New Signature and Multi-Signature Schemes with Tight Security Reduction Based on D-DDH Problem

Based on the newly introduced d-decisional Diffie-Hellman (d-DDH) intractable problem, a signature scheme and a multi-signature scheme are proposed. The main method in the constructions is a transformation of a knowledge proof on the equality of two discrete logarithms. The two schemes are proved secure in the random oracle model and the security reductions to the d-DDH problem are tight. Moreover, one can select different d for different security demand of applications. Thus the schemes are secure, efficient and practical.