A family of polycyclic groups over which the uniform conjugacy problem is NP-complete

In this paper we study the conjugacy problem in polycyclic groups. Our main result is that we create polycyclic groups Gn whose conjugacy problem is at least as hard as the subset sum problem with n indeterminates. As such, the conjugacy problem over the groups Gn is NP-complete where the parameters of the problem are taken in terms of n and the length of the elements given on input.