Generic Algorithms and Key Agreement Protocols Based on Group Actions

Abstract

We propose a Diffie-Hellman-like key agreement protocol based on the computational intractability of reversing group action. The concept of a group action generalizes exponentiation and provides an algorithmic problem harder than the discrete logarithm problem. Using the action of the general linear group on the direct product of two cyclic groups, we invent a key agreement protocol secure against an attacker who has power to solve the discrete logarithm problem. We discuss a semantic secure asymmetric encryption scheme as well. Its security is evaluated in terms of a generic algorithm, which is a model of probabilistic algorithms over black box groups (similar to a straight-line program) and does not depend on any specific property of the group representation.