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AntMan: Interactive Zero-Knowledge Proofs with Sublinear Communication

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Xiao WangAuthors Info & Claims

CCS '22: Proceedings of the 2022 ACM SIGSAC Conference on Computer and Communications Security

Pages 2901 - 2914

https://doi.org/10.1145/3548606.3560667

Published: 07 November 2022 Publication History

Abstract

Recent works on interactive zero-knowledge (ZK) protocols provide a new paradigm with high efficiency and scalability. However, these protocols suffer from high communication overhead, often linear to the circuit size. In this paper, we proposed two new ZK protocols with communication sublinear to the circuit size, while maintaining a similar level of computational efficiency.

(1) We designed a ZK protocol that can prove B executions of any circuit C in communication O(B + |C|) field elements (with free addition gates), while the best prior work requires a communication of O(B|C|) field elements. Our protocol is enabled by a new tool called as information-theoretic polynomial authentication code, which may be of independent interest.

(2) We developed an optimized implementation of this protocol which shows high practicality. For example, with B=2048, |C|=221, and under 50 Mbps bandwidth and 16 threads, QuickSilver, a state-of-the-art ZK protocol based on vector oblivious linear evaluation (VOLE), can only prove 0.71 million MULT gates per second (mgps) and send one field element per gate; our protocol can prove 15.74 mgps (22x improvement) and send 0.0061 field elements per gate (164x improvement) under the same hardware configuration.

(3) Extending the above idea, we constructed a ZK protocol that can prove a single execution of any circuit C in communication O(|C|3/4). This is the first ZK protocol with sublinear communication for an arbitrary circuit in the VOLE-based ZK family.

References

[1]

Scott Ames, Carmit Hazay, Yuval Ishai, and Muthuramakrishnan Venkitasubramaniam. 2017. Ligero: Lightweight Sublinear Arguments Without a Trusted Setup. In ACM CCS 2017, Bhavani M. Thuraisingham, David Evans, Tal Malkin, and Dongyan Xu (Eds.). ACM Press, Dallas, TX, USA, 2087--2104. https://doi.org/10.1145/3133956.3134104

Digital Library

[2]

Carsten Baum, Lennart Braun, Alexander Munch-Hansen, Benoît Razet, and Peter Scholl. 2021a. Appenzeller to Brie: Efficient Zero-Knowledge Proofs for Mixed-Mode Arithmetic and Z2k. In ACM CCS 2021, Giovanni Vigna and Elaine Shi (Eds.). ACM Press, Virtual Event, Republic of Korea, 192--211. https://doi.org/10.1145/3460120.3484812

Digital Library

[3]

Carsten Baum, Lennart Braun, Alexander Munch-Hansen, and Peter Scholl. 2022. Mozℤ2 k arella: Efficient Vector-OLE and Zero-Knowledge Proofs Over ℤ2 k. Cryptology ePrint Archive, Paper 2022/819. https://eprint.iacr.org/2022/819.

[4]

Carsten Baum, Alex J. Malozemoff, Marc B. Rosen, and Peter Scholl. 2021b. Mac'n'Cheese: Zero-Knowledge Proofs for Boolean and Arithmetic Circuits with Nested Disjunctions. In CRYPTO 2021, Part IV (LNCS, Vol. 12828), Tal Malkin and Chris Peikert (Eds.). Springer, Heidelberg, Germany, Virtual Event, 92--122. https://doi.org/10.1007/978-3-030-84259-8_4

Digital Library

[5]

Rikke Bendlin, Ivan Damgård, Claudio Orlandi, and Sarah Zakarias. 2011. Semi-homomorphic Encryption and Multiparty Computation. In EUROCRYPT 2011 (LNCS, Vol. 6632), Kenneth G. Paterson (Ed.). Springer, Heidelberg, Germany, Tallinn, Estonia, 169--188. https://doi.org/10.1007/978-3-642-20465-4_11

[6]

Nir Bitansky, Alessandro Chiesa, Yuval Ishai, Rafail Ostrovsky, and Omer Paneth. 2013. Succinct Non-interactive Arguments via Linear Interactive Proofs. In TCC 2013 (LNCS, Vol. 7785), Amit Sahai (Ed.). Springer, Heidelberg, Germany, Tokyo, Japan, 315--333. https://doi.org/10.1007/978-3-642-36594-2_18

[7]

Elette Boyle, Geoffroy Couteau, Niv Gilboa, and Yuval Ishai. 2018. Compressing Vector OLE. In ACM CCS 2019, David Lie, Mohammad Mannan, Michael Backes, and XiaoFeng Wang (Eds.). ACM Press, Toronto, ON, Canada, 896--912. https://doi.org/10.1145/3243734.3243868

Digital Library

[8]

Elette Boyle, Geoffroy Couteau, Niv Gilboa, Yuval Ishai, Lisa Kohl, Peter Rindal, and Peter Scholl. 2019. Efficient Two-Round OT Extension and Silent Non-Interactive Secure Computation. In ACM CCS 2019, Lorenzo Cavallaro, Johannes Kinder, XiaoFeng Wang, and Jonathan Katz (Eds.). ACM Press, London, UK, 291--308. https://doi.org/10.1145/3319535.3354255

Digital Library

[9]

Zvika Brakerski. 2012. Fully Homomorphic Encryption without Modulus Switching from Classical GapSVP. In CRYPTO 2012 (LNCS, Vol. 7417), Reihaneh Safavi-Naini and Ran Canetti (Eds.). Springer, Heidelberg, Germany, Santa Barbara, CA, USA, 868--886. https://doi.org/10.1007/978-3-642-32009-5_50

Digital Library

[10]

Zvika Brakerski, Craig Gentry, and Vinod Vaikuntanathan. 2012. (Leveled) fully homomorphic encryption without bootstrapping. In ITCS 2012, Shafi Goldwasser (Ed.). ACM, Cambridge, MA, USA, 309--325. https://doi.org/10.1145/2090236.2090262

Digital Library

[11]

Ran Canetti. 2001. Universally Composable Security: A New Paradigm for Cryptographic Protocols. In 42nd FOCS. IEEE Computer Society Press, Las Vegas, NV, USA, 136--145. https://doi.org/10.1109/SFCS.2001.959888

[12]

Geoffroy Couteau, Peter Rindal, and Srinivasan Raghuraman. 2021. Silver: Silent VOLE and Oblivious Transfer from Hardness of Decoding Structured LDPC Codes. In CRYPTO 2021, Part III (LNCS, Vol. 12827), Tal Malkin and Chris Peikert (Eds.). Springer, Heidelberg, Germany, Virtual Event, 502--534. https://doi.org/10.1007/978-3-030-84252-9_17

Digital Library

[13]

Ivan Damgr ard, Jesper Buus Nielsen, Michael Nielsen, and Samuel Ranellucci. 2017. The TinyTable Protocol for 2-Party Secure Computation, or: Gate-Scrambling Revisited. In CRYPTO 2017, Part I (LNCS, Vol. 10401), Jonathan Katz and Hovav Shacham (Eds.). Springer, Heidelberg, Germany, Santa Barbara, CA, USA, 167--187. https://doi.org/10.1007/978-3-319-63688-7_6

[14]

Ivan Damgård, Valerio Pastro, Nigel P. Smart, and Sarah Zakarias. 2012. Multiparty Computation from Somewhat Homomorphic Encryption. In CRYPTO 2012 (LNCS, Vol. 7417), Reihaneh Safavi-Naini and Ran Canetti (Eds.). Springer, Heidelberg, Germany, Santa Barbara, CA, USA, 643--662. https://doi.org/10.1007/978-3-642-32009-5_38

Digital Library

[15]

Samuel Dittmer, Yuval Ishai, Steve Lu, and Rafail Ostrovsky. 2022. Improving Line-Point Zero Knowledge: Two Multiplications for the Price of One. ACM Press.

[16]

Samuel Dittmer, Yuval Ishai, and Rafail Ostrovsky. 2021. Line-Point Zero Knowledge and Its Applications. In 2nd Conference on Information-Theoretic Cryptography.

[17]

Junfeng Fan and Frederik Vercauteren. 2012. Somewhat Practical Fully Homomorphic Encryption. Cryptology ePrint Archive, Report 2012/144. https://eprint.iacr.org/2012/144.

[18]

Nicholas Franzese, Jonathan Katz, Steve Lu, Rafail Ostrovsky, Xiao Wang, and Chenkai Weng. 2021. Constant-Overhead Zero-Knowledge for RAM Programs. In ACM CCS 2021, Giovanni Vigna and Elaine Shi (Eds.). ACM Press, Virtual Event, Republic of Korea, 178--191. https://doi.org/10.1145/3460120.3484800

Digital Library

[19]

Shafi Goldwasser, Yael Tauman Kalai, and Guy N. Rothblum. 2008. Delegating computation: interactive proofs for muggles. In 40th ACM STOC, Richard E. Ladner and Cynthia Dwork (Eds.). ACM Press, Victoria, BC, Canada, 113--122. https://doi.org/10.1145/1374376.1374396

Digital Library

[20]

Vipul Goyal, Antigoni Polychroniadou, and Yifan Song. 2021. Unconditional Communication-Efficient MPC via Hall's Marriage Theorem. In CRYPTO 2021, Part II (LNCS, Vol. 12826), Tal Malkin and Chris Peikert (Eds.). Springer, Heidelberg, Germany, Virtual Event, 275--304. https://doi.org/10.1007/978--3-030--84245--1_10

Digital Library

[21]

Shai Halevi and Victor Shoup. 2014. Algorithms in HElib. In CRYPTO 2014, Part I (LNCS, Vol. 8616), Juan A. Garay and Rosario Gennaro (Eds.). Springer, Heidelberg, Germany, Santa Barbara, CA, USA, 554--571. https://doi.org/10.1007/978-3-662-44371-2_31

[22]

David Heath and Vladimir Kolesnikov. 2020. Stacked Garbling for Disjunctive Zero-Knowledge Proofs. In EUROCRYPT 2020, Part III (LNCS, Vol. 12107), Anne Canteaut and Yuval Ishai (Eds.). Springer, Heidelberg, Germany, Zagreb, Croatia, 569--598. https://doi.org/10.1007/978-3-030-45727-3_19

Digital Library

[23]

Yuval Ishai and Anat Paskin. 2007. Evaluating Branching Programs on Encrypted Data. In TCC 2007 (LNCS, Vol. 4392), Salil P. Vadhan (Ed.). Springer, Heidelberg, Germany, Amsterdam, The Netherlands, 575--594. https://doi.org/10.1007/978-3-540-70936-7_31

[24]

Marek Jawurek, Florian Kerschbaum, and Claudio Orlandi. 2013. Zero-knowledge using garbled circuits: how to prove non-algebraic statements efficiently. In ACM CCS 2013, Ahmad-Reza Sadeghi, Virgil D. Gligor, and Moti Yung (Eds.). ACM Press, Berlin, Germany, 955--966. https://doi.org/10.1145/2508859.2516662

Digital Library

[25]

Marcel Keller, Valerio Pastro, and Dragos Rotaru. 2018. Overdrive: Making SPDZ Great Again. In EUROCRYPT 2018, Part III (LNCS, Vol. 10822), Jesper Buus Nielsen and Vincent Rijmen (Eds.). Springer, Heidelberg, Germany, Tel Aviv, Israel, 158--189. https://doi.org/10.1007/978-3-319-78372-7_6

[26]

Jesper Buus Nielsen, Peter Sebastian Nordholt, Claudio Orlandi, and Sai Sheshank Burra. 2012. A New Approach to Practical Active-Secure Two-Party Computation. In CRYPTO 2012 (LNCS, Vol. 7417), Reihaneh Safavi-Naini and Ran Canetti (Eds.). Springer, Heidelberg, Germany, Santa Barbara, CA, USA, 681--700. https://doi.org/10.1007/978-3-642-32009-5_40

Digital Library

[27]

Phillipp Schoppmann, Adrià Gascón, Leonie Reichert, and Mariana Raykova. 2019. Distributed Vector-OLE: Improved Constructions and Implementation. In ACM CCS 2019, Lorenzo Cavallaro, Johannes Kinder, XiaoFeng Wang, and Jonathan Katz (Eds.). ACM Press, London, UK, 1055--1072. https://doi.org/10.1145/3319535.3363228

Digital Library

[28]

Xiao Wang, Alex J. Malozemoff, and Jonathan Katz. 2016. EMP-toolkit: Efficient MultiParty computation toolkit. https://github.com/emp-toolkit.

[29]

Chenkai Weng, Kang Yang, Jonathan Katz, and Xiao Wang. 2021a. Wolverine: Fast, Scalable, and Communication-Efficient Zero-Knowledge Proofs for Boolean and Arithmetic Circuits. In 2021 IEEE Symposium on Security and Privacy. IEEE Computer Society Press, San Francisco, CA, USA, 1074--1091. https://doi.org/10.1109/SP40001.2021.00056

[30]

Chenkai Weng, Kang Yang, Xiang Xie, Jonathan Katz, and Xiao Wang. 2021b. Mystique: Efficient Conversions for Zero-Knowledge Proofs with Applications to Machine Learning. In USENIX Security 2021, Michael Bailey and Rachel Greenstadt (Eds.). USENIX Association, 501--518.

[31]

Chenkai Weng, Kang Yang, Zhaomin Yang, Xiang Xie, and Xiao Wang. 2022. AntMan: Interactive Zero-Knowledge Proofs with Sublinear Communication. Cryptology ePrint Archive, Paper 2022/566. https://eprint.iacr.org/2022/566.

[32]

Kang Yang, Pratik Sarkar, Chenkai Weng, and Xiao Wang. 2021a. QuickSilver: Efficient and Affordable Zero-Knowledge Proofs for Circuits and Polynomials over Any Field. In ACM CCS 2021, Giovanni Vigna and Elaine Shi (Eds.). ACM Press, Virtual Event, Republic of Korea, 2986--3001. https://doi.org/10.1145/3460120.3484556

Digital Library

[33]

Kang Yang and Xiao Wang. 2022. Non-Interactive Zero-Knowledge Proofs to Multiple Verifiers. Cryptology ePrint Archive, Report 2022/063. https://eprint.iacr.org/2022/063.

[34]

Kang Yang, Chenkai Weng, Xiao Lan, Jiang Zhang, and Xiao Wang. 2020. Ferret: Fast Extension for Correlated OT with Small Communication. In ACM CCS 2020, Jay Ligatti, Xinming Ou, Jonathan Katz, and Giovanni Vigna (Eds.). ACM Press, Virtual Event, USA, 1607--1626. https://doi.org/10.1145/3372297.3417276

Digital Library

[35]

Zhaomin Yang, Xiang Xie, Huajie Shen, Shiying Chen, and Jun Zhou. 2021b. TOTA: Fully Homomorphic Encryption with Smaller Parameters and Stronger Security. Cryptology ePrint Archive, Paper 2021/1347. https://eprint.iacr.org/2021/1347 https://eprint.iacr.org/2021/1347.

[36]

Jiaheng Zhang, Tianyi Liu, Weijie Wang, Yinuo Zhang, Dawn Song, Xiang Xie, and Yupeng Zhang. 2021. Doubly Efficient Interactive Proofs for General Arithmetic Circuits with Linear Prover Time. In ACM CCS 2021, Giovanni Vigna and Elaine Shi (Eds.). ACM Press, Virtual Event, Republic of Korea, 159--177. https://doi.org/10.1145/3460120.3484767

Digital Library

Cited By

Bui DChu HCouteau GWang XWeng CYang KYu Y(2025)An Efficient ZK Compiler from SIMD Circuits to General CircuitsJournal of Cryptology10.1007/s00145-024-09531-438:1Online publication date: 1-Jan-2025
https://dl.acm.org/doi/10.1007/s00145-024-09531-4
Wang RHazay CVenkitasubramaniam M(2024)Ligetron: Lightweight Scalable End-to-End Zero-Knowledge Proofs Post-Quantum ZK-SNARKs on a Browser2024 IEEE Symposium on Security and Privacy (SP)10.1109/SP54263.2024.00086(1760-1776)Online publication date: 19-May-2024
https://doi.org/10.1109/SP54263.2024.00086
Ouyang YTang DXu Y(2024)Code-Based Zero-Knowledge from VOLE-in-the-Head and Their Applications: Simpler, Faster, and SmallerAdvances in Cryptology – ASIACRYPT 202410.1007/978-981-96-0935-2_14(436-470)Online publication date: 9-Dec-2024
https://doi.org/10.1007/978-981-96-0935-2_14
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Index Terms

AntMan: Interactive Zero-Knowledge Proofs with Sublinear Communication
1. Theory of computation
  1. Computational complexity and cryptography
    1. Cryptographic protocols

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cover image ACM Conferences

CCS '22: Proceedings of the 2022 ACM SIGSAC Conference on Computer and Communications Security

November 2022

3598 pages

ISBN:9781450394505

DOI:10.1145/3548606

General Chairs:
Heng Yin
University of California, Riverside
,
Angelos Stavrou
Virginia Tech
,
Program Chairs:
Cas Cremers
CISPA Helmholtz Center for Information Security
,
Elaine Shi
Carnegie Mellon University

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Published: 07 November 2022

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Cited By

Bui DChu HCouteau GWang XWeng CYang KYu Y(2025)An Efficient ZK Compiler from SIMD Circuits to General CircuitsJournal of Cryptology10.1007/s00145-024-09531-438:1Online publication date: 1-Jan-2025
https://dl.acm.org/doi/10.1007/s00145-024-09531-4
Wang RHazay CVenkitasubramaniam M(2024)Ligetron: Lightweight Scalable End-to-End Zero-Knowledge Proofs Post-Quantum ZK-SNARKs on a Browser2024 IEEE Symposium on Security and Privacy (SP)10.1109/SP54263.2024.00086(1760-1776)Online publication date: 19-May-2024
https://doi.org/10.1109/SP54263.2024.00086
Ouyang YTang DXu Y(2024)Code-Based Zero-Knowledge from VOLE-in-the-Head and Their Applications: Simpler, Faster, and SmallerAdvances in Cryptology – ASIACRYPT 202410.1007/978-981-96-0935-2_14(436-470)Online publication date: 9-Dec-2024
https://doi.org/10.1007/978-981-96-0935-2_14
Hazay CHeath DKolesnikov VVenkitasubramaniam MYang Y(2024)++: Optimizing Proofs of Disjunctive Statements in VOLE-Based ZKAdvances in Cryptology – ASIACRYPT 202410.1007/978-981-96-0935-2_12(367-401)Online publication date: 10-Dec-2024
https://dl.acm.org/doi/10.1007/978-981-96-0935-2_12
Lin FXing CYao Y(2024)Interactive Line-Point Zero-Knowledge with Sublinear Communication and Linear ComputationAdvances in Cryptology – ASIACRYPT 202410.1007/978-981-96-0935-2_11(337-366)Online publication date: 9-Dec-2024
https://doi.org/10.1007/978-981-96-0935-2_11
Baum CBeullens WMukherjee SOrsini ERamacher SRechberger CRoy LScholl P(2024)One Tree to Rule Them All: Optimizing GGM Trees and OWFs for Post-Quantum SignaturesAdvances in Cryptology – ASIACRYPT 202410.1007/978-981-96-0875-1_15(463-493)Online publication date: 10-Dec-2024
https://dl.acm.org/doi/10.1007/978-981-96-0875-1_15
Nguyen WDatta TChen BTyagi NBoneh D(2024)Mangrove: A Scalable Framework for Folding-Based SNARKsAdvances in Cryptology – CRYPTO 202410.1007/978-3-031-68403-6_10(308-344)Online publication date: 18-Aug-2024
https://dl.acm.org/doi/10.1007/978-3-031-68403-6_10
Lin FXing CYao Y(2024)More Efficient Zero-Knowledge Protocols over $$\mathbb {Z}_{2^k}$$ via Galois RingsAdvances in Cryptology – CRYPTO 202410.1007/978-3-031-68400-5_13(424-457)Online publication date: 16-Aug-2024
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Liu HWang XYang KYu Y(2024)The Hardness of LPN over Any Integer Ring and Field for PCG ApplicationsAdvances in Cryptology – EUROCRYPT 202410.1007/978-3-031-58751-1_6(149-179)Online publication date: 26-May-2024
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Cui HLiu HYan DYang KYu YZhang K(2024): Shorter Signatures from Regular Syndrome Decoding and VOLE-in-the-HeadPublic-Key Cryptography – PKC 202410.1007/978-3-031-57718-5_8(229-258)Online publication date: 15-Apr-2024
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