A new key exchange protocol based on the decomposition problem

TL;DR

This paper introduces a novel key exchange protocol leveraging the decomposition problem in non-commutative groups, enhancing security by concealing subgroups and adding complexity through centralizer problems.

Contribution

It proposes a new key establishment protocol based on the decomposition problem with innovative security improvements by hiding subgroups.

Findings

Enhanced security through subgroup concealment

Introduction of centralizer problem as an additional security layer

Potential resistance to known cryptanalytic attacks

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 In particular, we conceal (i.e., do not publish explicitly) one of the subgroups $A, B$, thus introducing an additional computationally hard problem for the adversary, namely, finding the centralizer of a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