Heisenberg Groups as Platform for the AAG Key-Exchange Protocol

Abstract

When the AAG protocol was first introduced, braid groups were proposed as platform group. However, there are studies that successful attack AAG with braid groups, one main attack method is the length-based attack. Searching for a new platform for AAG, Garber, Kahrobaei, and Lam studied polycyclic groups generated by number field and concluded that they are resistant against the length-based attack. Inspired by this result, we ask whether other type of polycyclic groups can be used as platform for AAG. In this paper, we discuss the use of Heisenberg groups, a type of polycyclic group, as a platform group for AAG by submitting them to one of AAG's major attacks, the length-based attack.