Advertisement

Two-Round Secure MPC from Indistinguishability Obfuscation

  • Sanjam Garg
  • Craig Gentry
  • Shai Halevi
  • Mariana Raykova
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8349)

Abstract

One fundamental complexity measure of an MPC protocol is its round complexity. Asharov et al. recently constructed the first three round protocol for general MPC in the CRS model. Here, we show how to achieve this result with only two rounds. We obtain UC security with abort against static malicious adversaries, and fairness if there is an honest majority. Additionally the communication in our protocol is only proportional to the input and output size of the function being evaluated and independent of its circuit size. Our main tool is indistinguishability obfuscation, for which a candidate construction was recently proposed by Garg et al.

The technical tools that we develop in this work also imply virtual black box obfuscation of a new primitive that we call a dynamic point function. This primitive may be of independent interest.

Keywords

Ideal Functionality Homomorphic Encryption Honest Party Random Coin Common Reference String 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. [AJLA+12]
    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)CrossRefGoogle Scholar
  2. [AJW+11]
    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)CrossRefGoogle Scholar
  3. [BGI+12]
    Barak, B., Goldreich, O., Impagliazzo, R., Rudich, S., Sahai, A., Vadhan, S.P., Yang, K.: On the (im)possibility of obfuscating programs. J. ACM 59(2), 6 (2012)CrossRefMathSciNetGoogle Scholar
  4. [BGV+12]
    Brakerski, Z., Gentry, C., Vaikuntanathan, V.: (leveled) fully homomorphic encryption without bootstrapping. In: ITCS (2012)Google Scholar
  5. [BV+11]
    Brakerski, Z., Vaikuntanathan, V.: Efficient fully homomorphic encryption from (standard) lwe. In: FOCS, pp. 97–106 (2011)Google Scholar
  6. [Can+01]
    Canetti, R.: Universally composable security: A new paradigm for cryptographic protocols. In: 42nd Annual Symposium on Foundations of Computer Science, Las Vegas, Nevada, USA, October 14-17, pp. 136–145. IEEE Computer Society Press (2001)Google Scholar
  7. [FLS+90]
    Feige, U., Lapidot, D., Shamir, A.: Multiple non-interactive zero knowledge proofs based on a single random string. In: Proceedings of the 31st Annual Symposium on Foundations of Computer Science, vol. 1, pp. 308–317 (1990)Google Scholar
  8. [Gen+09]
    Gentry, C.: A fully homomorphic encryption scheme. PhD thesis, Stanford University (2009), http://crypto.stanford.edu/craigGoogle Scholar
  9. [GGH+13a]
    Gentry, C., Sahai, A., Waters, B.: Homomorphic encryption from learning with errors: Conceptually-simpler, asymptotically-faster, attribute-based. In: Canetti, R., Garay, J.A. (eds.) CRYPTO 2013, Part I. LNCS, vol. 8042, pp. 75–92. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  10. [GGH+13b]
    Garg, S., Gentry, C., Halevi, S., Raykova, M., Sahai, A., Waters, B.: Candidate indistinguishability obfuscation and functional encryption for all circuits. In: FOCS 2013. IEEE (to appear, 2013), http://eprint.iacr.org/2013/451
  11. [GGHR+13]
    Garg, S., Gentry, C., Halevi, S., Raykova, M.: Two-round secure mpc from indistinguishability obfuscation. Cryptology ePrint Archive, Report 2013/601 (2013), http://eprint.iacr.org/
  12. [GGSW+13]
    Garg, S., Gentry, C., Sahai, A., Waters, B.: Witness encryption and its applications. In: STOC (2013)Google Scholar
  13. [GMW+87]
    Garg, S., Gentry, C., Sahai, A., Waters, B.: Witness encryption and its applications. In: STOC (2013)Google Scholar
  14. [Gol+04]
    Goldreich, O.: Foundations of Cryptography: Basic Applications, vol. 2. Cambridge University Press, Cambridge (2004)CrossRefGoogle Scholar
  15. [GSW+13]
    Gentry, C., Sahai, A., Waters, B.: Homomorphic encryption from learning with errors: Conceptually-simpler, asymptotically-faster, attribute-based. In: Canetti, R., Garay, J.A. (eds.) CRYPTO 2013, Part I. LNCS, vol. 8042, pp. 75–92. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  16. [HLP+11]
    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)CrossRefGoogle Scholar
  17. [IKO+05]
    Ishai, Y., Kushilevitz, E., Ostrovsky, R.: Sufficient conditions for collision-resistant hashing. In: Kilian, J. (ed.) TCC 2005. LNCS, vol. 3378, pp. 445–456. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  18. [LATV+12]
    López-Alt, A., Tromer, E., Vaikuntanathan, V.: On-the-fly multiparty computation on the cloud via multikey fully homomorphic encryption. In: STOC, pp. 1219–1234 (2012)Google Scholar
  19. [LP+09]
    Lindell, Y., Pinkas, B.: A proof of security of Yao’s protocol for two-party computation. Journal of Cryptology 22(2), 161–188 (2009)CrossRefzbMATHMathSciNetGoogle Scholar
  20. [MSS+11]
    Myers, S., Sergi, M., Shelat, A.: Threshold fully homomorphic encryption and secure computation. IACR Cryptology ePrint Archive 2011, 454 (2011)Google Scholar
  21. [RAD+78]
    Rivest, R., Adleman, L., Dertouzos, M.L.: On data banks and privacy homomorphisms. In: Foundations of Secure Computation, pp. 169–180 (1978)Google Scholar
  22. [SW+12]
    Sahai, A., Waters, B.: How to use indistinguishability obfuscation: Deniable encryption, and more. IACR Cryptology ePrint Archive 2013, 454 (2013)Google Scholar
  23. [vDGHV+10]
    van Dijk, M., Gentry, C., Halevi, S., Vaikuntanathan, V.: Fully homomorphic encryption over the integers. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 24–43. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  24. [Yao+82]
    Yao, A.C.: Protocols for secure computations. In: 23rd Annual Symposium on Foundations of Computer Science, Chicago, Illinois, November 3-5, pp. 160–164. IEEE Computer Society Press (1982)Google Scholar

Copyright information

© International Association for Cryptologic Research 2014

Authors and Affiliations

  • Sanjam Garg
    • 1
  • Craig Gentry
    • 1
  • Shai Halevi
    • 1
  • Mariana Raykova
    • 2
  1. 1.IBM T. J. WatsonUSA
  2. 2.SRI InternationalUSA

Personalised recommendations