We show that every language in NP has a statistical zero-knowledge
argument system under the (minimal) complexity assumption that one-way
functions exist. In such protocols, even a computationally unbounded verifier
cannot learn anything other than the fact that the assertion being proven is
true, whereas a polynomial-time prover cannot convince the verifier to accept a
false assertion except with negligible probability. This resolves an open
question posed by Naor, Ostrovsky, Venkatesan, and Yung (CRYPTO `92, J.
Departing from previous works on this problem, we do not construct standard statistically hiding commitments from any one-way function. Instead, we construct a relaxed variant of commitment schemes called "1-out-of-2-binding commitments," recently introduced by Nguyen and Vadhan (STOC `06).
This paper is superseded by Statistically Hiding Commitments and Statistical Zero-Knowledge Arguments from Any One-Way Function.