New signature schemes with tight security reductions

How to design efficient signature schemes with tight security reductions has attracted many cryptologists' attention during the past two decades. In this paper, we propose a new deterministic signature scheme based on the Computational Diffie-Hellman problem. Comparing with the previously signatures ' security reduction, ours is much tighter. Moreover, a new improved Rabin signature scheme is proposed with even 'tighter' security reduction (Exactly, the forger's probability is not influenced by the number of hash queries or signing queries and the time of reduction is almost the same as the time of forgery). We believe that the proposed Rabin-type signature's security is actually tight since the forger's probability is uniquely bounded by the hardness of factoring.