The Twin Conjugacy Search Problem and Applications

We propose a new computational problem over the noncommutative group, called the twin conjugacy search problem. This problem is related to the conjugacy search problem and can be used for almost all of the same cryptographic constructions that are based on the conjugacy search problem. However, our new problem is at least hard as the conjugacy search problem. Moreover, the twin conjugacy search problem have many applications. One of the most important applications, we propose a trapdoor test which can replace the function of the decision oracle. We also show other applications of the problem, including: a non-interactive key exchange protocol and a key exchange protocol, a new encryption scheme which is secure against chosen ciphertext attack, with a very simple and tight security proof and short ciphertexts, under a weak assumption, in the random oracle model.