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On the Bottleneck Complexity of MPC with Correlated Randomness

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Public-Key Cryptography – PKC 2022 (PKC 2022)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 13177))

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Abstract

At ICALP 2018, Boyle et al. introduced the notion of the bottleneck complexity of a secure multi-party computation (MPC) protocol. This measures the maximum communication complexity of any one party in the protocol, aiming to improve load-balancing among the parties.

In this work, we study the bottleneck complexity of MPC in the preprocessing model, where parties are given correlated randomness ahead of time. We present two constructions of bottleneck-efficient MPC protocols, whose bottleneck complexity is independent of the number of parties:

  1. 1.

    A protocol for computing abelian programs, based only on one-way functions.

  2. 2.

    A protocol for selection functions, based on any linearly homomorphic encryption scheme.

Compared with previous bottleneck-efficient constructions, our protocols can be based on a wider range of assumptions, and avoid the use of fully homomorphic encryption.

Research supported by: the Concordium Blockhain Research Center, Aarhus University, Denmark; the Carlsberg Foundation under the Semper Ardens Research Project CF18-112 (BCM); the European Research Council (ERC) under the European Unions’s Horizon 2020 research and innovation programme under grant agreement No 803096 (SPEC); the Aarhus University Research Foundation (AUFF); the Independent Research Fund Denmark (DFF) under project number 0165-00107B; the Digital Research Centre Denmark (DIREC);.

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Notes

  1. 1.

    However, this approach suffices for residual security, as shown in the NIMPC protocol of [HIKR18].

References

  1. Ananth, P., Badrinarayanan, S., Jain, A., Manohar, N., Sahai, A.: From FE combiners to secure MPC and back. In: Hofheinz, D., Rosen, A. (eds.) TCC 2019. LNCS, vol. 11891, pp. 199–228. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-36030-6_9

    Chapter  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

    Chapter  Google Scholar 

  3. Beimel, A., Gabizon, A., Ishai, Y., Kushilevitz, E., Meldgaard, S., Paskin-Cherniavsky, A.: Non-interactive secure multiparty computation. In: Garay, J.A., Gennaro, R. (eds.) CRYPTO 2014. LNCS, vol. 8617, pp. 387–404. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-662-44381-1_22

    Chapter  Google Scholar 

  4. Boyle, E., Goldwasser, S., Tessaro, S.: Communication locality in secure multi-party computation. In: Sahai, A. (ed.) TCC 2013. LNCS, vol. 7785, pp. 356–376. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-36594-2_21

    Chapter  Google Scholar 

  5. Ben-Or, M., Goldwasser, S., Wigderson, A.: Completeness theorems for non-cryptographic fault-tolerant distributed computation (extended abstract). In: 20th ACM STOC, pp. 1–10. ACM Press, May 1988

    Google Scholar 

  6. Bellare, M., Hoang, V.T., Rogaway, P.: Foundations of garbled circuits. In: Yu, T., Danezis, G., Gligor, V.D. (eds.) ACM CCS 2012, pp. 784–796. ACM Press, October 2012

    Google Scholar 

  7. Boyle, E., Jain, A., Prabhakaran, M., Yu, C.-H.: The bottleneck complexity of secure multiparty computation. In: Chatzigiannakis, I., Kaklamanis, C., Marx, D., Sannella, D. (eds.) ICALP 2018, LIPIcs, vol. 107, pp. 24:1–24:16. Schloss Dagstuhl, July 2018

    Google Scholar 

  8. Brakerski, Z., Vaikuntanathan, V.: Efficient fully homomorphic encryption from (standard) LWE. In: Ostrovsky, R. (ed.) 52nd FOCS, pp. 97–106. IEEE Computer Society Press, October 2011

    Google Scholar 

  9. Canetti, R.: Security and composition of multiparty cryptographic protocols. J. Cryptol. 13(1), 143–202 (2000)

    Article  MathSciNet  Google Scholar 

  10. Chaum, D., Crépeau, C., Damgård, I.: Multiparty unconditionally secure protocols (extended abstract). In: 20th ACM STOC, pp. 11–19. ACM Press, May 1988

    Google Scholar 

  11. Canetti, R., Lin, H., Tessaro, S., Vaikuntanathan, V.: Obfuscation of probabilistic circuits and applications. In: Dodis, Y., Nielsen, J.B. (eds.) TCC 2015. LNCS, vol. 9015, pp. 468–497. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-46497-7_19

    Chapter  MATH  Google Scholar 

  12. Couteau, G.: A note on the communication complexity of multiparty computation in the correlated randomness model. In: Ishai, Y., Rijmen, V. (eds.) EUROCRYPT 2019. LNCS, vol. 11477, pp. 473–503. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-17656-3_17

    Chapter  MATH  Google Scholar 

  13. Damgård, I., Faust, S., Hazay, C.: Secure two-party computation with low communication. In: Cramer, R. (ed.) TCC 2012. LNCS, vol. 7194, pp. 54–74. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-28914-9_4

    Chapter  Google Scholar 

  14. Damgård, I., Ishai, Y.: Scalable secure multiparty computation. In: Dwork, C. (ed.) CRYPTO 2006. LNCS, vol. 4117, pp. 501–520. Springer, Heidelberg (2006). https://doi.org/10.1007/11818175_30

    Chapter  Google Scholar 

  15. Damgård, I., Ishai, Y., Krøigaard, M., Nielsen, J.B., Smith, A.: Scalable multiparty computation with nearly optimal work and resilience. In: Wagner, D. (ed.) CRYPTO 2008. LNCS, vol. 5157, pp. 241–261. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-85174-5_14

    Chapter  Google Scholar 

  16. Damgård, I., Nielsen, J.B., Polychroniadou, A., Raskin, M.: On the communication required for unconditionally secure multiplication. In: Robshaw, M., Katz, J. (eds.) CRYPTO 2016. LNCS, vol. 9815, pp. 459–488. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-53008-5_16

    Chapter  Google Scholar 

  17. Eriguchi, R., Ohara, K., Yamada, S., Nuida, K.: Non-interactive secure multiparty computation for symmetric functions, revisited: more efficient constructions and extensions. In: Malkin, T., Peikert, C. (eds.) CRYPTO 2021. LNCS, vol. 12826, pp. 305–334. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-84245-1_11

    Chapter  Google Scholar 

  18. Fernando, R., Komargodski, I., Liu, Y., Shi, E.: Secure Massively parallel computation for dishonest majority. In: Pass, R., Pietrzak, K. (eds.) TCC 2020. LNCS, vol. 12551, pp. 379–409. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-64378-2_14

    Chapter  Google Scholar 

  19. Gordon, S.D., Malkin, T., Rosulek, M., Wee, H.: Multi-party computation of polynomials and branching programs without simultaneous interaction. In: Johansson, T., Nguyen, P.Q. (eds.) EUROCRYPT 2013. LNCS, vol. 7881, pp. 575–591. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-38348-9_34

    Chapter  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

    Google Scholar 

  21. Halevi, S., Ishai, Y., Jain, A., Kushilevitz, E., Rabin, T.: Secure multiparty computation with general interaction patterns. In: Sudan, M. (ed.) ITCS 2016, pp. 157–168. ACM, January 2016

    Google Scholar 

  22. Halevi, S., Ishai, Y., Kushilevitz, E., Rabin, T.: Best possible information-theoretic MPC. In: Beimel, A., Dziembowski, S. (eds.) TCC 2018. LNCS, vol. 11240, pp. 255–281. Springer, Cham (2018). https://doi.org/10.1007/978-3-030-03810-6_10

    Chapter  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

    Chapter  Google Scholar 

  24. Ishai, Y., Kushilevitz, E., Meldgaard, S., Orlandi, C., Paskin-Cherniavsky, A.: On the power of correlated randomness in secure computation. In: Sahai, A. (ed.) TCC 2013. LNCS, vol. 7785, pp. 600–620. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-36594-2_34

    Chapter  MATH  Google Scholar 

  25. Ishai, Y., Mittal, M., Ostrovsky, R.: On the message complexity of secure multiparty computation. In: Abdalla, M., Dahab, R. (eds.) PKC 2018. LNCS, vol. 10769, pp. 698–711. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-76578-5_24

    Chapter  Google Scholar 

  26. Ishai, Y., Paskin, A.: Evaluating branching programs on encrypted data. In: Vadhan, S.P. (ed.) TCC 2007. LNCS, vol. 4392, pp. 575–594. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-70936-7_31

    Chapter  Google Scholar 

  27. Lindell, Y., Nissim, K., Orlandi, C.: Hiding the input-size in secure two-party computation. In: Sako, K., Sarkar, P. (eds.) ASIACRYPT 2013. LNCS, vol. 8270, pp. 421–440. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-42045-0_22

    Chapter  MATH  Google Scholar 

  28. Naor, M., Nissim, K.: Communication preserving protocols for secure function evaluation. In: 33rd ACM STOC, pp. 590–599. ACM Press, July 2001

    Google Scholar 

  29. Quach, W., Wee, H., Wichs, D.: Laconic function evaluation and applications. In: Thorup, M. (ed.) 59th FOCS, pp. 859–870. IEEE Computer Society Press, October 2018

    Google Scholar 

  30. Regev, O.: On lattices, learning with errors, random linear codes, and cryptography. In: Gabow, H.N., Fagin, R. (eds.) 37th ACM STOC, pp. 84–93. ACM Press, May 2005

    Google Scholar 

  31. Yao, A.C.-C.: Protocols for secure computations (extended abstract). In: 23rd FOCS, pp. 160–164. IEEE Computer Society Press, November 1982

    Google Scholar 

  32. Yao, A.C.-C.: How to generate and exchange secrets (extended abstract). In: 27th FOCS, pp. 162–167. IEEE Computer Society Press, October 1986

    Google Scholar 

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Authors and Affiliations

  1. Aarhus University, Aarhus, Denmark

    Claudio Orlandi, Divya Ravi & Peter Scholl

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  1. Claudio Orlandi
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  2. Divya Ravi
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  3. Peter Scholl
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Correspondence to Divya Ravi .

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Editors and Affiliations

  1. National Institute of Advanced Industrial Science and Technology (AIST), Tokyo, Japan

    Goichiro Hanaoka

  2. Yokohama National University, Yokohama, Japan

    Junji Shikata

  3. The University of Electro-Communications, Tokyo, Japan

    Yohei Watanabe

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Orlandi, C., Ravi, D., Scholl, P. (2022). On the Bottleneck Complexity of MPC with Correlated Randomness. In: Hanaoka, G., Shikata, J., Watanabe, Y. (eds) Public-Key Cryptography – PKC 2022. PKC 2022. Lecture Notes in Computer Science(), vol 13177. Springer, Cham. https://doi.org/10.1007/978-3-030-97121-2_8

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  • DOI: https://doi.org/10.1007/978-3-030-97121-2_8

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