Precise Time and Space Simulatable Zero-Knowledge.
Ning Ding, Dawu Gu · 2009
Traditionally, the definition of zero-knowledge states that an interactive proof of x ∈ L provides zero (additional) knowledge if the view of any polynomial-time verifier can be reconstructed by a polynomial-time simulator. Since this definition only requires that the worst-case running-time of the verifier and simulator are polynomials, zero-knowledge becomes a worst-case notion. In STOC’06, Micali and Pass proposed a new notion of precise zero-knowledge, which captures the idea that the view of any verifier in every interaction can be reconstructed in (almost) the same time (i.e., the view can be “indistinguishably reconstructed”). This is the strongest notion among the known works towards precislization of the definition of zero-knowledge. However, as we know, there are two kinds of computational resources (i.e. time and space) that every algorithm consumes in computation. Although the view of a verifier in the interaction of a precise zero-knowledge protocol can be reconstructed in almost the same time, the simulator may run in very large space while at the same time the verifier only runs in very small space. In this case it is still doubtful to take indifference for the verifier to take part in the interaction or