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Round Optimal Secure Multiparty Computation from Minimal Assumptions

Part of the Lecture Notes in Computer Science book series (LNSC,volume 12551)

Abstract

We construct a four round secure multip arty computation (MPC) protocol in the plain model that achieves security against any dishonest majority. The security of our protocol relies only on the existence of four round oblivious transfer. This culminates the long line of research on constructing round-efficient MPC from minimal assumptions (at least w.r.t. black-box simulation).

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Fig. 1.
Fig. 2.

Notes

  1. 1.

    A detailed discussion on related works can be found in the full version.

  2. 2.

    Roughly speaking, such adversaries behave like semi-honest adversaries, except that they may choose arbitrary random tapes.

  3. 3.

    Roughly speaking, a delayed semi-malicious adversary is similar to semi-malicious adversary, except that in the second last round of a k-round protocol, it is required to output (on a special tape) a witness (namely, its input and randomness) that establishes its honest behavior in all the rounds so far.

  4. 4.

    There are some exceptions; we refer the reader to the full version for discussion on other models.

  5. 5.

    A proof system is said to be delayed input if the instance is only required for computing the last round of the proof.

  6. 6.

    That is, where the instances are sampled from a public distribution.

  7. 7.

    Note that if the protocol does progress to the fourth round, then we do not need to shield promise ZK anymore.

  8. 8.

    We note that this property was also used by [5] in their construction of k-round malicious-secure MPC.

  9. 9.

    The commitment scheme of [3] also achieves some security properties, in addition to bounded rewind security, that are not required by our compiler. Hence, we use a simplified variant of their scheme.

  10. 10.

    This means the extractor can output a non \(\perp \) value if the commitment has no valid opening.

  11. 11.

    These values can be obtained from the malicious sender via an expected PPT rewinding procedure. The expected PPT simulator in our applications performs the necessary rewindings and then feeds these values to the extractor \(\mathsf {TDExt}\).

References

  1. Aiello, B., Ishai, Y., Reingold, O.: Priced oblivious transfer: how to sell digital goods. In: Pfitzmann, B. (ed.) EUROCRYPT 2001. LNCS, vol. 2045, pp. 119–135. Springer, Heidelberg (2001). https://doi.org/10.1007/3-540-44987-6_8

    CrossRef  Google Scholar 

  2. Ananth, P., Choudhuri, A.R., Jain, A.: A new approach to round-optimal secure multiparty computation. In: Katz, J., Shacham, H. (eds.) CRYPTO 2017. LNCS, vol. 10401, pp. 468–499. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-63688-7_16

    CrossRef  Google Scholar 

  3. Badrinarayanan, S., Goyal, V., Jain, A., Kalai, Y.T., Khurana, D., Sahai, A.: Promise zero knowledge and its applications to round optimal MPC. In: Shacham, H., Boldyreva, A. (eds.) CRYPTO 2018. LNCS, vol. 10992, pp. 459–487. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-96881-0_16

    CrossRef  Google Scholar 

  4. Beaver, D., Micali, S., Rogaway, P.: The round complexity of secure protocols (extended abstract). In: 22nd ACM STOC, pp. 503–513. ACM Press, May 1990. https://doi.org/10.1145/100216.100287

  5. Benhamouda, F., Lin, H.: k-round multiparty computation from k-round oblivious transfer via garbled interactive circuits. In: Nielsen, J.B., Rijmen, V. (eds.) EUROCRYPT 2018. LNCS, vol. 10821, pp. 500–532. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-78375-8_17

    CrossRef  Google Scholar 

  6. Brakerski, Z., Halevi, S., Polychroniadou, A.: Four round secure computation without setup. In: Kalai, Y., Reyzin, L. (eds.) TCC 2017. LNCS, vol. 10677, pp. 645–677. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-70500-2_22

    CrossRef  Google Scholar 

  7. Choudhuri, A.R., Ciampi, M., Goyal, V., Jain, A., Ostrovsky, R.: Round optimal secure multiparty computation from minimal assumptions. Cryptology ePrint Archive, Report 2019/216 (2019). https://eprint.iacr.org/2019/216

  8. Ciampi, M., Ostrovsky, R., Siniscalchi, L., Visconti, I.: Delayed-input non-malleable zero knowledge and multi-party coin tossing in four rounds. In: Kalai, Y., Reyzin, L. (eds.) TCC 2017. LNCS, vol. 10677, pp. 711–742. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-70500-2_24

    CrossRef  Google Scholar 

  9. Ciampi, M., Ostrovsky, R., Siniscalchi, L., Visconti, I.: Round-optimal secure two-party computation from trapdoor permutations. In: Kalai, Y., Reyzin, L. (eds.) TCC 2017. LNCS, vol. 10677, pp. 678–710. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-70500-2_23

    CrossRef  Google Scholar 

  10. Dolev, D., Dwork, C., Naor, M.: Non-malleable cryptography (extended abstract). In: 23rd ACM STOC, pp. 542–552. ACM Press, May 1991. https://doi.org/10.1145/103418.103474

  11. Dwork, C., Naor, M.: Zaps and their applications. In: 41st FOCS, pp. 283–293. IEEE Computer Society Press, November 2000. https://doi.org/10.1109/SFCS.2000.892117

  12. Garg, S., Gentry, C., Sahai, A., Waters, B.: Witness encryption and its applications. In: Boneh, D., Roughgarden, T., Feigenbaum, J. (eds.) 45th ACM STOC, pp. 467–476. ACM Press, June 2013. https://doi.org/10.1145/2488608.2488667

  13. Garg, S., Mukherjee, P., Pandey, O., Polychroniadou, A.: The exact round complexity of secure computation. In: Fischlin, M., Coron, J.-S. (eds.) EUROCRYPT 2016. LNCS, vol. 9666, pp. 448–476. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-49896-5_16

    CrossRef  Google Scholar 

  14. Garg, S., Srinivasan, A.: Two-round multiparty secure computation from minimal assumptions. In: Nielsen, J.B., Rijmen, V. (eds.) EUROCRYPT 2018. LNCS, vol. 10821, pp. 468–499. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-78375-8_16

    CrossRef  Google Scholar 

  15. Gertner, Y., Kannan, S., Malkin, T., Reingold, O., Viswanathan, M.: The relationship between public key encryption and oblivious transfer. In: 41st FOCS, pp. 325–335. IEEE Computer Society Press, November 2000. https://doi.org/10.1109/SFCS.2000.892121

  16. Goldreich, O., Kahan, A.: How to construct constant-round zero-knowledge proof systems for NP. J. Cryptol. 9(3), 167–189 (1996). https://doi.org/10.1007/BF00208001

    MathSciNet  CrossRef  MATH  Google Scholar 

  17. Goldreich, O., Krawczyk, H.: On the composition of zero-knowledge proof systems. SIAM J. Comput. 25(1), 169–192 (1996). https://doi.org/10.1137/S0097539791220688

  18. Goldreich, O., Micali, S., Wigderson, A.: How to play any mental game or A completeness theorem for protocols with honest majority. In: Aho, A. (ed.) 19th ACM STOC, pp. 218–229. ACM Press (May 1987). https://doi.org/10.1145/28395.28420

  19. Goldreich, O., Micali, S., Wigderson, A.: How to prove all NP statements in zero-knowledge and a methodology of cryptographic protocol design (extended abstract). In: Odlyzko, A.M. (ed.) CRYPTO 1986. LNCS, vol. 263, pp. 171–185. Springer, Heidelberg (1987). https://doi.org/10.1007/3-540-47721-7_11

    CrossRef  Google Scholar 

  20. Goldwasser, S., Micali, S., Rackoff, C.: The knowledge complexity of interactive proof systems. SIAM J. Comput. 18(1), 186–208 (1989)

    MathSciNet  CrossRef  Google Scholar 

  21. Goyal, V.: Constant round non-malleable protocols using one way functions. In: Fortnow, L., Vadhan, S.P. (eds.) 43rd ACM STOC, pp. 695–704. ACM Press, June 2011. https://doi.org/10.1145/1993636.1993729

  22. Goyal, V., Pandey, O., Richelson, S.: Textbook non-malleable commitments. In: Wichs, D., Mansour, Y. (eds.) 48th ACM STOC, pp. 1128–1141. ACM Press, June 2016. https://doi.org/10.1145/2897518.2897657

  23. Goyal, V., Richelson, S.: Non-malleable commitments using Goldreich-Levin list decoding. In: Zuckerman, D. (ed.) 60th FOCS, pp. 686–699. IEEE Computer Society Press, November 2019. https://doi.org/10.1109/FOCS.2019.00047

  24. Goyal, V., Richelson, S.: Non-malleable commitments using goldreich-levin list decoding. In: FOCS (2019)

    Google Scholar 

  25. Halevi, S., Hazay, C., Polychroniadou, A., Venkitasubramaniam, M.: Round-optimal secure multi-party computation. In: Shacham, H., Boldyreva, A. (eds.) CRYPTO 2018. LNCS, vol. 10992, pp. 488–520. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-96881-0_17

    CrossRef  Google Scholar 

  26. 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

    CrossRef  Google Scholar 

  27. Jain, A., Kalai, Y.T., Khurana, D., Rothblum, R.: Distinguisher-dependent simulation in two rounds and its applications. In: Katz, J., Shacham, H. (eds.) CRYPTO 2017. LNCS, vol. 10402, pp. 158–189. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-63715-0_6

    CrossRef  MATH  Google Scholar 

  28. Katz, J., Ostrovsky, R.: Round-optimal secure two-party computation. In: Franklin, M. (ed.) CRYPTO 2004. LNCS, vol. 3152, pp. 335–354. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-28628-8_21

    CrossRef  Google Scholar 

  29. Katz, J., Ostrovsky, R., Smith, A.: Round efficiency of multi-party computation with a dishonest majority. In: Biham, E. (ed.) EUROCRYPT 2003. LNCS, vol. 2656, pp. 578–595. Springer, Heidelberg (2003). https://doi.org/10.1007/3-540-39200-9_36

    CrossRef  Google Scholar 

  30. Kilian, J.: Founding cryptography on oblivious transfer. In: 20th ACM STOC, pp. 20–31. ACM Press, May 1988. https://doi.org/10.1145/62212.62215

  31. Lombardi, A., Schaeffer, L.: A note on key agreement and non-interactive commitments. Cryptology ePrint Archive, Report 2019/279 (2019). https://eprint.iacr.org/2019/279

  32. Pass, R.: Bounded-concurrent secure multi-party computation with a dishonest majority. In: Babai, L. (ed.) 36th ACM STOC, pp. 232–241. ACM Press, June 2004. https://doi.org/10.1145/1007352.1007393

  33. Pass, R., Wee, H.: Constant-round non-malleable commitments from sub-exponential one-way functions. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 638–655. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-13190-5_32

    CrossRef  Google Scholar 

  34. Prabhakaran, M., Rosen, A., Sahai, A.: Concurrent zero knowledge with logarithmic round-complexity. In: 43rd FOCS, pp. 366–375. IEEE Computer Society Press, November 2002. https://doi.org/10.1109/SFCS.2002.1181961

  35. Rosen, A.: A note on constant-round zero-knowledge proofs for NP. In: Naor, M. (ed.) TCC 2004. LNCS, vol. 2951, pp. 191–202. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-24638-1_11

    CrossRef  Google Scholar 

  36. Wee, H.: Black-box, round-efficient secure computation via non-malleability amplification. In: 51st FOCS, pp. 531–540. IEEE Computer Society Press, October 2010. https://doi.org/10.1109/FOCS.2010.87

  37. Yao, A.C.C.: How to generate and exchange secrets (extended abstract). In: 27th FOCS, pp. 162–167. IEEE Computer Society Press, October 1986. https://doi.org/10.1109/SFCS.1986.25

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Acknowledgments

We would like to thank Alex Lombardi and Luke Schaeffer for pointing out to us that any OT with perfect completeness implies non-interactive commitment schemes, and, for suggesting to us to revise our theorem statements to reflect this observation. Vipul Goyal is supported in part by the NSF award 1916939, a gift from Ripple, a JP Morgan Faculty Fellowship, a PNC center for financial services innovation award, and a Cylab seed funding award. Arka Rai Choudhuri and Abhishek Jain are supported in part by DARPA/ARL Safeware Grant W911NF-15-C-0213, NSF CNS-1814919, NSF CAREER 1942789, Samsung Global Research Outreach award and Johns Hopkins University Catalyst award. Arka Rai Choudhuri is also supported by NSF Grants CNS-1908181, CNS-1414023, and the Office of Naval Research Grant N00014-19-1-2294. Rafail Ostrovsky is supported in part by NSF-BSF Grant 1619348, DARPA/SPAWAR N66001-15-C-4065, ODNI/IARPA 2019-1902070008 US-Israel BSF grant 2012366, JP Morgan Faculty Award, Google Faculty Research Award, OKAWA Foundation Research Award, IBM Faculty Research Award, Xerox Faculty Research Award, B. John Garrick Foundation Award, Teradata Research Award, and Lockheed-Martin Corporation Research Award. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official views or policies, either expressed or implied, of the Department of Defense, DARPA, ODNI, IARPA, or the U.S. Government. The U.S. Government is authorized to reproduce and distribute reprints for governmental purposes notwithstanding any copyright annotation therein. Michele Ciampi was partially supported by H2020 project PRIVILEDGE #780477.

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Rai Choudhuri, A., Ciampi, M., Goyal, V., Jain, A., Ostrovsky, R. (2020). Round Optimal Secure Multiparty Computation from Minimal Assumptions. In: Pass, R., Pietrzak, K. (eds) Theory of Cryptography. TCC 2020. Lecture Notes in Computer Science(), vol 12551. Springer, Cham. https://doi.org/10.1007/978-3-030-64378-2_11

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