Cryptanalysis of a combinatorial public key cryptosystem

Abstract We discuss pitfalls in the security of the combinatorial public key cryptosystem based on Nielsen transformations inspired by the ElGamal cryptosystem proposed by Fine, Moldenhauer and Rosenberger. We introduce three different types of attacks to possible combinatorial public key encryption schemes and apply these attacks to the scheme corresponding to the cryptosystem under discussion. As a result of our observation, we show that under some natural assumptions the scheme is vulnerable to at least one of the proposed attacks.