Skip to main content
SpringerLink
Log in

Round-Optimal Multi-party Computation with Identifiable Abort

  • Conference paper
  • First Online:
Advances in Cryptology – EUROCRYPT 2022 (EUROCRYPT 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13275))

Abstract

Secure multi-party computation (MPC) protocols that are resilient to a dishonest majority allow the adversary to get the output of the computation while, at the same time, forcing the honest parties to abort. Aumann and Lindell introduced the enhanced notion of security with identifiable abort, which still allows the adversary to trigger an abort but, at the same time, it enables the honest parties to agree on the identity of the party that led to the abort. More recently, in Eurocrypt 2016, Garg et al. showed that, assuming access to a simultaneous message exchange channel for all the parties, at least four rounds of communication are required to securely realize non-trivial functionalities in the plain model.

Following Garg et al., a sequence of works has matched this lower bound, but none of them achieved security with identifiable abort. In this work, we close this gap and show that four rounds of communication are also sufficient to securely realize any functionality with identifiable abort using standard and generic polynomial-time assumptions. To achieve this result we introduce the new notion of bounded-rewind secure MPC that guarantees security even against an adversary that performs a mild form of reset attacks. We show how to instantiate this primitive starting from any MPC protocol and by assuming trapdoor-permutations.

The notion of bounded-rewind secure MPC allows for easier parallel composition of MPC protocols with other (interactive) cryptographic primitives. Therefore, we believe that this primitive can be useful in other contexts in which it is crucial to combine multiple primitives with MPC protocols while keeping the round complexity of the final protocol low.

D. Ravi—Funded by the European Research Council (ERC) under the European Unions’s Horizon 2020 research and innovation programme under grant agreement No. 803096 (SPEC).

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 99.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 129.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

Notes

  1. 1.

    In each round all the parties can send a message. That is, the channel allows for a simultaneous exchange of messages in each round. Unless otherwise specified we implicitly refer to this model of communication when referring to broadcast.

  2. 2.

    All our results are with respect to black-box simulation. Hereafter we assume that this is implicitly stated in our claims.

  3. 3.

    Some of the tools used in our constructions require the trapdoor permutations to be certifiable. Any time that we refer to trapdoor permutations we implicitly assume that they are certifiable. Note that such trapdoor permutations can be instantiated using RSA with suitable parameters [21].

  4. 4.

    We require an additional property on the OT, which we elaborate further in the next section.

  5. 5.

    In this model, the identities of the corrupted parties are not fixed at the beginning of the experiment and the adversary can decide which party to corrupt during the execution of the protocol.

  6. 6.

    A synchronizing adversary is an adversary that sends its message for every round before obtaining the honest party’s message for the next round.

  7. 7.

    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 inputs these values to the extractor \(\mathsf {TDExt}\).

  8. 8.

    For the wires corresponding to their own third-round message (i.e. \(\mathsf {msg}_i^3\) in \(\mathtt {GC}_i\)), the labels can be broadcasted directly in the last round.

References

  1. Ananth, P., Choudhuri, A.R., Goel, A., Jain, A.: Two round information-theoretic MPC with malicious security. In: Ishai, Y., Rijmen, V. (eds.) EUROCRYPT 2019. LNCS, vol. 11477, pp. 532–561. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-17656-3_19

    Chapter  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

    Chapter  Google Scholar 

  3. Aumann, Y., Lindell, Y.: Security against covert adversaries: efficient protocols for realistic adversaries. J. Cryptol. 23(2), 281–343 (2009). https://doi.org/10.1007/s00145-009-9040-7

    Article  MathSciNet  MATH  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

    Chapter  Google Scholar 

  5. Baum, C., Orsini, E., Scholl, P., Soria-Vazquez, E.: Efficient constant-round MPC with identifiable abort and public verifiability. In: Micciancio, D., Ristenpart, T. (eds.) CRYPTO 2020. LNCS, vol. 12171, pp. 562–592. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-56880-1_20

    Chapter  Google Scholar 

  6. 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

  7. 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

    Chapter  Google Scholar 

  8. Brandt, N.: Tight setup bounds for identifiable abort. Cryptology ePrint Archive, Report 2021/684 (2021). https://eprint.iacr.org/2021/684

  9. Brandt, N.P., Maier, S., Müller, T., Müller-Quade, J.: Constructing secure multi-party computation with identifiable abort. Cryptology ePrint Archive, Report 2020/153 (2020). https://eprint.iacr.org/2020/153

  10. Rai Choudhuri, A., Ciampi, M., Goyal, V., Jain, A., Ostrovsky, R.: Round optimal secure multiparty computation from minimal assumptions. In: Pass, R., Pietrzak, K. (eds.) TCC 2020. LNCS, vol. 12551, pp. 291–319. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-64378-2_11

    Chapter  Google Scholar 

  11. 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

    Chapter  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

    Chapter  Google Scholar 

  13. Cleve, R.: Limits on the security of coin flips when half the processors are faulty (extended abstract). In: 18th ACM STOC, pp. 364–369. ACM Press, May 1986. https://doi.org/10.1145/12130.12168

  14. Cohen, R., Garay, J., Zikas, V.: Broadcast-optimal two-round MPC. In: Canteaut, A., Ishai, Y. (eds.) EUROCRYPT 2020. LNCS, vol. 12106, pp. 828–858. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-45724-2_28

    Chapter  Google Scholar 

  15. Cohen, R., Lindell, Y.: Fairness versus guaranteed output delivery in secure multiparty computation. In: Sarkar, P., Iwata, T. (eds.) ASIACRYPT 2014. LNCS, vol. 8874, pp. 466–485. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-662-45608-8_25

    Chapter  MATH  Google Scholar 

  16. Cunningham, R.K., Fuller, B., Yakoubov, S.: Catching MPC cheaters: identification and openability. In: Shikata, J. (ed.) ICITS 17. LNCS, vol. 10681, pp. 110–134. Springer, Heidelberg (2017)

    Google Scholar 

  17. Damgård, I., Keller, M., Larraia, E., Pastro, V., Scholl, P., Smart, N.P.: Practical covertly secure MPC for dishonest majority – or: breaking the SPDZ limits. In: Crampton, J., Jajodia, S., Mayes, K. (eds.) ESORICS 2013. LNCS, vol. 8134, pp. 1–18. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-40203-6_1

    Chapter  Google Scholar 

  18. Damgård, I., Magri, B., Ravi, D., Siniscalchi, L., Yakoubov, S.: Broadcast-optimal two round MPC with an honest majority. In: Malkin, T., Peikert, C. (eds.) CRYPTO 2021. LNCS, vol. 12826, pp. 155–184. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-84245-1_6

    Chapter  Google Scholar 

  19. 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

    Chapter  Google Scholar 

  20. 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

  21. 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

  22. 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

    Chapter  Google Scholar 

  23. Garg, S., Sahai, A.: Adaptively secure multi-party computation with dishonest majority. In: Safavi-Naini, R., Canetti, R. (eds.) CRYPTO 2012. LNCS, vol. 7417, pp. 105–123. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-32009-5_8

    Chapter  Google Scholar 

  24. Goldreich, O., Krawczyk, H.: On the composition of zero-knowledge proof systems. SIAM J. Comput. 25(1), 169–192 (1996)

    Article  MathSciNet  Google Scholar 

  25. 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

  26. 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

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

  28. Goyal, V., Richelson, S., Rosen, A., Vald, M.: An algebraic approach to non-malleability. In: 55th FOCS, pp. 41–50. IEEE Computer Society Press, October 2014. https://doi.org/10.1109/FOCS.2014.13

  29. 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

    Chapter  Google Scholar 

  30. Hazay, C., Venkitasubramaniam, M.: Round-optimal fully black-box zero-knowledge arguments from one-way permutations. In: Beimel, A., Dziembowski, S. (eds.) TCC 2018. LNCS, vol. 11239, pp. 263–285. Springer, Cham (2018). https://doi.org/10.1007/978-3-030-03807-6_10

    Chapter  Google Scholar 

  31. Ishai, Y., Ostrovsky, R., Seyalioglu, H.: Identifying cheaters without an honest majority. In: Cramer, R. (ed.) TCC 2012. LNCS, vol. 7194, pp. 21–38. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-28914-9_2

    Chapter  Google Scholar 

  32. Ishai, Y., Ostrovsky, R., Zikas, V.: Secure multi-party computation with identifiable abort. In: Garay, J.A., Gennaro, R. (eds.) CRYPTO 2014. LNCS, vol. 8617, pp. 369–386. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-662-44381-1_21

    Chapter  Google Scholar 

  33. 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

    Chapter  Google Scholar 

  34. 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

    Chapter  Google Scholar 

  35. 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

    Chapter  Google Scholar 

  36. Khurana, D.: Round optimal concurrent non-malleability from polynomial hardness. In: Kalai, Y., Reyzin, L. (eds.) TCC 2017. LNCS, vol. 10678, pp. 139–171. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-70503-3_5

    Chapter  Google Scholar 

  37. 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

  38. Lin, H., Pass, R., Venkitasubramaniam, M.: Concurrent non-malleable commitments from any one-way function. In: Canetti, R. (ed.) TCC 2008. LNCS, vol. 4948, pp. 571–588. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-78524-8_31

    Chapter  Google Scholar 

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

  40. Pass, R., Rosen, A.: Concurrent non-malleable commitments. In: 46th FOCS, pp. 563–572. IEEE Computer Society Press, October 2005. https://doi.org/10.1109/SFCS.2005.27

  41. 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

    Chapter  Google Scholar 

  42. Scholl, P., Simkin, M., Siniscalchi, L.: Multiparty computation with covert security and public verifiability. Cryptology ePrint Archive, Report 2021/366 (2021). https://eprint.iacr.org/2021/366

  43. Simkin, M., Siniscalchi, L., Yakoubov, S.: On sufficient oracles for secure computation with identifiable abort. Cryptology ePrint Archive, Report 2021/151 (2021). https://eprint.iacr.org/2021/151

  44. Spini, G., Fehr, S.: Cheater detection in SPDZ multiparty computation. In: Nascimento, A.C.A., Barreto, P. (eds.) ICITS 2016. LNCS, vol. 10015, pp. 151–176. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-49175-2_8

    Chapter  Google Scholar 

  45. 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

  46. 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

Acknowledgements

We are grateful to Maciej Obremski, our tall lighthouse who illuminated our path toward proving the complexity of our simulators.

Author information

Authors and Affiliations

  1. The University of Edinburgh, Edinburgh, UK

    Michele Ciampi & Hendrik Waldner

  2. Aarhus University, Aarhus, Denmark

    Divya Ravi & Luisa Siniscalchi

  3. Concordium Blockchain Research Center, Aarhus, Denmark

    Luisa Siniscalchi

Authors
  1. Michele Ciampi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Divya Ravi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Luisa Siniscalchi
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Hendrik Waldner
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Luisa Siniscalchi .

Editor information

Editors and Affiliations

  1. University of Haifa, Haifa, Haifa, Israel

    Orr Dunkelman

  2. University of Warsaw, Warsaw, Poland

    Stefan Dziembowski

Rights and permissions

Reprints and permissions

Copyright information

© 2022 International Association for Cryptologic Research

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Ciampi, M., Ravi, D., Siniscalchi, L., Waldner, H. (2022). Round-Optimal Multi-party Computation with Identifiable Abort. In: Dunkelman, O., Dziembowski, S. (eds) Advances in Cryptology – EUROCRYPT 2022. EUROCRYPT 2022. Lecture Notes in Computer Science, vol 13275. Springer, Cham. https://doi.org/10.1007/978-3-031-06944-4_12

Download citation

  • DOI: https://doi.org/10.1007/978-3-031-06944-4_12

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-06943-7

  • Online ISBN: 978-3-031-06944-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Societies and partnerships

Search

Navigation