research-article

Black-box non-black-box zero knowledge

Authors:

Rafail Ostrovsky,

Alessandra Scafuro,

Ivan ViscontiAuthors Info & Claims

STOC '14: Proceedings of the forty-sixth annual ACM symposium on Theory of computing

Pages 515 - 524

https://doi.org/10.1145/2591796.2591879

Published: 31 May 2014 Publication History

Abstract

Motivated by theoretical and practical interest, the challenging task of designing cryptographic protocols having only black-box access to primitives has generated various breakthroughs in the last decade. Despite such positive results, even though nowadays we know black-box constructions for secure two-party and multi-party computation even in constant rounds, there still are in Cryptography several constructions that critically require non-black-box use of primitives in order to securely realize some fundamental tasks. As such, the study of the gap between black-box and nonblack-box constructions still includes major open questions.

In this work we make progress towards filling the above gap. We consider the case of black-box constructions for computations requiring that even the size of the input of a player remains hidden. We show how to commit to a string of arbitrary size and to prove statements over the bits of the string. Both the commitment and the proof are succinct, hide the input size and use standard primitives in a blackbox way. We achieve such a result by giving a black-box construction of an extendable Merkle tree that relies on a novel use of the "MPC in the head" paradigm of Ishai et al. [STOC 2007].

We show the power of our new techniques by giving the first black-box constant-round public-coin zero knowledge argument for NP. To achieve this result we use the nonblack-box simulation technique introduced by Barak [FOCS 2001], the PCP of Proximity introduced by Ben-Sasson et al. [STOC 2004], together with a black-box public-coin witness indistinguishable universal argument that we construct along the way.

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Cited By

Hazay CVenkitasubramaniam MWeiss M(2023)Beyond MPC-in-the-Head: Black-Box Constructions of Short Zero-Knowledge ProofsTheory of Cryptography10.1007/978-3-031-48615-9_1(3-33)Online publication date: 27-Nov-2023
https://doi.org/10.1007/978-3-031-48615-9_1
Ishai YOstrovsky RShah A(2023)Succinct Arguments for RAM Programs via Projection CodesAdvances in Cryptology – CRYPTO 202310.1007/978-3-031-38545-2_6(159-192)Online publication date: 9-Aug-2023
https://doi.org/10.1007/978-3-031-38545-2_6
Chia NChung KLiang XYamakawa T(2022)Post-quantum Simulatable Extraction with Minimal Assumptions: Black-Box and Constant-RoundAdvances in Cryptology – CRYPTO 202210.1007/978-3-031-15982-4_18(533-563)Online publication date: 12-Oct-2022
https://doi.org/10.1007/978-3-031-15982-4_18
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Index Terms

Black-box non-black-box zero knowledge
1. Theory of computation

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cover image ACM Conferences

STOC '14: Proceedings of the forty-sixth annual ACM symposium on Theory of computing

May 2014

984 pages

ISBN:9781450327107

DOI:10.1145/2591796

Program Chair:
David Shmoys
Cornell University

Copyright © 2014 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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SIGACT: ACM Special Interest Group on Algorithms and Computation Theory

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 31 May 2014

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Research-article

Funding Sources

Xerox
Teradata Research Award
B. John Garrick Foundation Award
Division of Computer and Network Systems
United States-Israel Binational Science Foundation
Defense Advanced Research Projects Agency
Okawa Foundation for Information and Telecommunications
Division of Information and Intelligent Systems
International Business Machines Corporation
Lockheed Martin Corporation
Division of Computing and Communication Foundations

Conference

STOC '14

Sponsor:

SIGACT

STOC '14: Symposium on Theory of Computing

May 31 - June 3, 2014

New York, New York

Acceptance Rates

STOC '14 Paper Acceptance Rate 91 of 319 submissions, 29%;

Overall Acceptance Rate 1,469 of 4,586 submissions, 32%

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Cited By

Hazay CVenkitasubramaniam MWeiss M(2023)Beyond MPC-in-the-Head: Black-Box Constructions of Short Zero-Knowledge ProofsTheory of Cryptography10.1007/978-3-031-48615-9_1(3-33)Online publication date: 27-Nov-2023
https://doi.org/10.1007/978-3-031-48615-9_1
Ishai YOstrovsky RShah A(2023)Succinct Arguments for RAM Programs via Projection CodesAdvances in Cryptology – CRYPTO 202310.1007/978-3-031-38545-2_6(159-192)Online publication date: 9-Aug-2023
https://doi.org/10.1007/978-3-031-38545-2_6
Chia NChung KLiang XYamakawa T(2022)Post-quantum Simulatable Extraction with Minimal Assumptions: Black-Box and Constant-RoundAdvances in Cryptology – CRYPTO 202210.1007/978-3-031-15982-4_18(533-563)Online publication date: 12-Oct-2022
https://doi.org/10.1007/978-3-031-15982-4_18
VISCONTI IPointcheval D(2022)Zero‐Knowledge ProofsAsymmetric Cryptography10.1002/9781394188369.ch3(63-84)Online publication date: 30-Nov-2022
https://doi.org/10.1002/9781394188369.ch3
Liang XPandey O(2021)Towards a Unified Approach to Black-Box Constructions of Zero-Knowledge ProofsAdvances in Cryptology – CRYPTO 202110.1007/978-3-030-84259-8_2(34-64)Online publication date: 16-Aug-2021
https://dl.acm.org/doi/10.1007/978-3-030-84259-8_2
Garg SLiang XPandey OVisconti I(2020)Black-Box Constructions of Bounded-Concurrent Secure ComputationSecurity and Cryptography for Networks10.1007/978-3-030-57990-6_5(87-107)Online publication date: 7-Sep-2020
https://doi.org/10.1007/978-3-030-57990-6_5
Kiyoshima S(2020)Round-Optimal Black-Box Commit-and-Prove with Succinct CommunicationAdvances in Cryptology – CRYPTO 202010.1007/978-3-030-56880-1_19(533-561)Online publication date: 10-Aug-2020
https://doi.org/10.1007/978-3-030-56880-1_19
Miao P(2020)Cut-and-Choose for Garbled RAMTopics in Cryptology – CT-RSA 202010.1007/978-3-030-40186-3_26(610-637)Online publication date: 14-Feb-2020
https://doi.org/10.1007/978-3-030-40186-3_26
Libert BNguyen KTan BWang H(2019)Zero-Knowledge Elementary Databases with More Expressive QueriesPublic-Key Cryptography – PKC 201910.1007/978-3-030-17253-4_9(255-285)Online publication date: 6-Apr-2019
https://doi.org/10.1007/978-3-030-17253-4_9
Iovino VVisconti I(2019)Non-interactive Zero Knowledge Proofs in the Random Oracle ModelCodes, Cryptology and Information Security10.1007/978-3-030-16458-4_9(118-141)Online publication date: 28-Mar-2019
https://doi.org/10.1007/978-3-030-16458-4_9
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