A Brief Retrospective Look at the Cayley-Purser Public-key Cryptosystem, 19 Years Later

TL;DR

This paper reviews the Cayley-Purser cryptosystem after 19 years, presenting two attacks including a new one, and analyzing a patented variant, demonstrating its insecurity.

Contribution

It provides the first detailed analysis of the Cayley-Purser cryptosystem after nearly two decades, including new attack methods and security assessments of variants.

Findings

Two effective attacks on Cayley-Purser

A novel attack method introduced

Patented variant also found insecure

Abstract

The purpose of this paper is to describe and analyze the Cayley-Purser algorithm, which is a public-key cryptosystem proposed by Flannery in 1999. I will present two attacks on it, one of which is apparently new. I will also examine a variant of the Cayley-Purser algorithm that was patented by Slavin in 2008, and show that it is also insecure.