Cryptanalysis of the TRMC-4 public key cryptosystem

Abstract

In 2006, the inventors of TRMC public key cryptosystem proposed a new variant of TRMC, TRMC-4, which can resist the existing attack, in particular, the Joux et al attack. In this paper, we show that the new version is vulnerable to attack via the linearization equations (LE) method. For any given valid ciphertext and its corresponding TRMC-4 public key, we can derive the corresponding plaintext within 224 double-struck F sign 28-operations, after performing once for the public key a computation of complexity less than 234. Our results are confirmed by computer experiments. © Springer-Verlag Berlin Heidelberg 2007.