New Public-Key Cipher System Based Upon the Diophantine Equations

The public key system proposed by Lin Chang and Lee is insecure even if used as a private key system Index Terms Public key cryptography knapsack cryptosystems This author s research supported by EPSRC Research Grant No GR H This author acknowledges the support of the Nu eld Foundation This author s research supported by a Lloyd s of London Tercentenary Foundation Research Fellowship In the authors present a public key system based on an integer knap sack problem Following the notation of let D f wg The message block m mn where mi D is encrypted to C Pn i misi where s sn forms the public key The method for choosing si to allow a form of trapdoor decryption is given in We show below that this method produces an insecure cryptosystem Lemma There is a unique m j D such that C m jsj mod qj Proof Clearly a solution exists since noting qj j si for i j