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On Round Optimal Statistical Zero Knowledge Arguments

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Advances in Cryptology – CRYPTO 2019 (CRYPTO 2019)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 11694))

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Abstract

We construct the first three message statistical zero knowledge arguments for all of NP, matching the known lower bound. We do so based on keyless multi-collision resistant hash functions and the Learning with Errors assumption—the same assumptions used to obtain round optimal computational zero knowledge.

The main component in our construction is a statistically witness indistinguishable argument of knowledge based on a new notion of statistically hiding commitments with subset opening.

N. Bitansky—Member of the Check Point Institute of Information Security. Supported by ISF grant 18/484, the Alon Young Faculty Fellowship, and by Len Blavatnik and the Blavatnik Family Foundation.

O. Paneth—Supported by NSF Grants CNS-1413964, CNS-1350619 and CNS-1414119, and the Defense Advanced Research Projects Agency (DARPA) and the U.S. Army Research Office under contracts W911NF-15-C-0226 and W911NF-15-C-0236.

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Notes

  1. 1.

    Here LWE is used to realize several generic primitives, which we address in the body.

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Author information

Authors and Affiliations

  1. Tel Aviv University, Tel Aviv-Yafo, Israel

    Nir Bitansky

  2. MIT and Northeastern University, Cambridge, USA

    Omer Paneth

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  1. Nir Bitansky
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  2. Omer Paneth
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Correspondence to Nir Bitansky or Omer Paneth .

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Editors and Affiliations

  1. Georgia Institute of Technology, Atlanta, GA, USA

    Alexandra Boldyreva

  2. University of California at San Diego, La Jolla, CA, USA

    Daniele Micciancio

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Bitansky, N., Paneth, O. (2019). On Round Optimal Statistical Zero Knowledge Arguments. In: Boldyreva, A., Micciancio, D. (eds) Advances in Cryptology – CRYPTO 2019. CRYPTO 2019. Lecture Notes in Computer Science(), vol 11694. Springer, Cham. https://doi.org/10.1007/978-3-030-26954-8_5

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  • DOI: https://doi.org/10.1007/978-3-030-26954-8_5

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