A New Signature Scheme without Random Oracles and Its Applications

In this paper, we propose a new signature scheme that is existentially unforgeable under a chosen message attack without random oracle. The security of our scheme depends on a new complexity assumption called the k+1 square roots assumption. We also discuss the relationship between the k+1 square roots assumption and some related problems and provide some conjectures. Moreover, the k+1 square roots assumption can be used to construct shorter signatures under the random oracle model. As some applications, a new chameleon hash signature scheme and a on-line/off-line signature scheme and a new efficient anonymous credential scheme based on the proposed signature scheme are presented.