One-Time Signatures and Chameleon Hash Functions

In this work we show a general construction for transforming any chameleon hash function to a strongly unforgeable one-time signature scheme. Combined with the result of [Bellare and Ristov, PKC 2007], this also implies a general construction of strongly unforgeable one-time signatures from Σ-protocols in the standard model. Our results explain and unify several works in the literature which either use chameleon hash functions or one-time signatures, by showing that several of the constructions in the former category can be interpreted as efficient instantiations of those in the latter. They also imply that any “noticeable” improvement to the efficiency of constructions for chameleon hash functions leads to similar improvements for one-time signatures. This makes such improvements challenging since efficiency of one-time signatures has been studied extensively. We further demonstrate the usefulness of our general construction by studying and optimizing specific instantiations based on the hardness of factoring, the discrete-log problem, and the worst-case lattice-based assumptions. Some of these signature schemes match or improve the efficiency of the best previous constructions or relax the underlying hardness assumptions. Two of the schemes have very fast signing (no exponentiations) which makes them attractive in scenarios where the signer has limited computational resources.