A Ptime Solution To The Restricted Conjugacy Problem In Generalized Heisenberg Groups

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