ABSTRACT
We present a novel approach to honest majority secure multiparty computation in the preprocessing model with information theoretic security that achieves the best online communication complexity. The online phase of our protocol requires 12 elements in total per multiplication gate with circuit-dependent preprocessing, or 20 elements in total with circuit-independent preprocessing. Prior works achieved linear online communication complexity in n, the number of parties, with the best prior existing solution involving 1.5n elements per multiplication gate. Only one recent work packing [28] achieves constant online communication complexity, but the constants are large (108 elements for passive security, and twice that for active security). That said, our protocol offers a very efficient information theoretic online phase for any number of parties.
The total end-to-end communication cost with the preprocessing phase is linear in n, i.e., 10n + 44, which is larger than the 4n complexity of the state-of-the-art protocols. The gap is not significant when the online phase must be optimized as a priority and a reasonably large number of parties is involved. Unlike previous works based on packed secret-sharing to reduce communication complexity, we further reduce the communication by avoiding the use of complex and expensive network routing or permutations tools. Furthermore, we also allow for a maximal honest majority adversary, while most previous works require the set of honest parties to be strictly larger than a majority.
Our protocol is simple and offers concrete efficiency. To illustrate this we present a full-fledged implementation together with experimental results that show improvements in online phase runtimes that go up to 5x in certain settings (e.g. 45 parties, LAN network, circuit of depth 10 with 1M gates).
- Mark Abspoel, Ronald Cramer, Daniel Escudero, Ivan Damgård, and Chaoping Xing. 2021. Improved single-round secure multiplication using regenerating codes. In International Conference on the Theory and Application of Cryptology and Information Security. Springer, 222--244.Google ScholarDigital Library
- Donald Beaver. 1992. Efficient Multiparty Protocols Using Circuit Randomization. In Advances in Cryptology -- CRYPTO '91, Joan Feigenbaum (Ed.). Springer Berlin Heidelberg, Berlin, Heidelberg, 420--432.Google Scholar
- Gabrielle Beck, Aarushi Goel, Abhishek Jain, and Gabriel Kaptchuk. 2021a. Order-C Secure Multiparty Computation for Highly Repetitive Circuits. In Advances in Cryptology -- EUROCRYPT 2021. Springer International Publishing, Cham, 663--693.Google ScholarDigital Library
- Gabrielle Beck, Aarushi Goel, Abhishek Jain, and Gabriel Kaptchuk. 2021b. Order-C Secure Multiparty Computation for Highly Repetitive Circuits. In Annual International Conference on the Theory and Applications of Cryptographic Techniques. Springer, 663--693.Google Scholar
- Aner Ben-Efraim, Michael Nielsen, and Eran Omri. 2019. Turbospeedz: Double your online spdz! improving SPDZ using function dependent preprocessing. In International Conference on Applied Cryptography and Network Security. Springer, 530--549.Google ScholarDigital Library
- Rikke Bendlin, Ivan Damgård, Claudio Orlandi, and Sarah Zakarias. 2011. Semi-homomorphic encryption and multiparty computation. In Annual International Conference on the Theory and Applications of Cryptographic Techniques. Springer, 169--188.Google ScholarCross Ref
- Fabrice Benhamouda, Elette Boyle, Niv Gilboa, Shai Halevi, Yuval Ishai, and Ariel Nof. 2021. Generalized Pseudorandom Secret Sharing and Efficient Straggler-Resilient Secure Computation. In Theory of Cryptography,, Kobbi Nissim and Brent Waters (Eds.). Springer International Publishing, Cham, 129--161.Google Scholar
- Dan Boneh, Elette Boyle, Henry Corrigan-Gibbs, Niv Gilboa, and Yuval Ishai. 2019. Zero-Knowledge Proofs on Secret-Shared Data via Fully Linear PCPs. In Advances in Cryptology -- CRYPTO 2019. Springer International Publishing, Cham, 67--97.Google ScholarDigital Library
- Elette Boyle, Niv Gilboa, Yuval Ishai, and Ariel Nof. 2019. Practical Fully Secure Three-Party Computation via Sublinear Distributed Zero-Knowledge Proofs. In Proceedings of the 2019 ACM SIGSAC Conference on Computer and Communications Security (London, United Kingdom) (CCS 19). Association for Computing Machinery, New York, NY, USA, 869--886. https://doi.org/10.1145/3319535.3363227Google ScholarDigital Library
- Elette Boyle, Niv Gilboa, Yuval Ishai, and Ariel Nof. 2020. Efficient Fully Secure Computation via Distributed Zero-Knowledge Proofs. In Advances in Cryptology -- ASIACRYPT 2020. Springer International Publishing, Cham, 244--276.Google ScholarDigital Library
- Koji Chida, Daniel Genkin, Koki Hamada, Dai Ikarashi, Ryo Kikuchi, Yehuda Lindell, and Ariel Nof. 2018. Fast Large-Scale Honest-Majority MPC for Malicious Adversaries. In Annual International Cryptology Conference. Springer, 34--64.Google Scholar
- Anders Dalskov and Daniel Escudero. 2021a. Honest Majority MPC with Abort with Minimal Online Communication. In International Conference on Cryptology and Information Security in Latin America. Springer, 453--472.Google Scholar
- Anders Dalskov and Daniel Escudero. 2021b. Honest Majority MPC with Abort with Minimal Online Communication. In International Conference on Cryptology and Information Security in Latin America. Springer, 453--472.Google Scholar
- Ivan Damgård, Yuval Ishai, and Mikkel Krøigaard. 2010. Perfectly secure multiparty computation and the computational overhead of cryptography. In Annual international conference on the theory and applications of cryptographic techniques. Springer, 445--465.Google ScholarDigital Library
- Ivan Damgård, Marcel Keller, Enrique Larraia, Valerio Pastro, Peter Scholl, and Nigel P Smart. 2013. Practical covertly secure MPC for dishonest majority--or: breaking the SPDZ limits. In European Symposium on Research in Computer Security. Springer, 1--18.Google ScholarCross Ref
- Ivan Damgård, Kasper Green Larsen, and Jesper Buus Nielsen. 2019. Communication lower bounds for statistically secure MPC, with or without preprocessing. In Annual International Cryptology Conference. Springer, 61--84.Google ScholarDigital Library
- Ivan Damgård and Jesper Buus Nielsen. 2007. Scalable and unconditionally secure multiparty computation. In Annual International Cryptology Conference. Springer, 572--590.Google ScholarCross Ref
- Ivan Damgård, Jesper Buus Nielsen, Antigoni Polychroniadou, and Michael Raskin. 2016. On the communication required for unconditionally secure multiplication. In Annual International Cryptology Conference. Springer, 459--488.Google ScholarDigital Library
- Ivan Damgård, Valerio Pastro, Nigel Smart, and Sarah Zakarias. 2012. Multiparty computation from somewhat homomorphic encryption. In Annual Cryptology Conference. Springer, 643--662.Google ScholarDigital Library
- Daniel Escudero and Eduardo Soria-Vazquez. 2021. Efficient Information-Theoretic Multi-party Computation over Non-commutative Rings. In Annual International Cryptology Conference. Springer, 335--364.Google ScholarDigital Library
- Matthew Franklin and Moti Yung. 1992. Communication Complexity of Secure Computation (Extended Abstract). In Proceedings of the Twenty-Fourth Annual ACM Symposium on Theory of Computing (Victoria, British Columbia, Canada) (STOC '92). Association for Computing Machinery, New York, NY, USA, 699--710. https://doi.org/10.1145/129712.129780Google ScholarDigital Library
- Juan Garay, Yuval Ishai, Rafail Ostrovsky, and Vassilis Zikas. 2017. The Price of Low Communication in Secure Multi-party Computation. In Advances in Cryptology -- CRYPTO 2017. Springer International Publishing, Cham, 420--446.Google ScholarCross Ref
- Daniel Genkin, Yuval Ishai, and Antigoni Polychroniadou. 2015. Efficient multi-party computation: from passive to active security via secure SIMD circuits. In Annual Cryptology Conference. Springer, 721--741.Google ScholarDigital Library
- Daniel Genkin, Yuval Ishai, Manoj M. Prabhakaran, Amit Sahai, and Eran Tromer. 2014. Circuits Resilient to Additive Attacks with Applications to Secure Computation. In Proceedings of the Forty-sixth Annual ACM Symposium on Theory of Computing (New York, New York) (STOC '14). ACM, New York, NY, USA, 495--504. https://doi.org/10.1145/2591796.2591861Google ScholarDigital Library
- S Dov Gordon, Daniel Starin, and Arkady Yerukhimovich. 2021. The more the merrier: reducing the cost of large scale MPC. In Annual International Conference on the Theory and Applications of Cryptographic Techniques. Springer, 694--723.Google ScholarDigital Library
- Vipul Goyal, Hanjun Li, Rafail Ostrovsky, Antigoni Polychroniadou, and Yifan Song. 2021a. ATLAS: Efficient and Scalable MPC in the Honest Majority Setting. In Advances in Cryptology -- CRYPTO 2021. Springer International Publishing, Cham, 244--274.Google Scholar
- Vipul Goyal, Antigoni Polychroniadou, and Yifan Song. 2021b. Unconditional communication-efficient MPC via hall's marriage theorem. In Annual International Cryptology Conference. Springer, 275--304.Google ScholarDigital Library
- Vipul Goyal, Antigoni Polychroniadou, and Yifan Song. 2022. Sharing Transformation and Dishonest Majority MPC with Packed Secret Sharing. Annual International Cryptology Conference (2022).Google Scholar
- Vipul Goyal and Yifan Song. 2020. Malicious Security Comes Free in Honest-Majority MPC. Cryptology ePrint Archive, Report 2020/134. https://eprint.iacr.org/2020/134.Google Scholar
- Vipul Goyal, Yifan Song, and Chenzhi Zhu. 2020. Guaranteed Output Delivery Comes Free in Honest Majority MPC. In Advances in Cryptology -- CRYPTO 2020. Springer International Publishing, Cham, 618--646.Google ScholarDigital Library
- Yehuda Lindell, Benny Pinkas, Nigel P. Smart, and Avishay Yanai. 2019. Efficient Constant-Round Multi-party Computation Combining BMR and SPDZ. Journal of Cryptology, Vol. 32, 3 (2019), 1026--1069. https://doi.org/10.1007/s00145-019-09322-2Google ScholarDigital Library
- Jesper Buus Nielsen, Thomas Schneider, and Roberto Trifiletti. 2017. Constant Round Maliciously Secure 2PC with Function-independent Preprocessing using LEGO. In Network and Distributed System Security Symposium (NDSS).Google ScholarCross Ref
- Peter Sebastian Nordholt and Meilof Veeningen. 2018. Minimising Communication in Honest-Majority MPC by Batchwise Multiplication Verification. In Applied Cryptography and Network Security. Springer International Publishing, Cham, 321--339.Google Scholar
- Adi Shamir. 1979. How to Share a Secret. Commun. ACM, Vol. 22, 11 (Nov. 1979), 612--613. https://doi.org/10.1145/359168.359176Google ScholarDigital Library
- Xiao Wang, Samuel Ranellucci, and Jonathan Katz. 2017a. Authenticated Garbling and Efficient Maliciously Secure Two-Party Computation. In Proceedings of the 2017 ACM SIGSAC Conference on Computer and Communications Security (Dallas, Texas, USA) (CCS '17). Association for Computing Machinery, New York, NY, USA, 21--37. https://doi.org/10.1145/3133956.3134053Google ScholarDigital Library
- Xiao Wang, Samuel Ranellucci, and Jonathan Katz. 2017b. Global-Scale Secure Multiparty Computation. In Proceedings of the 2017 ACM SIGSAC Conference on Computer and Communications Security (Dallas, Texas, USA) (CCS '17). Association for Computing Machinery, New York, NY, USA, 39--56. https://doi.org/10.1145/3133956.3133979showDOIGoogle ScholarCross Ref
Index Terms
- TurboPack: Honest Majority MPC with Constant Online Communication
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