Cryptanalysis of a homomorphic public-key cryptosystem over a finite group

The paper cryptanalyses a public-key cryptosystem recently proposed by Grigoriev and Ponomarenko, which encrypts an element from a fixed finite group defined in terms of generators and relations to produce a ciphertext from . The paper presents a heuristic method for recovering the secret key from the public key, and so this cryptosystem should not be used in practice