Hybrid Trapdoor Commitments and Their Applications

We introduce the notion of hybrid trapdoor commitment schemes. Intuitively an hybrid trapdoor commitment scheme is a primitive which can be either an unconditionally binding commitment scheme or a trapdoor commitment scheme depending on the distribution of commitment parameters. Moreover, such two distributions are computationally indistinguishable. Hybrid trapdoor commitments are related but different with respect to

mixed

commitments (introduced by Damgård and Nielsen at Crypto 2002). In particular hybrid trapdoor commitments can either be polynomially trapdoor commitments or unconditionally binding commitments, while mixed commitment can be either trapdoor commitments or extractable commitments. In this paper we show that strong notions (e.g., simulation sound, multi-trapdoor) of hybrid trapdoor commitments admit constructions based on the sole assumption that one-way functions exist as well as efficient constructions based on standard number-theoretic assumptions. To further stress the difference between hybrid and mixed commitments, we remark here that mixed commitments seems to require stronger theoretical assumptions (and the known number-theoretic constructions are less efficient). The main application of our results is that we show how to construct concurrent and simulation-sound zero-knowledge proof (in contrast to the arguments recently presented in [1,2,3]) systems in the common reference string model. We crucially use hybrid commitment since we present general constructions based on the sole assumption that one-way functions exists and very efficient constructions based on number-theoretic assumptions.