New Online/Offline Signature Schemes Without Random Oracles

In this paper, we propose new signature schemes provably secure under the strong RSA assumption in the standard model. Our proposals utilize Shamir-Tauman's generic construction for building EF-CMA secure online/offline signature schemes from trapdoor commitments and less secure basic signature schemes. We introduce a new natural intractability assumption for hash functions, which can be interpreted as a generalization of second pre-image collision resistance. Assuming the validity of this assumption, we are able to construct new signature schemes provably secure under the strong RSA assumption without random oracles. In contrast to Cramer-Shoup's signature scheme based on strong RSA in the standard model, no costly generation of prime numbers is required for the signer in our proposed schemes. Moreover, the security of our schemes relies on weaker assumptions placed on the hash function than Gennaro, Halevi and Rabin's solution.

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