A Complete Problem for Statistical Zero Knowledge

Abstract. We present the first complete problem for SZK, the class of promise problems possessing statistical zero-knowledge proofs (against an honest verifier). The problem, called STATISTICAL DIFFERENCE, is to decide whether two efficiently samplable distributions are either statistically close or far apart. This gives a new characterization of SZK that makes no reference to interaction or zero knowledge. We propose the use of complete problems to unify and extend the study of statistical zero knowledge. To this end, we examine several consequences of our Completeness Theorem and its proof, such as: --A way to make every (honest-verifier) statistical zero-knowledge proof very communication efficient, with the prover sending only one bit to the verifier (to achieve soundness error 1/2). Preliminary versions of this work appeared as SAHAI, A., AND VADHAN, S. P. 1997. A complete promise problem for statistical zero-knowledge, In Proceedings of the 38th Annual Symposium on Foundations of...

• Type: Journal
• Year: 2000
• Where: ECCC
• Authors: Amit Sahai, Salil P. Vadhan
• Keywords: Computer Science, DOD NDSEG Graduate, ECCC 2000, Zero-knowledge Proof