research-article

Succinct delegation for low-space non-deterministic computation

Authors:

Saikrishna Badrinarayanan,

Yael Tauman Kalai,

Dakshita Khurana,

Daniel WichsAuthors Info & Claims

STOC 2018: Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing

Pages 709 - 721

https://doi.org/10.1145/3188745.3188924

Published: 20 June 2018 Publication History

Abstract

We construct a delegation scheme for verifying non-deterministic computations, with complexity proportional only to the non-deterministic space of the computation. Specifically, letting n denote the input length, we construct a delegation scheme for any language verifiable in non-deterministic time and space (T(n), S(n)) with communication complexity poly(S(n)), verifier runtime n.polylog(T(n))+poly(S(n)), and prover runtime poly(T(n)).

Our scheme consists of only two messages and has adaptive soundness, assuming the existence of a sub-exponentially secure private information retrieval (PIR) scheme, which can be instantiated under standard (albeit, sub-exponential) cryptographic assumptions, such as the sub-exponential LWE assumption. Specifically, the verifier publishes a (short) public key ahead of time, and this key can be used by any prover to non-interactively prove the correctness of any adaptively chosen non-deterministic computation. Such a scheme is referred to as a non-interactive delegation scheme. Our scheme is privately verifiable, where the verifier needs the corresponding secret key in order to verify proofs.

Prior to our work, such results were known only in the Random Oracle Model, or under knowledge assumptions. Our results yield succinct non-interactive arguments based on sub-exponential LWE, for many natural languages believed to be outside of P.

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References

[1]

Eric Allender, Shiteng Chen, Tiancheng Lou, Periklis A. Papakonstantinou, and Bangsheng Tang. 2014. Width-Parametrized SAT: Time–Space Tradeoffs. Theory of Computing 10 (2014), 297–339.

[2]

Prabhanjan Ananth, Yu-Chi Chen, Kai-Min Chung, Huijia Lin, and Wei-Kai Lin. 2015.

[3]

Delegating RAM Computations with Adaptive Soundness and Privacy. IACR Cryptology ePrint Archive 2015 (2015), 1082.

[4]

László Babai, Lance Fortnow, and Carsten Lund. 1991. Non-Deterministic Exponential Time has Two-Prover Interactive Protocols. Computational Complexity 1 (1991), 3–40.

Digital Library

[5]

Michael Ben-Or, Shafi Goldwasser, Joe Kilian, and Avi Wigderson. 1988. Multi-Prover Interactive Proofs: How to Remove Intractability Assumptions. 113–131.

Digital Library

[6]

Eli Ben-Sasson, Alessandro Chiesa, Christina Garman, Matthew Green, Ian Miers, Eran Tromer, and Madars Virza. 2014.

[7]

Zerocash: Decentralized Anonymous Payments from Bitcoin. In 2014 IEEE Symposium on Security and Privacy, SP 2014, Berkeley, CA, USA, May 18-21, 2014. 459–474.

Digital Library

[8]

Ingrid Biehl, Bernd Meyer, and Susanne Wetzel. 1998. Ensuring the Integrity of Agent-Based Computations by Short Proofs. In Mobile Agents, Second International Workshop, MA’98, Stuttgart, Germany, September 1998, Proceedings. 183–194.

Digital Library

[9]

Nir Bitansky, Ran Canetti, Alessandro Chiesa, Shafi Goldwasser, Huijia Lin, Aviad Rubinstein, and Eran Tromer. 2014. The Hunting of the SNARK. IACR Cryptology ePrint Archive 2014 (2014), 580. http://eprint.iacr.org/2014/580

[10]

Nir Bitansky, Ran Canetti, Alessandro Chiesa, and Eran Tromer. 2013. Recursive composition and bootstrapping for SNARKS and proof-carrying data. In STOC. ACM, 111–120.

Digital Library

[11]

Nir Bitansky, Alessandro Chiesa, Yuval Ishai, Rafail Ostrovsky, and Omer Paneth. 2013. Succinct Non-interactive Arguments via Linear Interactive Proofs. In TCC. 315–333. 3- 642- 36594- 2_18

Digital Library

[12]

Nir Bitansky, Sanjam Garg, Huijia Lin, Rafael Pass, and Sidharth Telang. 2015.

[13]

Succinct Randomized Encodings and their Applications. IACR Cryptology ePrint Archive 2015 (2015), 356.

[14]

Dan Boneh, Yuval Ishai, Amit Sahai, and David J. Wu. 2017. Lattice-Based SNARGs and Their Application to More Efficient Obfuscation. In Advances in Cryptology - EUROCRYPT 2017 - 36th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Paris, France, April 30 - May 4, 2017, Proceedings, Part III. 247–277. 3- 319- 56617- 7_9

[15]

Zvika Brakerski, Justin Holmgren, and Yael Tauman Kalai. 2017. Non-interactive delegation and batch NP verification from standard computational assumptions. In Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing, STOC 2017, Montreal, QC, Canada, June 19-23, 2017. 474–482.

Digital Library

[16]

Zvika Brakerski and Yael Tauman Kalai. 2018. A Toolbox for Succinct and Private Delegation with Applications to Access Control.

[17]

Ran Canetti, Yilei Chen, Justin Holmgren, and Mariana Raykova. 2015. Succinct Adaptive Garbled RAM. IACR Cryptology ePrint Archive 2015 (2015), 1074.

[18]

Ran Canetti and Justin Holmgren. 2016. Fully Succinct Garbled RAM. In ITCS. ACM, 169–178.

Digital Library

[19]

Ran Canetti, Justin Holmgren, Abhishek Jain, and Vinod Vaikuntanathan. 2015.

[20]

Succinct Garbling and Indistinguishability Obfuscation for RAM Programs. In STOC. ACM, 429–437.

[21]

Yu-Chi Chen, Sherman S. M. Chow, Kai-Min Chung, Russell W. F. Lai, Wei-Kai Lin, and Hong-Sheng Zhou. 2016.

[22]

Cryptography for Parallel RAM from Indistinguishability Obfuscation. In ITCS. ACM, 179–190.

Digital Library

[23]

Ivan Damgård. 1992.

[24]

Towards Practical Public Key Systems Secure Against Chosen Ciphertext attacks. Springer Berlin Heidelberg, Berlin, Heidelberg, 445–456. 540- 46766- 1_36

[25]

Ivan Damgård, Sebastian Faust, and Carmit Hazay. 2012.

[26]

Secure Two-Party Computation with Low Communication. In Theory of Cryptography - 9th Theory of Cryptography Conference, TCC 2012, Taormina, Sicily, Italy, March 19-21, 2012. Proceedings. 54–74. 3- 642- 28914- 9_4

Digital Library

[27]

Yevgeniy Dodis, Shai Halevi, Ron D. Rothblum, and Daniel Wichs. 2016. Spooky Encryption and its Applications. Cryptology ePrint Archive, Report 2016/272. http://eprint.iacr.org/.

[28]

Cynthia Dwork, Michael Langberg, Moni Naor, Kobbi Nissim, and Omer Reingold. 2001. Succinct Proofs for NP and Spooky Interactions. Unpublished manuscript.

[29]

Cynthia Dwork, Moni Naor, and Guy N. Rothblum. 2016. Spooky Interaction and its Discontents: Compilers for Succinct Two-Message Argument Systems. Cryptology ePrint Archive, Report 2016/291. http://eprint.iacr.org/.

[30]

Rosario Gennaro, Craig Gentry, Bryan Parno, and Mariana Raykova. 2013. Quadratic Span Programs and Succinct NIZKs without PCPs. In Advances in Cryptology - EUROCRYPT 2013, 32nd Annual International Conference on the Theory and Applications of Cryptographic Techniques, Athens, Greece, May 26-30, 2013. Proceedings. 626–645. 3- 642- 38348- 9_37

[31]

Craig Gentry and Daniel Wichs. 2011.

[32]

Separating Succinct Non-interactive Arguments from All Falsifiable Assumptions. In Proceedings of the Forty-third Annual ACM Symposium on Theory of Computing (STOC ’11). ACM, New York, NY, USA, 99–108.

Digital Library

[33]

Shafi Goldwasser, Yael Tauman Kalai, and Guy N. Rothblum. 2008. Delegating computation: interactive proofs for muggles. In Proceedings of the 40th Annual ACM Symposium on Theory of Computing, Victoria, British Columbia, Canada, May 17-20, 2008, Cynthia Dwork (Ed.). ACM, 113–122. 1374376.1374396 Full version in { ? }.

Digital Library

[34]

Jens Groth. 2010. Short Pairing-Based Non-interactive Zero-Knowledge Arguments. In ASIACRYPT (Lecture Notes in Computer Science), Vol. 6477. Springer, 321–340.

[35]

Pavel Hubacek and Daniel Wichs. 2015.

[36]

On the Communication Complexity of Secure Function Evaluation with Long Output. In Proceedings of the 2015 Conference on Innovations in Theoretical Computer Science (ITCS ’15). ACM, New York, NY, USA, 163–172.

Digital Library

[37]

Yael Tauman Kalai and Omer Paneth. 2015. Delegating RAM Computations. IACR Cryptology ePrint Archive 2015 (2015), 957.

[38]

Yael Tauman Kalai and Ran Raz. 2009. Probabilistically Checkable Arguments. In Advances in Cryptology - CRYPTO 2009, 29th Annual International Cryptology Conference, Santa Barbara, CA, USA, August 16-20, 2009. Proceedings. 143–159. 3- 642- 03356- 8_9

Digital Library

[39]

Yael Tauman Kalai, Ran Raz, and Ron D. Rothblum. 2013. Delegation for bounded space. In Symposium on Theory of Computing Conference, STOC’13, Palo Alto, CA, USA, June 1-4, 2013, Dan Boneh, Tim Roughgarden, and Joan Feigenbaum (Eds.). ACM, 565–574.

Digital Library

[40]

Yael Tauman Kalai, Ran Raz, and Ron D. Rothblum. 2014.

[41]

How to delegate computations: the power of no-signaling proofs. In STOC. ACM, 485–494.

[42]

Joe Kilian. 1992.

[43]

A Note on Efficient Zero-Knowledge Proofs and Arguments (Extended Abstract). In STOC. ACM, 723–732.

[44]

Venkata Koppula, Allison Bishop Lewko, and Brent Waters. 2015. Indistinguishability Obfuscation for Turing Machines with Unbounded Memory. In STOC. ACM, 419–428.

Digital Library

[45]

Helger Lipmaa. 2012. Progression-Free Sets and Sublinear Pairing-Based Non-Interactive Zero-Knowledge Arguments. In TCC. 169–189.

Digital Library

[46]

Silvio Micali. 1994. CS Proofs (Extended Abstracts). In 35th Annual Symposium on Foundations of Computer Science, Santa Fe, New Mexico, USA, 20-22 November 1994. IEEE Computer Society, 436–453. Full version in { ? }.

Digital Library

[47]

Omer Paneth and Guy N. Rothblum. 2017.

[48]

On Zero-Testable Homomorphic Encryption and Publicly Verifiable Non-Interactive Arguments. Cryptology ePrint Archive, Report 2017/903. http://eprint.iacr.org/2017/903.

[49]

Omer Reingold, Guy N. Rothblum, and Ron D. Rothblum. 2016. Constant-round interactive proofs for delegating computation. In Proceedings of the 48th Annual ACM SIGACT Symposium on Theory of Computing, STOC 2016, Cambridge, MA, USA, June 18-21, 2016. 49–62.

Digital Library

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Freitag CPaneth OPass R(2024)Public-Coin, Complexity-Preserving, Succinct Arguments of Knowledge for NP from Collision-ResistanceAdvances in Cryptology – EUROCRYPT 202410.1007/978-3-031-58737-5_5(112-141)Online publication date: 28-Apr-2024
https://doi.org/10.1007/978-3-031-58737-5_5
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Index Terms

Succinct delegation for low-space non-deterministic computation
1. Theory of computation
  1. Computational complexity and cryptography
    1. Interactive proof systems

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cover image ACM Conferences

STOC 2018: Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing

June 2018

1332 pages

ISBN:9781450355599

DOI:10.1145/3188745

General Chairs:
Ilias Diakonikolas
University of Southern California, USA
,
David Kempe
University of Southern California, USA
,
Program Chair:
Monika Henzinger
University of Vienna, Austria

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Published: 20 June 2018

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Cited By

Jin ZKalai YLombardi AVaikuntanathan VMohar BShinkar IO'Donnell R(2024)SNARGs under LWE via Propositional ProofsProceedings of the 56th Annual ACM Symposium on Theory of Computing10.1145/3618260.3649770(1750-1757)Online publication date: 10-Jun-2024
https://dl.acm.org/doi/10.1145/3618260.3649770
Freitag CPaneth OPass R(2024)Public-Coin, Complexity-Preserving, Succinct Arguments of Knowledge for NP from Collision-ResistanceAdvances in Cryptology – EUROCRYPT 202410.1007/978-3-031-58737-5_5(112-141)Online publication date: 28-Apr-2024
https://doi.org/10.1007/978-3-031-58737-5_5
Kiyoshima S(2023)No-Signaling Linear PCPsJournal of Cryptology10.1007/s00145-023-09448-436:2Online publication date: 22-Mar-2023
https://dl.acm.org/doi/10.1007/s00145-023-09448-4
Kiyoshima S(2023)Holographic SNARGs for P and Batch-NP from (Polynomially Hard) Learning with ErrorsTheory of Cryptography10.1007/978-3-031-48621-0_12(333-362)Online publication date: 29-Nov-2023
https://dl.acm.org/doi/10.1007/978-3-031-48621-0_12
Aldema Tshuva EBoyle ECohen RMoran TOshman R(2023)Locally Verifiable Distributed SNARGsTheory of Cryptography10.1007/978-3-031-48615-9_3(65-90)Online publication date: 27-Nov-2023
https://doi.org/10.1007/978-3-031-48615-9_3
Brakerski ZBrodsky MKalai YLombardi APaneth O(2023)SNARGs for Monotone Policy Batch NPAdvances in Cryptology – CRYPTO 202310.1007/978-3-031-38545-2_9(252-283)Online publication date: 20-Aug-2023
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Campanelli MGanesh CKhoshakhlagh HSiim J(2023)Impossibilities in Succinct Arguments: Black-Box Extraction and MoreProgress in Cryptology - AFRICACRYPT 202310.1007/978-3-031-37679-5_20(465-489)Online publication date: 13-Jul-2023
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Ghosal RSahai AWaters B(2023)Non-Interactive Publicly-Verifiable Delegation of Committed ProgramsPublic-Key Cryptography – PKC 202310.1007/978-3-031-31371-4_20(575-605)Online publication date: 2-May-2023
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Ben-David SKalai YPaneth O(2023)Verifiable Private Information RetrievalTheory of Cryptography10.1007/978-3-031-22368-6_1(3-32)Online publication date: 1-Jan-2023
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Devadas LGoyal RKalai YVaikuntanathan V(2022)Rate-1 Non-Interactive Arguments for Batch-NP and Applications2022 IEEE 63rd Annual Symposium on Foundations of Computer Science (FOCS)10.1109/FOCS54457.2022.00103(1057-1068)Online publication date: Oct-2022
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