A new key exchange protocol based on the decomposition problem

Details A new key exchange protocol based on the decomposition problem A new key exchange protocol based on the decomposition problem

2005-12-06

arxiv.org/abs/math/0512140v1

Mathematics

Group Theory

7 pages

Scientific paper

In this paper we present a new key establishment protocol based on the decomposition problem in non-commutative groups which is: given two elements $w, w_1$ 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 In particular, we conceal (i.e., do not publish explicitly) one of the subgroups $A, B$, thus introducing an additional computationally hard problem for the adversary, namely, finding the centralizer of a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.

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