In this paper we present a new key establishment protocol based on the
decomposition problem in non-commutative groups which is: given two elements
w,w1 of the platform group G and two subgroups A,B⊆G (not
necessarily distinct), find elements a∈A,b∈B such that w1=awb. Here we introduce two new ideas that improve the security of key
establishment protocols based on the decomposition problem. In particular, we
conceal (i.e., do not publish explicitly) one of the subgroups A,B, thus
introducing an additional computationally hard problem for the adversary,
namely, finding the centralizer of a given finitely generated subgroup.Comment: 7 page