Secure Signature Schemes Based on|
A method is proposed for constructing from interactive protocols digital signature schemes secure against adaptively chosen message attacks. Our main result is that practical secure signature schemes can now also be based on computationally difficult problems other than factoring, such as the discrete logarithm problem.
More precisely, given only an interactive protocol of a certain type as a primitive, we can build a (non-interactive) signature scheme that is secure in the strongest sense of Goldwasser, Micali and Rivest (GMR): not existentially forgeable under adaptively chosen message attacks. There are numerous examples of primitives that satisfy our conditions, e.g. Feige-Fiat-Shamir, Schnorr, Guillou-Quisquater, Okamoto and Brickell-Mc.Curley.
In fact, the existence of one-way group homomorphisms is a sufficient assumption to support our construction. As we also demonstrate that our construction can be based on claw-free pairs of trapdoor one-way permutations, our results can be viewed as a generalization of the GMR signature scheme