Efficient Secure Multiparty Computation with Identifiable Abort

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9985)

Abstract

We study secure multiparty computation (MPC) in the dishonest majority setting providing security with identifiable abort, where if the protocol aborts, the honest parties can agree upon the identity of a corrupt party. All known constructions that achieve this notion require expensive zero-knowledge techniques to obtain active security, so are not practical.

In this work, we present the first efficient MPC protocol with identifiable abort. Our protocol has an information-theoretic online phase with message complexity \(O(n^2)\) for each secure multiplication (where n is the number of parties), similar to the BDOZ protocol (Bendlin et al., Eurocrypt 2011), which is a factor in the security parameter lower than the identifiable abort protocol of Ishai et al. (Crypto 2014). A key component of our protocol is a linearly homomorphic information-theoretic signature scheme, for which we provide the first definitions and construction based on a previous non-homomorphic scheme. We then show how to implement the preprocessing for our protocol using somewhat homomorphic encryption, similarly to the SPDZ protocol (Damgård et al., Crypto 2012).

Keywords

Secure multiparty computation Identifiable abort 

References

  1. [AJL+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. [AL10]
    Aumann, Y., Lindell, Y.: Security against covert adversaries: efficient protocols for realistic adversaries. J. Cryptology 23(2), 281–343 (2010)MathSciNetCrossRefMATHGoogle Scholar
  3. [BDOZ11]
    Bendlin, R., Damgård, I., Orlandi, C., Zakarias, S.: Semi-homomorphic encryption and multiparty computation. In: Paterson, K.G. (ed.) EUROCRYPT 2011. LNCS, vol. 6632, pp. 169–188. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  4. [BDTZ16]
    Baum, C., Damgård, I., Toft, T., Zakarias, R.: Better preprocessing for secure multiparty computation. In: Manulis, M., Sadeghi, A.-R., Schneider, S. (eds.) ACNS 2016. LNCS, vol. 9696, pp. 327–345. Springer, Heidelberg (2016). doi:10.1007/978-3-319-39555-5_18 CrossRefGoogle Scholar
  5. [Bea91]
    Beaver, D.: Efficient multiparty protocols using circuit randomization. In: Feigenbaum, J. (ed.) CRYPTO 1991. LNCS, vol. 576, pp. 420–432. Springer, Heidelberg (1992)Google Scholar
  6. [BFKW09]
    Boneh, D., Freeman, D.M., Katz, J., Waters, B.: Signature schemes for network coding: signing a linear subspace. In: Public Key Cryptography - PKC, pp. 68–87 (2009)Google Scholar
  7. [BGV12]
    Brakerski, Z., Gentry, C., Vaikuntanathan, V.: (leveled) fully homomorphic encryption without bootstrapping. In: ITCS 2012, pp. 309–325 (2012)Google Scholar
  8. [BLOO11]
    Beimel, A., Lindell, Y., Omri, E., Orlov, I.: 1/p-secure multiparty computation without honest majority and the best of both worlds. In: Rogaway, P. (ed.) CRYPTO 2011. LNCS, vol. 6841, pp. 277–296. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  9. [Can01]
    Canetti, R.: Universally composable security: a new paradigm for cryptographic protocols. In: FOCS, pp. 136–145 (2001)Google Scholar
  10. [CDD+99]
    Cramer, R., Damgård, I.B., Dziembowski, S., Hirt, M., Rabin, T.: Efficient multiparty computations secure against an adaptive adversary. In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol. 1592, pp. 311–326. Springer, Heidelberg (1999)Google Scholar
  11. [CJL09]
    Charles, D.X., Jain, K., Lauter, K.E.: Signatures for network coding. IJICoT 1(1), 3–14 (2009)MathSciNetCrossRefMATHGoogle Scholar
  12. [CL14]
    Cohen, R., Lindell, Y.: Fairness versus guaranteed output delivery in secure multiparty computation. In: Sarkar, P., Iwata, T. (eds.) ASIACRYPT 2014, Part II. LNCS, vol. 8874, pp. 466–485. Springer, Heidelberg (2014)Google Scholar
  13. [Cle86]
    Cleve, R.: Limits on the security of coin flips when half the processors are faulty (extended abstract). In: STOC 1986, pp. 364–369 (1986)Google Scholar
  14. [CR91]
    Chaum, David, Roijakkers, Sandra: Unconditionally-Secure Digital Signatures. In: Menezes, Alfred, J., Vanstone, Scott, A. (eds.) CRYPTO 1990. LNCS, vol. 537, pp. 206–214. Springer, Heidelberg (1991). doi:10.1007/3-540-38424-3_15 CrossRefGoogle Scholar
  15. [DKL+12]
    Damgård, I., Keller, M., Larraia, E., Miles, C., Smart, N.P.: Implementing AES via an actively/covertly secure dishonest-majority MPC protocol. In: SCN, pp. 241–263 (2012)Google Scholar
  16. [DKL+13]
    Damgård, I., Keller, M., Larraia, E., Pastro, V., Scholl, P., Smart, N.P.: Practical covertly secure MPC for dishonest majority – or: breaking the SPDZ limits. In: Crampton, J., Jajodia, S., Mayes, K. (eds.) ESORICS 2013. LNCS, vol. 8134, pp. 1–18. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  17. [DPSZ12]
    Damgård, I., Pastro, V., Smart, N., Zakarias, S.: Multiparty computation from somewhat homomorphic encryption. In: Safavi-Naini, R., Canetti, R. (eds.) CRYPTO 2012. LNCS, vol. 7417, pp. 643–662. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  18. [DS83]
    Dolev, D., Strong, H.R.: Authenticated algorithms for byzantine agreement. SIAM J. Comput. 12(4), 656–666 (1983)MathSciNetCrossRefMATHGoogle Scholar
  19. [DZ13]
    Damgård, I., Zakarias, S.: Constant-overhead secure computation of boolean circuits using preprocessing. In: Sahai, A. (ed.) TCC 2013. LNCS, vol. 7785, pp. 621–641. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  20. [GKKO07]
    Garay, J.A., Katz, J., Koo, C.-Y., Ostrovsky, R.: Round complexity of authenticated broadcast with a dishonest majority. In: FOCS 2007, pp. 658–668 (2007)Google Scholar
  21. [GL05]
    Goldwasser, S., Lindell, Y.: Secure multi-party computation without agreement. J. Cryptology 18(3), 247–287 (2005)MathSciNetCrossRefMATHGoogle Scholar
  22. [GMO16]
    Giacomelli, I., Madsen, J., Orlandi, C.: ZKBoo: faster zero-knowledge for boolean circuits. In: 25th USENIX Security Symposium (USENIX Security 2016), pp. 1069–1083 (2016)Google Scholar
  23. [GMW87]
    Goldreich, O., Micali, S., Wigderson, A.: How to play any mental game or a completeness theorem for protocols with honest majority. In: STOC 1987, pp. 218–229 (1987)Google Scholar
  24. [Gol01]
    Goldreich, O.: The Foundations of Cryptography - Basic Techniques, vol. 1. Cambridge University Press, Cambridge (2001)CrossRefMATHGoogle Scholar
  25. [GVW15]
    Gorbunov, S., Vaikuntanathan, V., Wichs, D.: Leveled fully homomorphic signatures from standard lattices. In: STOC 2015, pp. 469–477 (2015)Google Scholar
  26. [HR14]
    Hirt, M., Raykov, P.: Multi-valued byzantine broadcast: The t<n case. In: Sarkar, P., Iwata, T. (eds.) ASIACRYPT 2014. LNCS, vol. 8874, pp. 448–465. Springer, Heidelberg (2014). doi:10.1007/978-3-662-45608-8_24 Google Scholar
  27. [HSZI00]
    Hanaoka, G., Shikata, J., Zheng, Y., Imai, H.: Unconditionally secure digital signature schemes admitting transferability. In: Okamoto, T. (ed.) ASIACRYPT 2000. LNCS, vol. 1976, pp. 130–142. Springer, Heidelberg (2000). doi:10.1007/3-540-44448-3_11 CrossRefGoogle Scholar
  28. [IKOS07]
    Ishai, Y., Kushilevitz, E., Ostrovsky, R., Sahai, A.: Zero-knowledge from secure multiparty computation. In: STOC 2007, pp. 21–30 (2007)Google Scholar
  29. [IOS12]
    Ishai, Y., Ostrovsky, R., Seyalioglu, H.: Identifying cheaters without an honest majority. In: Cramer, R. (ed.) TCC 2012. LNCS, vol. 7194, pp. 21–38. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  30. [IOZ14]
    Ishai, Y., Ostrovsky, R., Zikas, V.: Secure multi-party computation with identifiable abort. In: Garay, J.A., Gennaro, R. (eds.) CRYPTO 2014, Part II. LNCS, vol. 8617, pp. 369–386. Springer, Heidelberg (2014)CrossRefGoogle Scholar
  31. [LZ13]
    Lindell, Y., Zarosim, H.: On the feasibility of extending oblivious transfer. In: Sahai, A. (ed.) TCC 2013. LNCS, vol. 7785, pp. 519–538. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  32. [PW92]
    Pfitzmann, B., Waidner, M.: Unconditional byzantine agreement for any number of faulty processors. In: STACS 1992, pp. 339–350 (1992)Google Scholar
  33. [Sey12]
    Seyalioglu, H.A.-J.: Reducing trust when trust is essential. Ph.D. thesis, University of California, Los Angeles 2012. https://escholarship.org/uc/item/7301296m
  34. [SS11]
    Swanson, C.M., Stinson, D.R.: Unconditionally secure signature schemes revisited. In: Fehr, S. (ed.) ICITS 2011. LNCS, vol. 6673, pp. 100–116. Springer, Heidelberg (2011)CrossRefGoogle Scholar

Copyright information

© International Association for Cryptologic Research 2016

Authors and Affiliations

  1. 1.Department of Computer ScienceAarhus UniversityAarhusDenmark
  2. 2.Department of Computer ScienceUniversity of BristolBristolUK

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