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Going Beyond Dual Execution: MPC for Functions with Efficient Verification

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Part of the Lecture Notes in Computer Science book series (LNCS, volume 12111)

Abstract

The dual execution paradigm of Mohassel and Franklin (PKC’06) and Huang, Katz and Evans (IEEE ’12) shows how to achieve the notion of 1-bit leakage security at roughly twice the cost of semi-honest security for the special case of two-party secure computation. To date, there are no multi-party computation (MPC) protocols that offer such a strong trade-off between security and semi-honest performance.

Our main result is to address this shortcoming by designing 1-bit leakage protocols for the multi-party setting, albeit for a special class of functions. We say that function f(x, y) is efficiently verifiable by g if the running time of g is always smaller than f and \(g(x,y,z)=1\) if and only if \(f(x,y)=z\).

In the two-party setting, we first improve dual execution by observing that the “second execution” can be an evaluation of g instead of f, and that by definition, the evaluation of g is asymptotically more efficient.

Our main MPC result is to construct a 1-bit leakage protocol for such functions from any passive protocol for f that is secure up to additive errors and any active protocol for g. An important result by Genkin et al. (STOC ’14) shows how the classic protocols by Goldreich et al. (STOC ’87) and Ben-Or et al. (STOC ’88) naturally support this property, which allows to instantiate our compiler with two-party and multi-party protocols.

A key technical result we prove is that the passive protocol for distributed garbling due to Beaver et al. (STOC ’90) is in fact secure up to additive errors against malicious adversaries, thereby, yielding another powerful instantiation of our paradigm in the constant-round multi-party setting.

As another concrete example of instantiating our approach, we present a novel protocol for computing perfect matching that is secure in the 1-bit leakage model and whose communication complexity is less than the honest-but-curious implementations of textbook algorithms for perfect matching.

Keywords

Secure computation Semi-honest security Dual execution Greedy algorithms 
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Notes

Acknowledgements

We thank the anonymous PKC 2020 reviewers for their valuable feedback. The first author is supported by the BIU Center for Research in Applied Cryptography and Cyber Security in conjunction with the Israel National Cyber Bureau in the Prime Minister’s Office, and by ISF grant 1316/18. The second author is supported by NSF Awards 1664445 and 1646671. The third author is supported by Google Faculty Research Grant and NSF Award CNS-1618884. The views expressed are those of the authors and do not reflect the official policy or position of Google, the Department of Defense, the National Science Foundation, or the U.S. Government.

References

  1. [ADI+17]
    Applebaum, B., Damgård, I., Ishai, Y., Nielsen, M., Zichron, L.: Secure arithmetic computation with constant computational overhead. In: Katz, J., Shacham, H. (eds.) CRYPTO 2017. LNCS, vol. 10401, pp. 223–254. Springer, Cham (2017).  https://doi.org/10.1007/978-3-319-63688-7_8CrossRefGoogle Scholar
  2. [Bea91]
    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_34CrossRefGoogle Scholar
  3. [BGW88]
    Ben-Or, M., Goldwasser, S., Wigderson, A.: Completeness theorems for non-cryptographic fault-tolerant distributed computation (extended abstract). In: STOC, pp. 1–10 (1988)Google Scholar
  4. [BMR90]
    Beaver, D., Micali, S., Rogaway, P.: The round complexity of secure protocols (extended abstract). In: STOC, pp. 503–513 (1990)Google Scholar
  5. [BNP08]
    Ben-David, A., Nisan, N., Pinkas, B.: FairplayMP: a system for secure multi-party computation. In: CCS, pp. 257–266 (2008)Google Scholar
  6. [cal]
  7. [CDF+08]
    Cramer, R., Dodis, Y., Fehr, S., Padró, C., Wichs, D.: Detection of algebraic manipulation with applications to robust secret sharing and fuzzy extractors. In: Smart, N. (ed.) EUROCRYPT 2008. LNCS, vol. 4965, pp. 471–488. Springer, Heidelberg (2008).  https://doi.org/10.1007/978-3-540-78967-3_27CrossRefGoogle Scholar
  8. [CGH+18]
    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_2CrossRefGoogle Scholar
  9. [CGMA85]
    Chor, B., Goldwasser, S., Micali, S., Awerbuch, B.: Verifiable secret sharing and achieving simultaneity in the presence of faults (extended abstract). In: FOCS, pp. 383–395 (1985)Google Scholar
  10. [FLOP18]
    Frederiksen, T.K., Lindell, Y., Osheter, V., Pinkas, B.: Fast distributed RSA key generation for semi-honest and malicious adversaries. In: Shacham, H., Boldyreva, A. (eds.) CRYPTO 2018. LNCS, vol. 10992, pp. 331–361. Springer, Cham (2018).  https://doi.org/10.1007/978-3-319-96881-0_12CrossRefGoogle Scholar
  11. [Fre77]
    Freivalds, F.: Probabilistic machines can use less running time. In: IFIP Congress, pp. 839–842 (1977)Google Scholar
  12. [GIKR01]
    Gennaro, R., Ishai, Y., Kushilevitz, E., Rabin, T.: The round complexity of verifiable secret sharing and secure multicast. In: STOC, pp. 580–589 (2001)Google Scholar
  13. [GIP+14]
    Genkin, D., Ishai, Y., Prabhakaran, M., Sahai, A., Tromer, E.: Circuits resilient to additive attacks with applications to secure computation. In: STOC, pp. 495–504 (2014)Google Scholar
  14. [GIP15]
    Genkin, D., Ishai, Y., Polychroniadou, A.: Efficient multi-party computation: from passive to active security via secure SIMD circuits. In: Gennaro, R., Robshaw, M. (eds.) CRYPTO 2015. LNCS, vol. 9216, pp. 721–741. Springer, Heidelberg (2015).  https://doi.org/10.1007/978-3-662-48000-7_35CrossRefGoogle Scholar
  15. [GIW16]
    Genkin, D., Ishai, Y., Weiss, M.: Binary AMD circuits from secure multiparty computation. In: Hirt, M., Smith, A. (eds.) TCC 2016. LNCS, vol. 9985, pp. 336–366. Springer, Heidelberg (2016).  https://doi.org/10.1007/978-3-662-53641-4_14CrossRefGoogle Scholar
  16. [GMW87]
    Goldreich, O., Micali, S., Wigderson, A.: How to play any mental game or a completeness theorem for protocols with honest majority. In: STOC, pp. 218–229 (1987)Google Scholar
  17. [Gol04]
    Goldreich, O.: The Foundations of Cryptography - Volume 2, Basic Applications. Cambridge University Press, Cambridge (2004)zbMATHGoogle Scholar
  18. [Har06]
    Harvey, N.J.A.: Algebraic structures and algorithms for matching and matroid problems. In: FOCS, pp. 531–542 (2006)Google Scholar
  19. [HEKM11]
    Huang, Y., Evans, D., Katz, J., Malka, L.: Faster secure two-party computation using garbled circuits. In: USENIX (2011)Google Scholar
  20. [HIV17]
    Hazay, C., Ishai, Y., Venkitasubramaniam, M.: Actively secure garbled circuits with constant communication overhead in the plain model. In: Kalai, Y., Reyzin, L. (eds.) TCC 2017. LNCS, vol. 10678, pp. 3–39. Springer, Cham (2017).  https://doi.org/10.1007/978-3-319-70503-3_1CrossRefGoogle Scholar
  21. [HKE12]
    Huang, Y., Katz, J., Evans, D.: Quid-pro-quo-tocols: strengthening semi-honest protocols with dual execution. In: IEEE Symposium on Security and Privacy, pp. 272–284 (2012)Google Scholar
  22. [HSS17]
    Hazay, C., Scholl, P., Soria-Vazquez, E.: Low cost constant round MPC combining BMR and oblivious transfer. In: Takagi, T., Peyrin, T. (eds.) ASIACRYPT 2017. LNCS, vol. 10624, pp. 598–628. Springer, Cham (2017).  https://doi.org/10.1007/978-3-319-70694-8_21CrossRefGoogle Scholar
  23. [IPS08]
    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_32CrossRefGoogle Scholar
  24. [IPS09]
    Ishai, Y., Prabhakaran, M., Sahai, A.: Secure arithmetic computation with no honest majority. In: Reingold, O. (ed.) TCC 2009. LNCS, vol. 5444, pp. 294–314. Springer, Heidelberg (2009).  https://doi.org/10.1007/978-3-642-00457-5_18CrossRefGoogle Scholar
  25. [Kin95]
    King, V.: A simpler minimum spanning tree verification algorithm. In: Akl, S.G., Dehne, F., Sack, J.-R., Santoro, N. (eds.) WADS 1995. LNCS, vol. 955, pp. 440–448. Springer, Heidelberg (1995).  https://doi.org/10.1007/3-540-60220-8_83CrossRefGoogle Scholar
  26. [KPR18]
    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_6CrossRefGoogle Scholar
  27. [KRRW18]
    Katz, J., Ranellucci, S., Rosulek, M., Wang, X.: Optimizing authenticated garbling for faster secure two-party computation. In: Shacham, H., Boldyreva, A. (eds.) CRYPTO 2018. LNCS, vol. 10993, pp. 365–391. Springer, Cham (2018).  https://doi.org/10.1007/978-3-319-96878-0_13CrossRefGoogle Scholar
  28. [KS14]
    Keller, M., Scholl, P.: Efficient, oblivious data structures for MPC. In: Sarkar, P., Iwata, T. (eds.) ASIACRYPT 2014. LNCS, vol. 8874, pp. 506–525. Springer, Heidelberg (2014).  https://doi.org/10.1007/978-3-662-45608-8_27CrossRefGoogle Scholar
  29. [KSMB13]
    Kreuter, B., Shelat, A., Mood, B., Butler, K.R.B.: PCF: a portable circuit format for scalable two-party secure computation. In: USENIX, pp. 321–336 (2013)Google Scholar
  30. [KSS12]
    Kreuter, B., Shelat, A., Shen, C.-H.: Billion-gate secure computation with malicious adversaries. In: USENIX, pp. 285–300 (2012)Google Scholar
  31. [LHS+14]
    Liu, C., Huang, Y., Shi, E., Katz, J., Hicks, M.W.: Automating efficient RAM-model secure computation. In: IEEE Symposium on Security and Privacy, pp. 623–638 (2014)Google Scholar
  32. [LP09]
    Lindell, Y., Pinkas, B.: A proof of security of Yao’s protocol for two-party computation. J. Cryptol. 22(2), 161–188 (2009).  https://doi.org/10.1007/s00145-008-9036-8MathSciNetCrossRefzbMATHGoogle Scholar
  33. [LP12]
    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/s00145-011-9107-0MathSciNetCrossRefzbMATHGoogle Scholar
  34. [LPSY15]
    Lindell, Y., Pinkas, B., Smart, N.P., Yanai, A.: Efficient constant round multi-party computation combining BMR and SPDZ. In: Gennaro, R., Robshaw, M. (eds.) CRYPTO 2015. LNCS, vol. 9216, pp. 319–338. Springer, Heidelberg (2015).  https://doi.org/10.1007/978-3-662-48000-7_16CrossRefGoogle Scholar
  35. [MF06]
    Mohassel, P., Franklin, M.: Efficiency tradeoffs for malicious two-party computation. In: Yung, M., Dodis, Y., Kiayias, A., Malkin, T. (eds.) PKC 2006. LNCS, vol. 3958, pp. 458–473. Springer, Heidelberg (2006).  https://doi.org/10.1007/11745853_30CrossRefGoogle Scholar
  36. [MNPS04]
    Malkhi, D., Nisan, N., Pinkas, B., Sella, Y.: Fairplay - secure two-party computation system. In: USENIX, pp. 287–302 (2004)Google Scholar
  37. [MOR03]
    MacKenzie, P.D., Oprea, A., Reiter, M.K.: Automatic generation of two-party computations. In: CCS, pp. 210–219 (2003)Google Scholar
  38. [MR13]
    Mohassel, P., Riva, B.: Garbled circuits checking garbled circuits: more efficient and secure two-party computation. In: Canetti, R., Garay, J.A. (eds.) CRYPTO 2013. LNCS, vol. 8043, pp. 36–53. Springer, Heidelberg (2013).  https://doi.org/10.1007/978-3-642-40084-1_3CrossRefGoogle Scholar
  39. [MS04]
    Mucha, M., Sankowski, P.: Maximum matchings via Gaussian elimination. In: FOCS, pp.248–255 (2004)Google Scholar
  40. [MZ17]
    Mohassel, P., Zhang, Y.: SecureML: a system for scalable privacy-preserving machine learning. In: IEEE SP 2017 (2017)Google Scholar
  41. [NNOB12]
    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_40CrossRefGoogle Scholar
  42. [NO09]
    Nielsen, J.B., Orlandi, C.: LEGO for two-party secure computation. In: Reingold, O. (ed.) TCC 2009. LNCS, vol. 5444, pp. 368–386. Springer, Heidelberg (2009).  https://doi.org/10.1007/978-3-642-00457-5_22CrossRefGoogle Scholar
  43. [RHH14]
    Rastogi, A., Hammer, M.A., Hicks, M.: Wysteria: a programming language for generic, mixed-mode multiparty computations. In: IEEE Symposium on Security and Privacy, pp. 655–670 (2014)Google Scholar
  44. [RV89]
    Rabin, M.O., Vazirani, V.V.: Maximum matchings in general graphs through randomization. J. Algorithms 10(4), 557–567 (1989)MathSciNetCrossRefGoogle Scholar
  45. [WRK17a]
    Wang, X., Ranellucci, S., Katz, J.: Authenticated garbling and efficient maliciously secure two-party computation. In: CCS, pp. 21–37 (2017)Google Scholar
  46. [WRK17b]
    Wang, X., Ranellucci, S., Katz, J.: Global-scale secure multiparty computation. In: CCS, pp. 39–56 (2017)Google Scholar
  47. [Yao86]
    Yao, A.C.-C.: How to generate and exchange secrets (extended abstract). In: FOCS, pp. 162–167 (1986)Google Scholar

Copyright information

© International Association for Cryptologic Research 2020

Authors and Affiliations

  1. 1.Bar-Ilan UniversityRamat GanIsrael
  2. 2.Northeastern UniversityBostonUSA
  3. 3.University of RochesterRochesterUSA

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