Cryptology ePrint Archive: Report 2017/330

Distinguisher-Dependent Simulation in Two Rounds and its Applications

Abhishek Jain and Yael Tauman Kalai and Dakshita Khurana and Ron Rothblum

Abstract: We devise a novel simulation technique that makes black-box use of the adversary as well as the distinguisher. Using this technique we construct several round-optimal protocols, many of which were previously unknown even using non-black-box simulation techniques:

- Two-round witness indistinguishable (WI) arguments for $\NP$ from different assumptions than previously known.

- Two-round arguments and three-round proofs of knowledge for $\NP$ that achieve strong WI, witness hiding (WH) and distributional weak zero knowledge (WZK) properties in a setting where the instance is only determined by the prover in the last round of the interaction. The soundness of these protocols is guaranteed against adaptive provers.

- Three-round two-party computation satisfying input-indistinguishable security as well as a weaker notion of simulation security against malicious adversaries.

- Three-round extractable commitments with guaranteed correctness of extraction from polynomial hardness assumptions.

Our three-round protocols can be based on DDH or QR or N^th residuosity and our two-round protocols require quasi-polynomial hardness of the same assumptions. In particular, prior to this work, two-round WI arguments for NP were only known based on assumptions such as the existence of trapdoor permutations, hardness assumptions on bilinear maps, or the existence of program obfuscation; we give the first construction based on (quasi-polynomial) DDH.

Our simulation technique bypasses known lower bounds on black-box simulation [Goldreich-Krawcyzk'96] by using the distinguisher's output in a meaningful way. We believe that this technique is likely to find more applications in the future.

Category / Keywords: cryptographic protocols / input-delayed, weak zero knowledge, strong witness indistinguishability, witness hiding, two rounds, input indistinguishable computation

Date: received 13 Apr 2017, last revised 13 Apr 2017

Contact author: dakshita at cs ucla edu

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Version: 20170417:154329 (All versions of this report)

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