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Currently, there are relatively few instances of "hash-and-sign" signatures in the standard model. Moreover, most current instances rely on strong and less studied assumptions such as the Strong RSA and q -Strong Diffie-Hellman assumptions. In this paper, we present a new approach for realizing hash-and-sign signatures in the standard model. In our approach, a signer associates each signature with an index i that represents how many signatures that signer has issued up to that point. Then, to make use of this association, we create simple and efficient techniques that restrict an adversary which makes q signature requests to forge on an index no greater than $2^{\lceil \lg(q) \rceil} . Finally, we develop methods for dealing with this restricted adversary. Our approach requires that a signer maintains a small amount of state -- a counter of the number of signatures issued. We achieve two new realizations for hash-and-sign signatures respectively based on the RSA assumption and the Computational Diffie-Hellman assumption in bilinear groups.

Realizing Hash-and-Sign Signatures under Standard Assumptions