Zaps and Their Applications

TLDR: This work presents a zap for every language in NP, based on the existence of noninteractive zero-knowledge proofs in the shared random string model, and characterize theexistence of zaps in terms of a primitive called verifiable pseudorandom bit generators.

Abstract: A zap is a 2-round, public coin witness-indistinguishable protocol in which the first round, consisting of a message from the verifier to the prover, can be fixed “once and for all” and applied to any instance. We present a zap for every language in NP, based on the existence of noninteractive zero-knowledge proofs in the shared random string model. The zap is in the standard model and hence requires no common guaranteed random string. We present several applications for zaps, including 3-round concurrent zero-knowledge and 2-round concurrent deniable authentication, in the timing model of Dwork, Naor, and Sahai [J. ACM, 51 (2004), pp. 851-898], using moderately hard functions. We also characterize the existence of zaps in terms of a primitive called verifiable pseudorandom bit generators.