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**2005/447**

**Title:**

A new key exchange protocol based on the decomposition problem

**Authors:**
Vladimir Shpilrain, Alexander Ushakov

**Abstract:**

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 of 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In particular, we conceal (i.e., do not publish explicitly) one of the subgroups A, B, thus introducing an additional computationally hard problem for the adversary, namely, finding the centralizer of a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.

**ePrint:**
https://eprint.iacr.org/2005/447

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