem of recovering an x ∈ G from given g ∈ G and h =
^x-1
gx. The alleged computational hardness of this problem in some groups was used in several recently suggested public key exchange protocols and the digital signature scheme, including the one due to Anshel, Anshel, and Goldfeld, and the one due to Ko, Lee et al. In this paper, using Miller group G as the platform, we propose a generalization of Schnorr's authentication and signature scheme whose security is based on the hardness of the conjugacy search problem. An important difference between Schnorr's scheme and our scheme is that our scheme may not change r for each signature. By this advantage, precomputations of x can be done long before Victor (or Bob) is present.