A new key exchange protocol based on the decomposition problem
Abstract
In this paper we present a new key establishment protocol based on the decomposition problem in noncommutative groups which is: given two elements $w, w_1$ of the platform group $G$ and two subgroups $A, B \subseteq G$ (not necessarily distinct), find elements $a \in A, b \in B$ such that $w_1 = a w b$. 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 In particular, we conceal (i.e., do not publish explicitly) one of the subgroups $A, B$, thus introducing an additional computationally hard problem for the adversary, namely, finding the centralizer of a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.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 December 2005
 arXiv:
 arXiv:math/0512140
 Bibcode:
 2005math.....12140S
 Keywords:

 Mathematics  Group Theory;
 Computer Science  Cryptography and Security
 EPrint:
 7 pages