TTP algorithm Clause Samples

TTP algorithm. The cornerstone part of the proposed key exchange is the choice of ⋆-commuting subgroups of the group G. The basic idea is to use Lemma 1.1 and choose commuting subgroups A and B in Bn and then pull them into G using the epi- morphism ϕ. The resulting subgroups ϕ(A) and ϕ(B) of G commute. Moreover, for any choice of π the subgroups ϕ(A) and ϕ(B) ⋆-commute. Before we present the algorithm we need to give some details about the braid group Bn. The group Bn has a cyclic center generated by the element ∆2, where ∆ is the element called the half twist and can be expressed in the generators of Bn as follows: ∆ = (σ1 . . . σn−1) · (σ1 . . . σn−2) · . . . · (σ1). Any element g ∈ Bn can be uniquely represented in the form