Abstract
In this work, we address communication, computation, and round efficiency of unconditionally secure multi-party computation for arithmetic circuits in the honest majority setting. We achieve both algorithmic and practical improvements:
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The best known result in the semi-honest setting has been due to Damgård and Nielsen (CRYPTO 2007). Over the last decade, their construction has played an important role in the progress of efficient secure computation. However despite a number of follow-up works, any significant improvements to the basic semi-honest protocol have been hard to come by. We show \(33\%\) improvement in communication complexity of this protocol. We show how to generalize this result to the malicious setting, leading to the best known unconditional honest majority MPC with malicious security.
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We focus on the round complexity of the Damgård and Nielsen protocol and improve it by a factor of 2. Our improvement relies on a novel observation relating to an interplay between Damgård and Nielsen multiplication and Beaver triple multiplication. An implementation of our constructions shows an execution run time improvement compared to the state of the art ranging from \(30\%\) to \(50\%\).
H. Li—Work done in part while at CMU.
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Notes
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The requirement of the field size is due to the use of so-called hyper-invertible matrices in our construction. See more discussion in Section 3.2 of [BTH08].
References
Araki, T., et al.: Optimized honest-majority MPC for malicious adversaries - breaking the 1 billion-gate per second barrier. In: 2017 IEEE Symposium on Security and Privacy (SP), pp. 843–862. IEEE (2017)
Boneh, D., Boyle, E., Corrigan-Gibbs, H., Gilboa, N., Ishai, Y.: Zero-knowledge proofs on secret-shared data via fully linear PCPs. In: Boldyreva, A., Micciancio, D. (eds.) CRYPTO 2019. LNCS, vol. 11694, pp. 67–97. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-26954-8_3
Beaver, D.: Efficient multiparty protocols using circuit randomization. In: Feigenbaum, J. (ed.) CRYPTO 1991. LNCS, vol. 576, pp. 420–432. Springer, Heidelberg (1992). https://doi.org/10.1007/3-540-46766-1_34
Ben-Or, M., Goldwasser, S., Wigderson, A.: Completeness theorems for non-cryptographic fault-tolerant distributed computation. In: Proceedings of the Twentieth Annual ACM Symposium on Theory of Computing, pp. 1–10. ACM (1988)
Ben-Sasson, E., Fehr, S., Ostrovsky, R.: Near-linear unconditionally-secure multiparty computation with a dishonest minority. In: Safavi-Naini, R., Canetti, R. (eds.) CRYPTO 2012. LNCS, vol. 7417, pp. 663–680. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-32009-5_39
Beerliová-Trubíniová, Z., Hirt, M.: Perfectly-secure MPC with linear communication complexity. In: Canetti, R. (ed.) TCC 2008. LNCS, vol. 4948, pp. 213–230. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-78524-8_13
Chaum, D., Crépeau, C., Damgård, I.: Multiparty unconditionally secure protocols. In: Proceedings of the Twentieth Annual ACM Symposium on Theory of Computing, pp. 11–19. ACM (1988)
Chaum, D., Damgård, I.B., van de Graaf, J.: Multiparty computations ensuring privacy of each party’s input and correctness of the result. In: Pomerance, C. (ed.) CRYPTO 1987. LNCS, vol. 293, pp. 87–119. Springer, Heidelberg (1988). https://doi.org/10.1007/3-540-48184-2_7
Chida, K., et al.: Fast large-scale honest-majority MPC for malicious adversaries. In: Shacham, H., Boldyreva, A. (eds.) CRYPTO 2018. LNCS, vol. 10993, pp. 34–64. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-96878-0_2
Damgård, I., Ishai, Y., Krøigaard, M.: Perfectly secure multiparty computation and the computational overhead of cryptography. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 445–465. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-13190-5_23
Damgård, I., Nielsen, J.B.: Scalable and unconditionally secure multiparty computation. In: Menezes, A. (ed.) CRYPTO 2007. LNCS, vol. 4622, pp. 572–590. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-74143-5_32
Damgård, I., Nielsen, J.B., Polychroniadou, A., Raskin, M.: On the communication required for unconditionally secure multiplication. In: Robshaw, M., Katz, J. (eds.) CRYPTO 2016. LNCS, vol. 9815, pp. 459–488. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-53008-5_16
Furukawa, J., Lindell, Y., Nof, A., Weinstein, O.: High-throughput secure three-party computation for malicious adversaries and an honest majority. In: Coron, J.-S., Nielsen, J.B. (eds.) EUROCRYPT 2017. LNCS, vol. 10211, pp. 225–255. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-56614-6_8
Genkin, D., Ishai, Y., Prabhakaran, M.M., Sahai, A., Tromer, E.: Circuits resilient to additive attacks with applications to secure computation. In: Proceedings of the Forty-sixth Annual ACM Symposium on Theory of Computing. STOC 2014, pp. 495–504. ACM, New York (2014)
Goyal, V., Li, H., Ostrovsky, R., Polychroniadou, A., Song, Y.: ATLAS: efficient and scalable MPC in the honest majority setting. Cryptology ePrint Archive, Report 2021/833 (2021)
Goyal, V., Liu, Y., Song, Y.: Communication-efficient unconditional MPC with guaranteed output delivery. In: Boldyreva, A., Micciancio, D. (eds.) CRYPTO 2019. LNCS, vol. 11693, pp. 85–114. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-26951-7_4
Goldreich, O., Micali, S., Wigderson, A.: How to play any mental game. In: Proceedings of the Nineteenth Annual ACM Symposium on Theory of Computing, pp. 218–229. ACM (1987)
Goyal, V., Song, Y.: Malicious security comes free in honest-majority MPC. Cryptology ePrint Archive, Report 2020/134 (2020). https://eprint.iacr.org/2020/134
Goyal, V., Song, Y., Zhu, C.: Guaranteed output delivery comes free in honest majority MPC. In: Micciancio, D., Ristenpart, T. (eds.) CRYPTO 2020. LNCS, vol. 12171, pp. 618–646. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-56880-1_22
Hirt, M., Maurer, U.: Robustness for free in unconditional multi-party computation. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 101–118. Springer, Heidelberg (2001). https://doi.org/10.1007/3-540-44647-8_6
Hirt, M., Maurer, U., Przydatek, B.: Efficient secure multi-party computation. In: Okamoto, T. (ed.) ASIACRYPT 2000. LNCS, vol. 1976, pp. 143–161. Springer, Heidelberg (2000). https://doi.org/10.1007/3-540-44448-3_12
Lindell, Y., Nof, A.: A framework for constructing fast MPC over arithmetic circuits with malicious adversaries and an honest-majority. In: Proceedings of the 2017 ACM SIGSAC Conference on Computer and Communications Security, pp. 259–276. ACM (2017)
Lindell, Y., Pinkas, B.: Secure two-party computation via cut-and-choose oblivious transfer. J. Cryptol. 25(4), 680–722 (2012). https://doi.org/10.1007/s00145-011-9107-0
Nielsen, J.B., Nordholt, P.S., Orlandi, C., Burra, S.S.: A new approach to practical active-secure two-party computation. In: Safavi-Naini, R., Canetti, R. (eds.) CRYPTO 2012. LNCS, vol. 7417, pp. 681–700. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-32009-5_40
Nordholt, P.S., Veeningen, M.: Minimising communication in honest-majority MPC by batchwise multiplication verification. In: Preneel, B., Vercauteren, F. (eds.) ACNS 2018. LNCS, vol. 10892, pp. 321–339. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-93387-0_17
Shamir, A.: How to share a secret. Commun. ACM 22(11), 612–613 (1979)
Yao, A.C.: Protocols for secure computations. In: 1982 23rd Annual Symposium on Foundations of Computer Science. SFCS’08, pp. 160–164. IEEE (1982)
Acknowledgements
V. Goyal, H. Li, Y. Song—Supported in part by the NSF award 1916939, DARPA SIEVE program, a gift from Ripple, a DoE NETL award, a JP Morgan Faculty Fellowship, a PNC center for financial services innovation award, and a Cylab seed funding award.
R. Ostrovsky—Supported in part by DARPA under Cooperative Agreement HR0011-20-2-0025, NSF grant CNS-2001096, US-Israel BSF grant 2015782, Google Faculty Award, JP Morgan Faculty Award, IBM Faculty Research Award, Xerox Faculty Research Award, OKAWA Foundation Research Award, B. John Garrick Foundation Award, Teradata Research Award, Lockheed-Martin Research Award and Sunday Group. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies, either expressed or implied, of DARPA, the Department of Defense, or the U.S. Government. The U.S. Government is authorized to reproduce and distribute reprints for governmental purposes not withstanding any copyright annotation therein.
A. Polychroniadou—This paper was prepared in part for information purposes by the Artificial Intelligence Research group of JPMorgan Chase & Co and its affiliates (“JP Morgan”), and is not a product of the Research Department of JP Morgan. JP Morgan makes no representation and warranty whatsoever and disclaims all liability, for the completeness, accuracy or reliability of the information contained herein. This document is not intended as investment research or investment advice, or a recommendation, offer or solicitation for the purchase or sale of any security, financial instrument, financial product or service, or to be used in any way for evaluating the merits of participating in any transaction, and shall not constitute a solicitation under any jurisdiction or to any person, if such solicitation under such jurisdiction or to such person would be unlawful. 2020 JPMorgan Chase & Co. All rights reserved.
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Goyal, V., Li, H., Ostrovsky, R., Polychroniadou, A., Song, Y. (2021). ATLAS: Efficient and Scalable MPC in the Honest Majority Setting. In: Malkin, T., Peikert, C. (eds) Advances in Cryptology – CRYPTO 2021. CRYPTO 2021. Lecture Notes in Computer Science(), vol 12826. Springer, Cham. https://doi.org/10.1007/978-3-030-84245-1_9
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