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)


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.


Encryption Scheme Commitment Scheme Honest Party Random Coin Challenge Ciphertext 
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.



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.


  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).
  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

Personalised recommendations