Discrete logarithms for finite groups

We present group-theoretic and cryptographic properties of a generalization of the traditional discrete logarithm problem from cyclic to arbitrary finite groups. Questions related to properties which contribute to cryptographic security are investigated, such as distributional, coverage and complexity properties. We show that the distribution of elements in a certain multiset tends to uniform. In particular we consider the family of finite non-abelian groups PSL2(F-p), p a prime, as possible candidates in the design of new cryptographic primitives, based on our new discrete logarithm.