An epistemic characterization of zero knowledge

Authors:
Joseph Y. Halpern;Rafael Pass;Vasumathi Raman
Affiliations:
Cornell University, Ithaca, NY;Cornell University, Ithaca, NY;Cornell University, Ithaca, NY
Venue:
Proceedings of the 12th Conference on Theoretical Aspects of Rationality and Knowledge
Year:
2009

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Abstract

Halpern, Moses and Tuttle presented a definition of interactive proofs using a notion they called practical knowledge, but left open the question of finding an epistemic formula that completely characterizes zero knowledge; that is, a formula that holds iff a proof is zero knowledge. We present such a formula, and show that it does characterize zero knowledge. Moreover, we show that variants of the formula characterize variants of zero knowledge such as concurrent zero knowledge [Dwork, Naor, and Sahai 2004] and proofs of knowledge [Feige, Fiat, and Shamir 1987; Tompa and Woll 1987].