A Generalisation of the Klchkp Public Key Cryptosystem and a New Public Key Cryptosystem Based on the Decomposition Problem

Recently cryptosystems have been developed based on the difficulty of the DH-DP and the conjugacy problem. These are KLCHKP (presented at ASIACRYPT 2001) and the AAG key establishment protocols. The AAG is a group theoretic scheme. Both the inventors suggest an implementation in braid groups.I present another new group theoretic cryptosystem which is as least as secure as the KLCHKP cryptosystem because it is also based on the DH-DP and there is more control of the public products its key is computed more efficiently. I give a partial implementation in braid groups. I present a generalisation of the KLCHKP public key cryptosystem