Cryptanalysis of group-based key agreement protocols using subgroup distance functions

TL;DR

This paper presents a novel cryptanalysis method for group-based key agreement protocols utilizing subgroup distance functions, demonstrated on the Thompson's group F protocol.

Contribution

It introduces a new cryptanalysis approach using subgroup distance functions for noncommutative group protocols, specifically applied to the Shpilrain-Ushakov protocol.

Findings

Effective cryptanalysis of the Shpilrain-Ushakov protocol

Demonstrates the utility of subgroup distance functions in cryptanalysis

Provides insights into vulnerabilities of noncommutative group protocols

Abstract

We introduce a new approach for cryptanalysis of key agreement protocols based on noncommutative groups. This approach uses functions that estimate the distance of a group element to a given subgroup. We test it against the Shpilrain-Ushakov protocol, which is based on Thompson's group F.