Unique Signatures and Verifiable Random Functions from the DH-DDH Separation

摘要: A unique signature scheme has the property that a ?PK(m) is (hard-to-compute) function of public key PK and message m, for all, even adversarially chosen, PK. Unique signatures, introduced by Goldwasser Ostrovsky, have been shown to be building block constructing verifiable random functions. Another useful signatures they are stateless: signer does not need update his secret after an invocation.The only previously known construction in plain model was based on RSA assumption. The other provably secure constructions stateless were Strong Here, we give generalization Diffie-Hellman assumption groups where decisional easy. Several recent results suggest plausibility such groups.We also few related functions (VRFs). VRFs, Micali, Rabin, Vadhan, objects combine properties pseudorandom (i.e. indistinguishability from querying) with verifiability property. Prior our work, VRFs exist under