Better Two-Round Adaptive Multi-party Computation

  • Ran Canetti
  • Oxana Poburinnaya
  • Muthuramakrishnan Venkitasubramaniam
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10175)

Abstract

The only known two-round multi-party computation protocol that withstands adaptive corruption of all parties is the ingenious protocol of Garg and Polychroniadou [TCC 15]. We present protocols that improve on the GP protocol in a number of ways. First, concentrating on the semi-honest case and taking a different approach than GP, we show a two-round, adaptively secure protocol where:
  • Only a global (i.e., non-programmable) reference string is needed. In contrast, in GP the reference string is programmable, even in the semi-honest case.

  • Only polynomially-secure indistinguishability obfuscation for circuits and injective one way functions are assumed. In GP, sub-exponentially secure IO is assumed.

Second, we show how to make the GP protocol have only RAM complexity, even for Byzantine corruptions. For this we construct the first statistically-sound non-interactive Zero-Knowledge scheme with RAM complexity.

Notes

Acknowledgments

We thank Justin Holmgren for pointing out that our MPC protocol can be used to compute a garbling scheme in [IK02] manner, which allows us to avoid the use of subexponentially-secure \(\mathsf {iO}\) even in the RAM setting.

References

  1. [AIK06]
    Applebaum, B., Ishai, Y., Kushilevitz, E.: Computationally private randomizing polynomials and their applications. Comput. Complex. 15(2), 115–162 (2006)MathSciNetCrossRefMATHGoogle Scholar
  2. [BCH12]
    Bitansky, N., Canetti, R., Halevi, S.: Leakage-tolerant interactive protocols. In: Cramer, R. (ed.) TCC 2012. LNCS, vol. 7194, pp. 266–284. Springer, Heidelberg (2012). doi:10.1007/978-3-642-28914-9_15 CrossRefGoogle Scholar
  3. [BCP15]
    Boyle, E., Chung, K.-M., Pass, R.: Large-scale secure computation: multi-party computation for (Parallel) RAM programs. In: Gennaro, R., Robshaw, M. (eds.) CRYPTO 2015. LNCS, vol. 9216, pp. 742–762. Springer, Heidelberg (2015). doi:10.1007/978-3-662-48000-7_36 CrossRefGoogle Scholar
  4. [BST14]
    Bellare, M., Stepanovs, I., Tessaro, S.: Poly-many hardcore bits for any one-way function and a framework for differing-inputs obfuscation. In: Sarkar, P., Iwata, T. (eds.) ASIACRYPT 2014. LNCS, vol. 8874, pp. 102–121. Springer, Heidelberg (2014). doi:10.1007/978-3-662-45608-8_6 Google Scholar
  5. [CDPW07]
    Canetti, R., Dodis, Y., Pass, R., Walfish, S.: Universally composable security with global setup. In: Vadhan, S.P. (ed.) TCC 2007. LNCS, vol. 4392, pp. 61–85. Springer, Heidelberg (2007). doi:10.1007/978-3-540-70936-7_4 CrossRefGoogle Scholar
  6. [CGP15]
    Canetti, R., Goldwasser, S., Poburinnaya, O.: Adaptively Secure Two-Party Computation from Indistinguishability Obfuscation. In: Dodis, Y., Nielsen, J.B. (eds.) TCC 2015. LNCS, vol. 9015, pp. 557–585. Springer, Heidelberg (2015). doi:10.1007/978-3-662-46497-7_22 CrossRefGoogle Scholar
  7. [CH16]
    Canetti, R., Holmgren, J.: Fully succinct garbled RAM. In: Proceedings of the ACM Conference on Innovations in Theoretical Computer Science. Cambridge, MA, USA, 14–16 January, pp. 169–178 (2016)Google Scholar
  8. [CHJV15]
    Canetti, R., Holmgren, J., Jain, A., Vaikuntanathan, V.: Succinct garbling and indistinguishability obfuscation for RAM programs. In: Proceedings of the Forty-Seventh Annual ACM on Symposium on Theory of Computing, STOC. Portland, OR, USA, 14–17 June, pp. 429–437 (2015)Google Scholar
  9. [CLOS02]
    Canetti, R., Lindell, Y., Ostrovsky, R., Sahai, A.: Universally composable two-party and multi-party secure computation. In Proceedings on 34th Annual ACM Symposium on Theory of Computing, 19–21 May. Montréal, Québec, Canada, pp. 494–503 (2002)Google Scholar
  10. [CPR16]
    Canetti, R., Poburinnaya, O., Raykova, M.: Optimal-rate non-committing encryption in a CRS model. IACR Cryptology ePrint Archive 2016:511 (2016)Google Scholar
  11. [CPV16]
    Canetti, R., Poburinnaya, O., Venkitasubramaniam, M.: Better two-round adaptive multiparty computation. In: Cryptology ePrint Archive, Report 2016/614 (2016). http://eprint.iacr.org/2016/614
  12. [DKR14]
    Dachman-Soled, D., Katz, J., Rao, V.: Adaptively secure, universally composable, multi-party computation in constant rounds. IACR Cryptology ePrint Archive 2014, 858 (2014)Google Scholar
  13. [DMN11]
    Damgård, I., Meldgaard, S., Nielsen, J.B.: Perfectly secure oblivious RAM without random oracles. In: Ishai, Y. (ed.) TCC 2011. LNCS, vol. 6597, pp. 144–163. Springer, Heidelberg (2011). doi:10.1007/978-3-642-19571-6_10 CrossRefGoogle Scholar
  14. [Gen09]
    Gentry, C.: A Fully Homomorphic Encryption Scheme. Ph.D. thesis. Stanford, CA, USA, AAI3382729 (2009)Google Scholar
  15. [GGHR14]
    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). doi:10.1007/978-3-642-54242-8_4 CrossRefGoogle Scholar
  16. [GOS06]
    Groth, J., Ostrovsky, R., Sahai, A.: Perfect non-interactive zero knowledge for NP. In: Vaudenay, S. (ed.) EUROCRYPT 2006. LNCS, vol. 4004, pp. 339–358. Springer, Heidelberg (2006). doi:10.1007/11761679_21 CrossRefGoogle Scholar
  17. [GP14]
    Garg, S., Polychroniadou, A.: Two-round adaptively secure MPC from indistinguishability obfuscation. IACR Cryptology ePrint Archive 2014:844 (2014)Google Scholar
  18. [Gro11]
    Groth, J.: Minimizing non-interactive zero-knowledge proofs using fully homomorphic encryption. IACR Cryptology ePrint Archive 2011:12 (2011)Google Scholar
  19. [IK02]
    Ishai, Y., Kushilevitz, E.: Perfect constant-round secure computation via perfect randomizing polynomials. In: Widmayer, P., Eidenbenz, S., Triguero, F., Morales, R., Conejo, R., Hennessy, M. (eds.) ICALP 2002. LNCS, vol. 2380, pp. 244–256. Springer, Heidelberg (2002). doi:10.1007/3-540-45465-9_22 CrossRefGoogle Scholar
  20. [IKOS10]
    Ishai, Y., Kumarasubramanian, A., Orlandi, C., Sahai, A.: Proceedings on invertible sampling and adaptive security. In: Abe, M. (ed.) ASIACRYPT 2010. LNCS, vol. 6477, pp. 466–482. Springer, Heidelberg (2010). doi:10.1007/978-3-642-17373-8_27 CrossRefGoogle Scholar
  21. [KSW14]
    Khurana, D., Sahai, A., Waters, B.: How to generate and use universal parameters. IACR Cryptology ePrint Archive 2014:507 (2014)Google Scholar
  22. [NY90]
    Naor, M., Yung, M.: Public-key cryptosystems provably secure against chosen ciphertext attacks. In: Proceedings of the 22nd Annual ACM Symposium on Theory of Computing. Baltimore, Maryland, USA, 13–17 May, pp. 427–437 (1990)Google Scholar
  23. [SW14]
    Sahai, A., Waters, B.: How to use indistinguishability obfuscation: deniable encryption, and more. In: Symposium on Theory of Computing, STOC 2014, New York, NY, USA, 31 May-03 June, pp. 475–484 (2014)Google Scholar
  24. [Wat15]
    Waters, B.: A punctured programming approach to adaptively secure functional encryption. In: Gennaro, R., Robshaw, M. (eds.) CRYPTO 2015. LNCS, vol. 9216, pp. 678–697. Springer, Heidelberg (2015). doi:10.1007/978-3-662-48000-7_33 CrossRefGoogle Scholar

Copyright information

© International Association for Cryptologic Research 2017

Authors and Affiliations

  • Ran Canetti
    • 1
    • 2
  • Oxana Poburinnaya
    • 1
  • Muthuramakrishnan Venkitasubramaniam
    • 3
  1. 1.Boston UniversityBostonUSA
  2. 2.Tel Aviv University and CPIISTel AvivIsrael
  3. 3.University of RochesterRochesterUSA

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