Skip to main content

The Round Complexity of Secure Computation Against Covert Adversaries

  • 388 Accesses

Part of the Lecture Notes in Computer Science book series (LNSC,volume 12238)

Abstract

We investigate the exact round complexity of secure multiparty computation (MPC) against covert adversaries who may attempt to cheat, but do not wish to be caught doing so. Covert adversaries lie in between semi-honest adversaries who follow protocol specification and malicious adversaries who may deviate arbitrarily.

Recently, two round protocols for semi-honest MPC and four round protocols for malicious-secure MPC were constructed, both of which are optimal. While these results can be viewed as constituting two end points of a security spectrum, we investigate the design of protocols that potentially span the spectrum.

Our main result is an MPC protocol against covert adversaries with variable round complexity: when the detection probability is set to the lowest setting, our protocol requires two rounds and offers same security as semi-honest MPC. By increasing the detecting probability, we can increase the security guarantees, with round complexity five in the extreme case. The security of our protocol is based on standard cryptographic assumptions.

We supplement our positive result with a negative result, ruling out strict three round protocols with respect to black-box simulation.

Keywords

  • Secure computation
  • Covert adversary
  • Round complexity

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • DOI: 10.1007/978-3-030-57990-6_30
  • Chapter length: 21 pages
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
eBook
USD   109.00
Price excludes VAT (USA)
  • ISBN: 978-3-030-57990-6
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD   139.99
Price excludes VAT (USA)

Notes

  1. 1.

    The work of [3] also provides two other formulations of security. In this work, we focus on the above formulation.

  2. 2.

    One may ask whether modeling protocol abort as cheating could lead to scenarios where honest parties, in the presence of network interruptions, are labeled as adversarial. We imagine that in such a scenario, one could put in place countermeasures, where, e.g., a party is allowed to prove (in zero knowledge) honest behavior in the protocol (up to the point of purported abort) to other parties in order to defend itself.

  3. 3.

    This in particular means we cannot ignore the verifier’s last message to transform the protocol to a three round protocol in the alternating message model as in [15].

References

  1. 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 

  2. Asharov, G., Jain, A., López-Alt, A., Tromer, E., Vaikuntanathan, V., Wichs, D.: Multiparty computation with low communication, computation and interaction via threshold FHE. In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT 2012. LNCS, vol. 7237, pp. 483–501. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-29011-4_29

    CrossRef  Google Scholar 

  3. Aumann, Y., Lindell, Y.: Security against covert adversaries: efficient protocols for realistic adversaries. In: Vadhan, S.P. (ed.) TCC 2007. LNCS, vol. 4392, pp. 137–156. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-70936-7_8

    CrossRef  Google Scholar 

  4. 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 

  5. 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

  6. 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 

  7. Boyle, E., Garg, S., Jain, A., Kalai, Y.T., Sahai, A.: Secure computation against adaptive auxiliary information. In: Canetti, R., Garay, J.A. (eds.) CRYPTO 2013. LNCS, vol. 8042, pp. 316–334. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-40041-4_18

    CrossRef  Google Scholar 

  8. 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 

  9. 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

  10. 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 

  11. Ciampi, M., Ostrovsky, R., Siniscalchi, L., Visconti, I.: Four-round concurrent non-malleable commitments from one-way functions. In: Katz, J., Shacham, H. (eds.) CRYPTO 2017. LNCS, vol. 10402, pp. 127–157. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-63715-0_5

    CrossRef  Google Scholar 

  12. 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 

  13. 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

  14. Garg, S., Gentry, C., Halevi, S., Raykova, M.: Two-round secure MPC from indistinguishability obfuscation. In: Lindell, Y. (ed.) TCC 2014. LNCS, vol. 8349, pp. 74–94. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-642-54242-8_4

    CrossRef  Google Scholar 

  15. 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 

  16. Garg, S., Srinivasan, A.: Garbled protocols and two-round MPC from bilinear maps. In: Umans, C. (ed.) 58th FOCS, pp. 588–599. IEEE Computer Society Press (October 2017). https://doi.org/10.1109/FOCS.2017.60

  17. 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 

  18. 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 

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

    MathSciNet  CrossRef  MATH  Google Scholar 

  20. 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

  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. 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 

  23. Halevi, S., Lindell, Y., Pinkas, B.: Secure computation on the web: computing without simultaneous interaction. In: Rogaway, P. (ed.) CRYPTO 2011. LNCS, vol. 6841, pp. 132–150. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-22792-9_8

    CrossRef  Google Scholar 

  24. 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 

  25. Mukherjee, P., Wichs, D.: Two round multiparty computation via multi-key FHE. In: Fischlin, M., Coron, J.-S. (eds.) EUROCRYPT 2016. LNCS, vol. 9666, pp. 735–763. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-49896-5_26

    CrossRef  Google Scholar 

  26. 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

  27. 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 

  28. 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

  29. 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

Download references

Acknowledgments

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 and CNS-1414023.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Arka Rai Choudhuri .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 2020 Springer Nature Switzerland AG

About this paper

Verify currency and authenticity via CrossMark

Cite this paper

Choudhuri, A.R., Goyal, V., Jain, A. (2020). The Round Complexity of Secure Computation Against Covert Adversaries. In: Galdi, C., Kolesnikov, V. (eds) Security and Cryptography for Networks. SCN 2020. Lecture Notes in Computer Science(), vol 12238. Springer, Cham. https://doi.org/10.1007/978-3-030-57990-6_30

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-57990-6_30

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-57989-0

  • Online ISBN: 978-3-030-57990-6

  • eBook Packages: Computer ScienceComputer Science (R0)