A note on efficient zero-knowledge proofs and arguments

Abstract

In this note, we present new zero-knowledge interactive proofs and arguments for languages in NP. To show that X ∈ L, with an error probability of at most 2-κ, our zero-knowledge proof system requires O(|x|C1) + O(lgCa |x|)κ ideal bit commitments, where c1 and c2 depend only on L. This construction is the first in the ideal bit commitment model that achieves large values of k more efficiently than by running k independent iterations of the base interactive proof system. Under suitable complexity assumptions, we exhibit a zero-knowledge arguments that require O(lgc |x|)kl bits of communication, where c depends only on L, and l is the security parameter for the prover.1 This is the first construction in which the total amount of communication can be less than that needed to transmit the N P witness. Our protocols are based on efficiently checkable proofs for N P [4].