A PTIME solution to the restricted conjugacy problem in generalized Heisenberg groups

Abstract

Abstract We examine the Anshel–Anshel–Goldfeld key exchange protocol with a generalized Heisenberg group, Hm, as a platform. We show that subgroup-restricted simultaneous conjugacy search problem in Hm can be solved in quasi-quintic time, which allows the computation of the private keys of the parties.