Cryptology ePrint Archive: Report 2020/1160

Characterizing Deterministic-Prover Zero Knowledge

Nir Bitansky and Arka Rai Choudhuri

Abstract: Randomness is typically thought to be essential for zero knowledge protocols. Following this intuition, Goldreich and Oren (Journal of Cryptology 94) proved that auxiliary-input zero knowledge cannot be achieved with a deterministic prover. On the other hand, positive results are only known in the honest-verifier setting, or when the prover is given at least a restricted source of entropy. We prove that removing (or just bounding) the verifier's auxiliary input, deterministic-prover zero knowledge becomes feasible:

- Assuming non-interactive witness-indistinguishable proofs and subexponential indistinguishability obfuscation and one-way functions, we construct deterministic-prover zero-knowledge arguments for $\mathsf{NP}\cap \mathsf{coNP}$ against verifiers with bounded non-uniform auxiliary input.

- Assuming also keyless hash functions that are collision-resistant against bounded-auxiliary-input quasipolynomial-time attackers, we construct similar arguments for all of $\mathsf{NP}$.

Together with the result of Goldreich and Oren, this characterizes when deterministic-prover zero knowledge is feasible. We also demonstrate the necessity of strong assumptions, by showing that deterministic prover zero knowledge arguments for a given language imply witness encryption for that language. We further prove that such arguments can always be collapsed to two messages and be made laconic. These implications rely on a more general connection with the notion of predictable arguments by Faonio, Nielsen, and Venturi (PKC 17).

Category / Keywords: foundations / zero knowledge

Original Publication (in the same form): IACR-TCC-2020

Date: received 23 Sep 2020, last revised 23 Sep 2020

Contact author: nirbitan at tau ac il,achoud@cs jhu edu

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Version: 20200925:184612 (All versions of this report)

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