Abstract
In the classical notion of multiparty computation (MPC), an honest party learning private inputs of others, either as a part of protocol specification or due to a malicious party’s unspecified messages, is not considered a potential breach. Several works in the literature exploit this seemingly minor loophole to achieve the strongest security of guaranteed output delivery via a trusted third party, which nullifies the purpose of MPC. Alon et al. (CRYPTO 2020) presented the notion of Friends and Foes (\(\texttt{FaF}\)) security, which accounts for such undesired leakage towards honest parties by modelling them as semi-honest (friends) who do not collude with malicious parties (foes). With real-world applications in mind, it’s more realistic to assume parties are semi-honest rather than completely honest, hence it is imperative to design efficient protocols conforming to the \(\texttt{FaF}\) security model.
Our contributions are not only motivated by the practical viewpoint, but also consider the theoretical aspects of \(\texttt{FaF}\) security. We prove the necessity of semi-honest oblivious transfer for \(\texttt{FaF}\)-secure protocols with optimal resiliency. On the practical side, we present QuadSquad, a ring-based 4PC protocol, which achieves fairness and GOD in the \(\texttt{FaF}\) model, with an optimal corruption of 1 malicious and 1 semi-honest party. QuadSquad is, to the best of our knowledge, the first practically efficient \(\texttt{FaF}\) secure protocol with optimal resiliency. Its performance is comparable to the state-of-the-art dishonest majority protocols while improving the security guarantee from abort to fairness and GOD. Further, QuadSquad elevates the security by tackling a stronger adversarial model over the state-of-the-art honest-majority protocols, while offering a comparable performance for the input-dependent computation. We corroborate these claims by benchmarking the performance of QuadSquad. We consider the application of liquidity matching that deals with sensitive financial transaction data, where \(\texttt{FaF}\) security is apt. We design a range of \(\texttt{FaF}\) secure building blocks to securely realize liquidity matching as well as other popular applications such as privacy-preserving machine learning. Inclusion of these blocks makes QuadSquad a comprehensive framework.
Full version available at https://eprint.iacr.org/2022/1207.pdf
A. Hegde—Work done while at International Institute of Information Technology Bangalore.
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Abspoel, M., Cramer, R., Damgård, I., Escudero, D., Yuan, C.: Efficient information-theoretic secure multiparty computation over \(\mathbb{Z}/p^k\mathbb{Z}\) via galois rings. In: Hofheinz, D., Rosen, A. (eds.) TCC 2019. LNCS, vol. 11891, pp. 471–501. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-36030-6_19
Abspoel, M., Dalskov, A., Escudero, D., Nof, A.: An efficient passive-to-active compiler for honest-majority MPC over rings. In: Sako, K., Tippenhauer, N.O. (eds.) ACNS 2021. LNCS, vol. 12727, pp. 122–152. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-78375-4_6
Alon, B., Omri, E., Paskin-Cherniavsky, A.: MPC with friends and foes. In: Micciancio, D., Ristenpart, T. (eds.) CRYPTO 2020. LNCS, vol. 12171, pp. 677–706. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-56880-1_24
Araki, T., et al.: Optimized honest-majority MPC for malicious adversaries - breaking the 1 billion-gate per second barrier. In: IEEE S &P (2017)
Araki, T., Furukawa, J., Lindell, Y., Nof, A., Ohara, K.: High-throughput semi-honest secure three-party computation with an honest majority. In: ACM CCS (2016)
Archer, D.W., et al.: From keys to databases-real-world applications of secure multi-party computation. Comput. J. (2018)
Atapoor, S., Smart, N.P., Alaoui, Y.T.: Private liquidity matching using MPC. IACR Cryptology ePrint Archive (2021)
Badrinarayanan, S., Jain, A., Manohar, N., Sahai, A.: Secure MPC: laziness leads to GOD. In: Moriai, S., Wang, H. (eds.) ASIACRYPT 2020. LNCS, vol. 12493, pp. 120–150. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-64840-4_5
Baum, C., Damgård, I., Toft, T., Zakarias, R.: Better preprocessing for secure multiparty computation. In: Manulis, M., Sadeghi, A.-R., Schneider, S. (eds.) ACNS 2016. LNCS, vol. 9696, pp. 327–345. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-39555-5_18
Baum, C., Orsini, E., Scholl, P.: Efficient secure multiparty computation with identifiable abort. In: Hirt, M., Smith, A. (eds.) TCC 2016. LNCS, vol. 9985, pp. 461–490. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-53641-4_18
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
Beaver, D.: Precomputing oblivious transfer. In: Coppersmith, D. (ed.) CRYPTO 1995. LNCS, vol. 963, pp. 97–109. Springer, Heidelberg (1995). https://doi.org/10.1007/3-540-44750-4_8
Ben-Efraim, A., Nielsen, M., Omri, E.: Turbospeedz: double your online SPDZ! Improving SPDZ using function dependent preprocessing. In: Deng, R.H., Gauthier-Umaña, V., Ochoa, M., Yung, M. (eds.) ACNS 2019. LNCS, vol. 11464, pp. 530–549. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-21568-2_26
Ben-Or, M., Goldwasser, S., Wigderson, A.: Completeness theorems for non-cryptographic fault-tolerant distributed computation (extended abstract). In: STOC (1988)
Bogdanov, D., Kamm, L., Kubo, B., Rebane, R., Sokk, V., Talviste, R.: Students and taxes: a privacy-preserving social study using secure computation. IACR Cryptology ePrint Archive (2015)
Bogdanov, D., Laur, S., Willemson, J.: Sharemind: a framework for fast privacy-preserving computations. In: Jajodia, S., Lopez, J. (eds.) ESORICS 2008. LNCS, vol. 5283, pp. 192–206. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-88313-5_13
Bogdanov, D., Talviste, R., Willemson, J.: Deploying secure multi-party computation for financial data analysis - (short paper). In: Keromytis, A.D. (ed.) FC 2012. LNCS, vol. 7397, pp. 57–64. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-32946-3_5
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
Boyle, E., Couteau, G., Gilboa, N., Ishai, Y., Kohl, L., Scholl, P.: Efficient pseudorandom correlation generators: silent OT extension and more. In: Boldyreva, A., Micciancio, D. (eds.) CRYPTO 2019. LNCS, vol. 11694, pp. 489–518. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-26954-8_16
Boyle, E., Gilboa, N., Ishai, Y., Nof, A.: Practical fully secure three-party computation via sublinear distributed zero-knowledge proofs. In: ACM CCS (2019)
Byali, M., Chaudhari, H., Patra, A., Suresh, A.: FLASH: fast and robust framework for privacy-preserving machine learning. In: PETS (2020)
Byali, M., Hazay, C., Patra, A., Singla, S.: Fast actively secure five-party computation with security beyond abort. In: ACM CCS (2019)
Byali, M., Joseph, A., Patra, A., Ravi, D.: Fast secure computation for small population over the internet. In: ACM CCS (2018)
Chaudhari, H., Choudhury, A., Patra, A., Suresh, A.: ASTRA: high throughput 3PC over rings with application to secure prediction. In: ACM CCSW@CCS (2019)
Chaudhari, H., Rachuri, R., Suresh, A.: Trident: efficient 4PC framework for privacy preserving machine learning. In: NDSS (2020)
Chaum, D.: The spymasters double-agent problem: multiparty computations secure unconditionally from minorities and cryptographically from majorities. In: Brassard, G. (ed.) CRYPTO 1989. LNCS, vol. 435, pp. 591–602. Springer, New York (1990). https://doi.org/10.1007/0-387-34805-0_52
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
Cleve, R.: Limits on the security of coin flips when half the processors are faulty (extended abstract). In: ACM STOC (1986)
Couteau, G., Rindal, P., Raghuraman, S.: Silver: silent VOLE and oblivious transfer from hardness of decoding structured LDPC codes. In: Malkin, T., Peikert, C. (eds.) CRYPTO 2021. LNCS, vol. 12827, pp. 502–534. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-84252-9_17
Cramer, R., Damgård, I., Escudero, D., Scholl, P., Xing, C.: SPD\(\mathbb{Z}_{2^k}\): efficient MPC mod \(2^k\) for dishonest majority. In: Shacham, H., Boldyreva, A. (eds.) CRYPTO 2018. LNCS, vol. 10992, pp. 769–798. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-96881-0_26
Dalskov, A., Escudero, D., Keller, M.: Fantastic four: honest-majority four-party secure computation with malicious security. In: USENIX Security (2021)
Damgård, I., Escudero, D., Frederiksen, T.K., Keller, M., Scholl, P., Volgushev, N.: New primitives for actively-secure MPC over rings with applications to private machine learning. In: IEEE S &P (2019)
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., Orlandi, C., Simkin, M.: Yet another compiler for active security or: efficient MPC over arbitrary rings. In: Shacham, H., Boldyreva, A. (eds.) CRYPTO 2018. LNCS, vol. 10992, pp. 799–829. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-96881-0_27
Damgård, I., Pastro, V., Smart, N., Zakarias, S.: Multiparty computation from somewhat homomorphic encryption. In: Safavi-Naini, R., Canetti, R. (eds.) CRYPTO 2012. LNCS, vol. 7417, pp. 643–662. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-32009-5_38
Demmler, D., Schneider, T., Zohner, M.: ABY - a framework for efficient mixed-protocol secure two-party computation. In: NDSS (2015)
Dolev, D., Dwork, C., Waarts, O., Yung, M.: Perfectly secure message transmission. J. ACM (JACM) (1993)
Dolev, D., Strong, H.R.: Authenticated algorithms for byzantine agreement. SIAM J. Comput. (1983)
Fitzi, M., Hirt, M., Maurer, U.: Trading correctness for privacy in unconditional multi-party computation. In: Krawczyk, H. (ed.) CRYPTO 1998. LNCS, vol. 1462, pp. 121–136. Springer, Heidelberg (1998). https://doi.org/10.1007/BFb0055724
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
Ghodosi, H., Pieprzyk, J.: Multi-party computation with omnipresent adversary. In: Jarecki, S., Tsudik, G. (eds.) PKC 2009. LNCS, vol. 5443, pp. 180–195. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-00468-1_11
Gilboa, N.: Two party RSA key generation. In: Wiener, M. (ed.) CRYPTO 1999. LNCS, vol. 1666, pp. 116–129. Springer, Heidelberg (1999). https://doi.org/10.1007/3-540-48405-1_8
Goldreich, O., Micali, S., Wigderson, A.: How to play any mental game or A completeness theorem for protocols with honest majority. In: STOC (1987)
Gordon, S.D., Ranellucci, S., Wang, X.: Secure computation with low communication from cross-checking. In: Peyrin, T., Galbraith, S. (eds.) ASIACRYPT 2018. LNCS, vol. 11274, pp. 59–85. Springer, Cham (2018). https://doi.org/10.1007/978-3-030-03332-3_3
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
Hazay, C., Lindell, Y.: A note on the relation between the definitions of security for semi-honest and malicious adversaries. IACR Cryptology ePrint Archive (2010)
Hirt, M., Mularczyk, M.: Efficient MPC with a mixed adversary. In: LIPIcs (2020)
Ishai, Y., Kilian, J., Nissim, K., Petrank, E.: Extending oblivious transfers efficiently. In: Boneh, D. (ed.) CRYPTO 2003. LNCS, vol. 2729, pp. 145–161. Springer, Heidelberg (2003). https://doi.org/10.1007/978-3-540-45146-4_9
Ishai, Y., Kumaresan, R., Kushilevitz, E., Paskin-Cherniavsky, A.: Secure computation with minimal interaction, revisited. In: Gennaro, R., Robshaw, M. (eds.) CRYPTO 2015. LNCS, vol. 9216, pp. 359–378. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-48000-7_18
Ishai, Y., Prabhakaran, M., Sahai, A.: Founding cryptography on oblivious transfer – efficiently. In: Wagner, D. (ed.) CRYPTO 2008. LNCS, vol. 5157, pp. 572–591. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-85174-5_32
Keller, M.: MP-SPDZ: a versatile framework for multi-party computation. In: ACM CCS (2020)
Keller, M., Orsini, E., Scholl, P.: Actively secure OT extension with optimal overhead. In: Gennaro, R., Robshaw, M. (eds.) CRYPTO 2015. LNCS, vol. 9215, pp. 724–741. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-47989-6_35
Keller, M., Orsini, E., Scholl, P.: MASCOT: faster malicious arithmetic secure computation with oblivious transfer. In: ACM CCS (2016)
Keller, M., Pastro, V., Rotaru, D.: Overdrive: making SPDZ great again. In: Nielsen, J.B., Rijmen, V. (eds.) EUROCRYPT 2018. LNCS, vol. 10822, pp. 158–189. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-78372-7_6
Koti, N., Pancholi, M., Patra, A., Suresh, A.: SWIFT: super-fast and robust privacy-preserving machine learning. In: USENIX Security (2021)
Koti, N., Patra, A., Rachuri, R., Suresh, A.: Tetrad: actively secure 4pc for secure training and inference. arXiv preprint arXiv:2106.02850 (2021)
LeCun, Y., Cortes, C.: MNIST handwritten digit database (2010). http://yann.lecun.com/exdb/mnist/
Lindell, Y., Nof, A.: A framework for constructing fast MPC over arithmetic circuits with malicious adversaries and an honest-majority. In: ACM CCS (2017)
Mazloom, S., Le, P.H., Ranellucci, S., Gordon, S.D.: Secure parallel computation on national scale volumes of data. In: USENIX Security (2020)
Mohassel, P., Rindal, P.: ABY\({}^{\text{3}}\): a mixed protocol framework for machine learning. In: ACM CCS (2018)
Mohassel, P., Rosulek, M., Zhang, Y.: Fast and secure three-party computation: the garbled circuit approach. In: ACM CCS (2015)
Mohassel, P., Zhang, Y.: SecureML: a system for scalable privacy-preserving machine learning. In: IEEE S &P (2017)
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
Orlandi, C.: Is multiparty computation any good in practice? In: IEEE ICASSP (2011)
Orsini, E., Smart, N.P., Vercauteren, F.: Overdrive2k: efficient secure MPC over \(\mathbb{Z}_{2^k}\) from somewhat homomorphic encryption. In: Jarecki, S. (ed.) CT-RSA 2020. LNCS, vol. 12006, pp. 254–283. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-40186-3_12
Patra, A., Schneider, T., Suresh, A., Yalame, H.: Aby2. 0: improved mixed-protocol secure two-party computation. In: USENIX Security (2021)
Patra, A., Suresh, A.: BLAZE: blazing fast privacy-preserving machine learning. In: NDSS (2020)
Shoup, V.: NTL: a library for doing number theory (2021). https://libntl.org/
Simonyan, K., Zisserman, A.: Very deep convolutional networks for large-scale image recognition. arXiv preprint arXiv:1409.1556 (2014)
Wagh, S., Tople, S., Benhamouda, F., Kushilevitz, E., Mittal, P., Rabin, T.: Falcon: honest-majority maliciously secure framework for private deep learning. arXiv preprint (2020)
Wang, X., Malozemoff, A.J., Katz, J.: EMP-toolkit: efficient MultiParty computation toolkit (2016). https://github.com/emp-toolkit
Yang, K., Weng, C., Lan, X., Zhang, J., Wang, X.: Ferret: fast extension for correlated OT with small communication. In: ACM CCS (2020)
Acknowledgements
Arpita Patra would like to acknowledge financial support from DST National Mission on Interdisciplinary Cyber-Physical Systems (NM-CPS) 2020–2025 and SERB MATRICS (Theoretical Sciences) Grant 2020–2023. Varsha Bhat Kukkala would like to acknowledge financial support from National Security Council, India. Nishat Koti would like to acknowledge support from Centre for Networked Intelligence (a Cisco CSR initiative) at the Indian Institute of Science, Bengaluru. Shravani Patil would like to acknowledge financial support from DST National Mission on Interdisciplinary Cyber-Physical Systems (NM-ICPS) 2020–2025. The authors would also like to acknowledge the support from Google Cloud for benchmarking.
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Hegde, A., Koti, N., Kukkala, V.B., Patil, S., Patra, A., Paul, P. (2022). Attaining GOD Beyond Honest Majority with Friends and Foes. In: Agrawal, S., Lin, D. (eds) Advances in Cryptology – ASIACRYPT 2022. ASIACRYPT 2022. Lecture Notes in Computer Science, vol 13791. Springer, Cham. https://doi.org/10.1007/978-3-031-22963-3_19
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