Everlasting Multi-party Computation

  • Dominique Unruh
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8043)

Abstract

A protocol has everlasting security if it is secure against adversaries that are computationally unlimited after the protocol execution. This models the fact that we cannot predict which cryptographic schemes will be broken, say, several decades after the protocol execution. In classical cryptography, everlasting security is difficult to achieve: even using trusted setup like common reference strings or signature cards, many tasks such as secure communication and oblivious transfer cannot be achieved with everlasting security. An analogous result in the quantum setting excludes protocols based on common reference strings, but not protocols using a signature card. We define a variant of the Universal Composability framework, everlasting quantum-UC, and show that in this model, we can implement secure communication and general multi-party computation using signature cards as trusted setup.

References

  1. 1.
    ECRYPT II: Yearly report on algorithms and keysizes. D.SPA.17 Rev. 1.0, ICT-2007-216676 (June 2011)Google Scholar
  2. 2.
    NIST: Recommendation for key management. Special Publication 800-57 Part 1 Rev. 3 (May 2011)Google Scholar
  3. 3.
    Bundesnetzagentur, B.S.I.: Algorithms for qualified electronic signatures (May 2011)Google Scholar
  4. 4.
    Bennett, C.H., Brassard, G.: Quantum cryptography: Public-key distribution and coin tossing. In: IEEE International Conference on Computers, Systems and Signal Processing 1984, pp. 175–179. IEEE (1984)Google Scholar
  5. 5.
    Crépeau, C., Kilian, J.: Achieving oblivious transfer using weakened security assumptions (extended abstract). In: FOCS 1988, pp. 42–52. IEEE (1988)Google Scholar
  6. 6.
    Kilian, J.: Founding cryptography on oblivious transfer. In: STOC 1988, pp. 20–31. ACM (1988)Google Scholar
  7. 7.
    Mayers, D.: Unconditionally secure quantum bit commitment is impossible. Physical Review Letters 78(17), 3414–3417 (1997)CrossRefGoogle Scholar
  8. 8.
    Lo, H.K.: Insecurity of quantum secure computations. Phys. Rev. A. 56, 1154–1162 (August 1997) Eprint on arXiv:quant-ph/9611031v2Google Scholar
  9. 9.
    Bernstein, D.: Cost-benefit analysis of quantum cryptography. Classical and Quantum Information Assurance Foundations and Practice, Dagstuhl Seminar 09311 (2009), Abstract at http://drops.dagstuhl.de/opus/volltexte/2010/2365, slides at http://cr.yp.to/talks/2009.07.28/slides.pdf
  10. 10.
    Unruh, D.: Universally composable quantum multi-party computation. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 486–505. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  11. 11.
    Alleaume, R., et al.: Secoqc white paper on quantum key distribution and cryptography. arXiv:quant-ph/0701168v1 (2007)Google Scholar
  12. 12.
    Damgård, I., Nielsen, J.B.: Perfect hiding and perfect binding universally composable commitment schemes with constant expansion factor. In: Yung, M. (ed.) CRYPTO 2002. LNCS, vol. 2442, pp. 581–596. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  13. 13.
    Müller-Quade, J., Unruh, D.: Long-term security and universal composability. Journal of Cryptology 23(4), 594–671 (2010)MathSciNetCrossRefMATHGoogle Scholar
  14. 14.
    Canetti, R.: Universally composable security: A new paradigm for cryptographic protocols. In: FOCS 2001, pp. 136–145. IEEE (2001)Google Scholar
  15. 15.
    Canetti, R., Fischlin, M.: Universally composable commitments. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 19–40. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  16. 16.
    Gesetz über Rahmenbedingungen für elektronische Signaturen. Bundesgesetzblatt I 2001, 876 (May 2001), http://bundesrecht.juris.de/sigg_2001/index.html
  17. 17.
    Unruh, D.: Quantum proofs of knowledge. In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT 2012. LNCS, vol. 7237, pp. 135–152. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  18. 18.
    Damgård, I., Fehr, S., Salvail, L., Schaffner, C.: Cryptography in the bounded quantum-storage model. In: FOCS 2005, pp. 449–458 (2005)Google Scholar
  19. 19.
    Unruh, D.: Concurrent composition in the bounded quantum storage model. In: Paterson, K.G. (ed.) EUROCRYPT 2011. LNCS, vol. 6632, pp. 467–486. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  20. 20.
    Maurer, U.: Conditionally-perfect secrecy and a provably-secure randomized cipher. Journal of Cryptology 5(1), 53–66 (1992)MathSciNetCrossRefMATHGoogle Scholar
  21. 21.
    Harnik, D., Naor, M.: On everlasting security in the hybrid bounded storage model. In: Bugliesi, M., Preneel, B., Sassone, V., Wegener, I. (eds.) ICALP 2006. LNCS, vol. 4052, pp. 192–203. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  22. 22.
    Crépeau, C., Dumais, P., Mayers, D., Salvail, L.: Computational collapse of quantum state with application to oblivious transfer. In: Naor, M. (ed.) TCC 2004. LNCS, vol. 2951, pp. 374–393. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  23. 23.
    Unruh, D.: Everlasting multi-party computation. IACR ePrint 2012/177, Full version of this paper (2013)Google Scholar
  24. 24.
    Renner, R., König, R.: Universally composable privacy amplification against quantum adversaries. In: Kilian, J. (ed.) TCC 2005. LNCS, vol. 3378, pp. 407–425. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  25. 25.
    Ben-Or, M., Horodecki, M., Leung, D.W., Mayers, D., Oppenheim, J.: The universal composable security of quantum key distribution. In: Kilian, J. (ed.) TCC 2005. LNCS, vol. 3378, pp. 386–406. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  26. 26.
    Raub, D., Steinwandt, R., Müller-Quade, J.: On the security and composability of the one time pad. In: Vojtáš, P., Bieliková, M., Charron-Bost, B., Sýkora, O. (eds.) SOFSEM 2005. LNCS, vol. 3381, pp. 288–297. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  27. 27.
    Damgård, I., Fehr, S., Lunemann, C., Salvail, L., Schaffner, C.: Improving the security of quantum protocols via commit-and-open. In: Halevi, S. (ed.) CRYPTO 2009. LNCS, vol. 5677, pp. 408–427. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  28. 28.
    Regev, O.: On lattices, learning with errors, random linear codes, and cryptography. J. ACM 56(6) (2009)Google Scholar
  29. 29.
    Goldreich, O.: Foundations of Cryptography – (Basic Tools), vol. 1. Cambridge University Press (August 2001)Google Scholar
  30. 30.
    Watrous, J.: Zero-knowledge against quantum attacks. SIAM J. Comput. 39(1), 25–58 (2009)MathSciNetCrossRefMATHGoogle Scholar
  31. 31.
    Ishai, Y., Prabhakaran, M., Sahai, A.: Founding cryptography on oblivious transfer – efficiently. In: Wagner, D. (ed.) CRYPTO 2008. LNCS, vol. 5157, pp. 572–591. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  32. 32.
    Wullschleger, J.: Oblivious-Transfer Amplification. PhD thesis, ETH Zurich, arXiv:cs/0608076v3 [cs.CR] (March 2007)Google Scholar

Copyright information

© International Association for Cryptologic Research 2013

Authors and Affiliations

  • Dominique Unruh
    • 1
  1. 1.University of TartuEstonia

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