Noncommutative Polly Cracker-type cryptosystems and chosen-ciphertext security

In this paper we consider chosen-ciphertext attacks against noncommutative Polly Cracker-type cryptosystems. We present several versions of these attacks, as well as techniques to counter them. First we introduce a chosen-ciphertext attack, which assumes a very simple private key. We then present generalizations of this attack which are valid in more general situations, and propose a simple but effective technique to counter these attacks. Finally, we show how this technique can also be used to counter the adaptive chosenciphertext attacks against noncommutative Polly Cracker-type cryptosystems.