Skip to main content
SpringerLink
Log in

List Oblivious Transfer and Applications to Round-Optimal Black-Box Multiparty Coin Tossing

  • Conference paper
  • First Online:
Advances in Cryptology – CRYPTO 2023 (CRYPTO 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14081))

Included in the following conference series:

  • 1109 Accesses

Abstract

In this work we study the problem of minimizing the round complexity for securely evaluating multiparty functionalities while making black-box use of polynomial time assumptions. In Eurocrypt 2016, Garg et al. showed that assuming all parties have access to a broadcast channel, then at least four rounds of communication are required to securely realize non-trivial functionalities in the plain model.

A sequence of works follow-up the result of Garg et al. matching this lower bound under a variety of assumptions. Unfortunately, none of these works make black-box use of the underlying cryptographic primitives. In Crypto 2021, Ishai, Khurana, Sahai, and Srinivasan came closer to matching the four-round lower bound, obtaining a five-round protocol that makes black-box use of oblivious transfer and PKE with pseudorandom public keys.

In this work, we show how to realize any input-less functionality (e.g., coin-tossing, generation of key-pairs, and so on) in four rounds while making black-box use of two-round oblivious transfer. As an additional result, we construct the first four-round MPC protocol for generic functionalities that makes black-box use of the underlying primitives, achieving security against non-aborting adversaries.

Our protocols are based on a new primitive called list two-party computation. This primitive offers relaxed security compared to the standard notion of secure two-party computation. Despite this relaxation, we argue that this tool suffices for our applications. List two-party computation is of independent interest, as we argue it can also be used for the generation of setups, like oblivious transfer correlated randomness, in three rounds. Prior to our work, generating such a setup required at least four rounds of interactions or a trusted third party.

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 89.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 119.99
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

Notes

  1. 1.

    All the results discussed and presented in this paper are with respect to black-box simulation. Hence, we will not specify this in the remainder of the paper.

  2. 2.

    We recall that an OT combiner allows combining two (or more) OT instances to obtain a new OT instance, that is guaranteed to be secure, as long as one of the input instances is not compromise. We refer to [16] for more details on OT combiners. Moreover, for our formal constructions we will not rely on a combiner in a black-box way, we will instead use techniques similar to those proposed in [16] to properly combine our OT protocols.

  3. 3.

    A defence of a protocol execution is represented by the randomness and input that explain the generated transcript.

  4. 4.

    Our formal construction directly uses \(\textsf{OT}^\textsf{list}\) to obtain a 3-round list 2PC protocol, so we do not need an intermediate step where we instantiate this special OT protocol, which is instead implicit in our 2PC protocol.

  5. 5.

    A split state non-malleable code has an encoding algorithm \(\textsf{Code}\) that, on input a message m returns two codewords L and R. The security of the non-malleable code guarantees that there are no tampering functions f and g, that taking as an input L and R, respectively, return \(\tilde{L}\) and \(\tilde{R}\), such that the decoding of these tampered codewords has a relation with the message m.

  6. 6.

    Here, \(\mathrm \varPhi _{2,i}\) is the function that takes \(\{y_{i,j}\}_{j\in [\ell ]}\) and \(\{x_{i,j,k}\}_{j\in [\ell ],k\in [\lambda ]}\) as inputs and first reconstructs \(\{x_{i,j}\}_{j\in [\ell ]}\) and then applies the function computed by the i-th server in the outer protocol \(\mathrm \varPhi \) on \(f,\{x_{i,j},y_{i,j}\}_{j\in [\ell ]}\).

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

    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, Part I. LNCS, vol. 10401, pp. 468–499. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-63688-7_16

    Chapter  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, Part II. LNCS, vol. 10992, pp. 459–487. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-96881-0_16

    Chapter  Google Scholar 

  4. Beaver, D., Micali, S., Rogaway, P.: The round complexity of secure protocols (extended abstract). In: 22nd Annual ACM Symposium on Theory of Computing, Baltimore, MD, USA, 14–16 May 1990, pp. 503–513. ACM Press (1990). https://doi.org/10.1145/100216.100287

  5. Brakerski, Z., Döttling, N.: Two-message statistically sender-private OT from LWE. In: Beimel, A., Dziembowski, S. (eds.) TCC 2018, Part II. LNCS, vol. 11240, pp. 370–390. Springer, Cham (2018). https://doi.org/10.1007/978-3-030-03810-6_14

    Chapter  Google Scholar 

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

    Chapter  Google Scholar 

  7. 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, Part II. LNCS, vol. 12551, pp. 291–319. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-64378-2_11

    Chapter  Google Scholar 

  8. Ciampi, M., Ostrovsky, R., Waldner, H., Zikas, V.: Round-optimal and communication-efficient multiparty computation. In: Dunkelman, O., Dziembowski, S. (eds.) EUROCRYPT 2022, Part I. LNCS, vol. 13275, pp. 65–95. Springer, Heidelberg (2022). https://doi.org/10.1007/978-3-031-06944-4_3

    Chapter  Google Scholar 

  9. Ciampi, M., Ravi, D., Siniscalchi, L., Waldner, H.: Round-optimal multi-party computation with identifiable abort. In: Dunkelman, O., Dziembowski, S. (eds.) EUROCRYPT 2022, Part I. LNCS, vol. 13275, pp. 335–364. Springer, Heidelberg (2022). https://doi.org/10.1007/978-3-031-06944-4_12

    Chapter  Google Scholar 

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

    Chapter  Google Scholar 

  11. 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 Annual ACM Symposium on Theory of Computing, New York City, NY, USA, 25–27 May 1987, pp. 218–229. ACM Press (1987). https://doi.org/10.1145/28395.28420

  12. Goyal, V.: Constant round non-malleable protocols using one way functions. In: Fortnow, L., Vadhan, S.P. (eds.) 43rd Annual ACM Symposium on Theory of Computing, San Jose, CA, USA, 6–8 June 2011, pp. 695–704. ACM Press (2011). https://doi.org/10.1145/1993636.1993729

  13. Goyal, V., Richelson, S., Rosen, A., Vald, M.: An algebraic approach to non-malleability. In: 55th Annual Symposium on Foundations of Computer Science, Philadelphia, PA, USA, 18–21 October 2014, pp. 41–50. IEEE Computer Society Press (2014). https://doi.org/10.1109/FOCS.2014.13

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

    Chapter  Google Scholar 

  15. Halevi, S., Hazay, C., Polychroniadou, A., Venkitasubramaniam, M.: Round-optimal secure multi-party computation. J. Cryptol. 34(3), 1–63 (2021). https://doi.org/10.1007/s00145-021-09382-3

    Article  MathSciNet  MATH  Google Scholar 

  16. Harnik, D., Kilian, J., Naor, M., Reingold, O., Rosen, A.: On robust combiners for oblivious transfer and other primitives. In: Cramer, R. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 96–113. Springer, Heidelberg (2005). https://doi.org/10.1007/11426639_6

    Chapter  Google Scholar 

  17. Ishai, Y., Khurana, D., Sahai, A., Srinivasan, A.: On the round complexity of black-box secure MPC. In: Malkin, T., Peikert, C. (eds.) CRYPTO 2021, Part II. LNCS, vol. 12826, pp. 214–243. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-84245-1_8

    Chapter  Google Scholar 

  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

    Chapter  Google Scholar 

  19. Kalai, Y.T.: Smooth projective hashing and two-message oblivious transfer. In: Cramer, R. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 78–95. Springer, Heidelberg (2005). https://doi.org/10.1007/11426639_5

    Chapter  Google Scholar 

  20. 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 

  21. 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 

  22. Khurana, D., Ostrovsky, R., Srinivasan, A.: Round optimal black-box “commit-and-prove’’. In: Beimel, A., Dziembowski, S. (eds.) TCC 2018, Part I. LNCS, vol. 11239, pp. 286–313. Springer, Cham (2018). https://doi.org/10.1007/978-3-030-03807-6_11

    Chapter  Google Scholar 

  23. Kilian, J.: Founding cryptography on oblivious transfer. In: 20th Annual ACM Symposium on Theory of Computing, Chicago, IL, USA, 2–4 May 1988, pp. 20–31. ACM Press (1988). https://doi.org/10.1145/62212.62215

  24. Naor, M., Pinkas, B.: Efficient oblivious transfer protocols. In: Kosaraju, S.R. (ed.) 12th Annual ACM-SIAM Symposium on Discrete Algorithms, Washington, DC, USA, 7–9 January 2001, pp. 448–457. ACM-SIAM (2001)

    Google Scholar 

  25. Pass, R.: Bounded-concurrent secure multi-party computation with a dishonest majority. In: Babai, L. (ed.) 36th Annual ACM Symposium on Theory of Computing, Chicago, IL, USA, 13–16 June 2004, pp. 232–241. ACM Press (2004). https://doi.org/10.1145/1007352.1007393

  26. 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 

  27. Shankar, B., Srinathan, K., Rangan, C.P.: Alternative protocols for generalized oblivious transfer. In: Rao, S., Chatterjee, M., Jayanti, P., Murthy, C.S.R., Saha, S.K. (eds.) ICDCN 2008. LNCS, vol. 4904, pp. 304–309. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-77444-0_31

    Chapter  Google Scholar 

  28. Wee, H.: Black-box, round-efficient secure computation via non-malleability amplification. In: 51st Annual Symposium on Foundations of Computer Science, Las Vegas, NV, USA, 23–26 October 2010, pp. 531–540. IEEE Computer Society Press (2010). https://doi.org/10.1109/FOCS.2010.87

  29. Yao, A.C.C.: How to generate and exchange secrets (extended abstract). In: 27th Annual Symposium on Foundations of Computer Science, Toronto, Ontario, Canada, 27–29 October 1986, pp. 162–167. IEEE Computer Society Press (1986). https://doi.org/10.1109/SFCS.1986.25

Download references

Acknowledgements

This work is supported in part by DARPA under Cooperative Agreement HR0011-20-2-0025, the Algorand Centers of Excellence programme managed by Algorand Foundation, NSF grants CNS-2246355, CCF-2220450 and CNS-2001096, US-Israel BSF grant 2015782, Amazon Faculty Award, Cisco Research Award and Sunday Group. Any views, opinions, findings, conclusions or recommendations contained herein are those of the author(s) and should not be interpreted as necessarily representing the official policies, either expressed or implied, of DARPA, the Department of Defense, the Algorand Foundation, or the U.S. Government. The U.S. Government is authorized to reproduce and distribute reprints for governmental purposes not withstanding any copyright annotation therein.

Author information

Authors and Affiliations

  1. The University of Edinburgh, Edinburgh, UK

    Michele Ciampi

  2. University of California, Los Angeles, USA

    Rafail Ostrovsky

  3. Danish Technical University, Copenhagen, Denmark

    Luisa Siniscalchi

  4. University of Maryland, College Park, USA

    Hendrik Waldner

  5. Max Planck Institute for Security and Privacy, Bochum, Germany

    Hendrik Waldner

Authors
  1. Michele Ciampi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Rafail Ostrovsky
    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 Michele Ciampi .

Editor information

Editors and Affiliations

  1. Rambus Inc., San Jose, CA, USA

    Helena Handschuh

  2. Brown University, Providence, RI, USA

    Anna Lysyanskaya

Rights and permissions

Reprints and permissions

Copyright information

© 2023 International Association for Cryptologic Research

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Ciampi, M., Ostrovsky, R., Siniscalchi, L., Waldner, H. (2023). List Oblivious Transfer and Applications to Round-Optimal Black-Box Multiparty Coin Tossing. In: Handschuh, H., Lysyanskaya, A. (eds) Advances in Cryptology – CRYPTO 2023. CRYPTO 2023. Lecture Notes in Computer Science, vol 14081. Springer, Cham. https://doi.org/10.1007/978-3-031-38557-5_15

Download citation

  • DOI: https://doi.org/10.1007/978-3-031-38557-5_15

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-38556-8

  • Online ISBN: 978-3-031-38557-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Societies and partnerships

Search

Navigation