Never trust victor: An alternative resettable zero-knowledge proof system

Abstract

We present a new resettable zero-knowledge proof system for graph 3-colorability with round complexity O(u(n) log2 n), where u: ℕ → ℝ>0 is any unbounded function and n denotes the number of vertices in the graph. Furthermore, we present a new formulation of the definition of resettable zero-knowledge and define and implement a knowledgeable commitment scheme: after the commitment phase the receiver is convinced that the sender knows a valid decommitment. This remains true even if the receiver is resettable, albeit with the drawback of non-constant round complexity. This is achieved by appending a resettable perfect witness-indistinguishable proof of knowledge of a decommitment to the original commit phase. We base all our constructions on a standard intractability assumption: the hardness of one of the many variants of the discrete logarithm problem.