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Adaptively Secure Two-Party Computation with Erasures

  • Andrew Y. Lindell
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5473)

Abstract

In the setting of multiparty computation a set of parties with private inputs wish to compute some joint function of their inputs, whilst preserving certain security properties (like privacy and correctness). An adaptively secure protocol is one in which the security properties are preserved even if an adversary can adaptively and dynamically corrupt parties during a computation. This provides a high level of security, that is arguably necessary in today’s world of active computer break-ins. Until now, the work on adaptively secure multiparty computation has focused almost exclusively on the setting of an honest majority, and very few works have considered the honest minority and two-party cases. In addition, significant computational and communication costs are incurred by most protocols that achieve adaptive security.

In this work, we consider the two-party setting and assume that honest parties may erase data. We show that in this model it is possible to securely compute any two-party functionality in the presence of adaptive semi-honest adversaries. Furthermore, our protocol remains secure under concurrent general composition (meaning that it remains secure irrespective of the other protocols running together with it). Our protocol is based on Yao’s garbled-circuit construction and, importantly, is as efficient as the analogous protocol for static corruptions. We argue that the model of adaptive corruptions with erasures has been unjustifiably neglected and that it deserves much more attention.

Keywords

Oblivious Transfer Honest Party Secure Multiparty Computation Malicious Adversary Corrupt Party 
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.

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References

  1. 1.
    Beaver, D.: Foundations of secure interactive computing. In: Feigenbaum, J. (ed.) CRYPTO 1991. LNCS, vol. 576, pp. 377–391. Springer, Heidelberg (1992)Google Scholar
  2. 2.
    Beaver, D.: Plug and play encryption. In: Kaliski Jr., B.S. (ed.) CRYPTO 1997. LNCS, vol. 1294, pp. 75–89. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  3. 3.
    Beaver, D., Haber, S.: Cryptographic protocols provably secure against dynamic adversaries. In: Rueppel, R.A. (ed.) EUROCRYPT 1992. LNCS, vol. 658, pp. 307–323. Springer, Heidelberg (1993)CrossRefGoogle Scholar
  4. 4.
    Ben-Or, M., Goldwasser, S., Wigderson, A.: Completeness Theorems for Non-Cryptographic Fault-Tolerant Distributed Computation. In: 20th STOC, pp. 1–10 (1988)Google Scholar
  5. 5.
    Canetti, R.: Security and Composition of Multiparty Cryptographic Protocols. Journal of Cryptology 13(1), 143–202 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Canetti, R.: Universally Composable Security: A New Paradigm for Cryptographic Protocols. In: 42nd FOCS, pp. 136–145 (2001), http://eprint.iacr.org/2000/067
  7. 7.
    Canetti, R., Damgård, I., Dziembowski, S., Ishai, Y., Malkin, T.: Adaptive versus Non-Adaptive Security of Multi-Party Protocols. Journal of Cryptology 17(3), 153–207 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Canetti, R., Feige, U., Goldreich, O., Naor, M.: Adaptively Secure Multi-Party Computation. In: 28th STOC, pp. 639–648 (1996)Google Scholar
  9. 9.
    Canetti, R., Gennaro, R., Jarecki, S., Krawczyk, H., Rabin, T.: Adaptive security for threshold cryptosystems. In: Wiener, M. (ed.) CRYPTO 1999. LNCS, vol. 1666, pp. 98–115. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  10. 10.
    Canetti, R., Lindell, Y., Ostrovsky, R., Sahai, A.: Universally Composable Two-Party and Multi-Party Computation. In: 34th STOC, pp. 494–503 (2002), http://eprint.iacr.org/2002/140
  11. 11.
    Chaum, D., Crépeau, C., Damgå, I.: rd. Multi-party Unconditionally Secure Protocols. In: 20th STOC, pp. 11–19 (1988)Google Scholar
  12. 12.
    Even, S., Goldreich, O., Lempel, A.: A Randomized Protocol for Signing Contracts. Communications of the ACM 28(6), 637–647 (1985)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Frankel, Y., MacKenzie, P.D., Yung, M.: Adaptively-secure optimal-resilience proactive RSA. In: Lam, K.-Y., Okamoto, E., Xing, C. (eds.) ASIACRYPT 1999. LNCS, vol. 1716, pp. 180–195. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  14. 14.
    Garay, J.A., MacKenzie, P.D., Yang, K.: Efficient and Universally Composable Committed Oblivious Transfer and Applications. In: Naor, M. (ed.) TCC 2004. LNCS, vol. 2951, pp. 297–316. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  15. 15.
    Goldreich, O.: Foundations of Cryptography. Basic Applications, vol. 2. Cambridge University Press, Cambridge (2004)CrossRefzbMATHGoogle Scholar
  16. 16.
    Goldreich, O., Micali, S., Wigderson, A.: How to Play any Mental Game – A Completeness Theorem for Protocols with Honest Majority. In: 19th STOC, pp. 218–229 (1987); for details see [15]Google Scholar
  17. 17.
    Goldwasser, S., Levin, L.A.: Fair computation of general functions in presence of immoral majority. In: Menezes, A., Vanstone, S.A. (eds.) CRYPTO 1990. LNCS, vol. 537, pp. 77–93. Springer, Heidelberg (1991)Google Scholar
  18. 18.
    Kushilevitz, E., Lindell, Y., Rabin, T.: Information-Theoretically Secure Protocols and Security Under Composition. In: The em 38th STOC, pp. 109–118 (2006)Google Scholar
  19. 19.
    Jarecki, S., Lysyanskaya, A.: Adaptively secure threshold cryptography: Introducing concurrency, removing erasures (Extended abstract). In: Preneel, B. (ed.) EUROCRYPT 2000. LNCS, vol. 1807, pp. 221–242. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  20. 20.
    Lindell, Y.: General Composition and Universal Composability in Secure Multi-Party Computation. In: 44th FOCS, pp. 394–403 (2003)Google Scholar
  21. 21.
    Lindell, Y.: Adaptively Secure Two-Party Computation with Erasures (full version of this paper). Cryptology ePrint Archive (2009)Google Scholar
  22. 22.
    Lindell, Y., Pinkas, B.: A Proof of Security of Yao’s Protocol for Two-Party Computation. the Journal of Cryptology (to appear)Google Scholar
  23. 23.
    Lindell, Y., Pinkas, B.: An efficient protocol for secure two-party computation in the presence of malicious adversaries. In: Naor, M. (ed.) EUROCRYPT 2007. LNCS, vol. 4515, pp. 52–78. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  24. 24.
    Lindell, Y., Zarosim, H.: Adaptive Zero-Knowledge Proofs and Adaptively Secure Oblivious Transfer. In: Reingold, O. (ed.) TCC 2009. LNCS, vol. 5444, pp. 183–201. Springer, Heidelberg (2009)Google Scholar
  25. 25.
    Micali, S., Rogaway, P.: Secure computation. In: Feigenbaum, J. (ed.) CRYPTO 1991. LNCS, vol. 576, pp. 392–404. Springer, Heidelberg (1992)Google Scholar
  26. 26.
    Wolf, S., Wullschleger, J.: Oblivious transfer is symmetric. In: Vaudenay, S. (ed.) EUROCRYPT 2006. LNCS, vol. 4004, pp. 222–232. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  27. 27.
    Yao, A.: How to Generate and Exchange Secrets. In: 27th FOCS, pp. 162–167 (1986)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Andrew Y. Lindell
    • 1
  1. 1.Aladdin Knowledge Systems and Bar-Ilan UniversityIsrael

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