Secure Two-Party Quantum Evaluation of Unitaries against Specious Adversaries

  • Frédéric Dupuis
  • Jesper Buus Nielsen
  • Louis Salvail
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6223)

Abstract

We describe how any two-party quantum computation, specified by a unitary which simultaneously acts on the registers of both parties, can be privately implemented against a quantum version of classical semi-honest adversaries that we call specious. Our construction requires two ideal functionalities to garantee privacy: a private SWAP between registers held by the two parties and a classical private AND-box equivalent to oblivious transfer. If the unitary to be evaluated is in the Clifford group then only one call to SWAP is required for privacy. On the other hand, any unitary not in the Clifford requires one call to an AND-box per R-gate in the circuit. Since SWAP is itself in the Clifford group, this functionality is universal for the private evaluation of any unitary in that group. SWAP can be built from a classical bit commitment scheme or an AND-box but an AND-box cannot be constructed from SWAP. It follows that unitaries in the Clifford group are to some extent the easy ones. We also show that SWAP cannot be implemented privately in the bare model.

References

  1. 1.
    Aharonov, D., Ben-Or, M.: Fault-tolerant quantum computation with constant error. In: 29th Annual ACM Symposium on Theory of Computing (STOC), pp. 176–188 (1997)Google Scholar
  2. 2.
    Ambainis, A., Mosca, M., Tapp, A., de Wolf, R.: Private quantum channels. In: 41st Annual IEEE Symposium on Foundations of Computer Science (FOCS), pp. 547–553 (2000)Google Scholar
  3. 3.
    Ben-Or, M., Crépeau, C., Gottesman, D., Hassidim, A., Smith, A.: Secure multiparty quantum computation with (only) a strict honest majority. In: 47th Annual IEEE Symposium on Foundations of Computer Science (FOCS), pp. 249–260 (2006)Google Scholar
  4. 4.
    Broadbent, A., Fitzsimons, J., Kashefi, E.: Universal blind quantum computation (December 2009), http://arxiv.org/abs/0807.4154
  5. 5.
    Crépeau, C., Gottesman, D., Smith, A.: Secure multi-party quantum computation. In: 34th Annual ACM Symposium on Theory of Computing (STOC), pp. 643–652 (2002)Google Scholar
  6. 6.
    Gottesman, D., Chuang, I.L.: Demonstrating the viability of universal quantum computation using teleportation and single-qubit operations. Nature 402, 390–393 (1999)CrossRefGoogle Scholar
  7. 7.
    Gottesman, D., Chuang, I.L.: Quantum teleportation is a universal computational primitive (August 1999), http://arxiv.org/abs/quant-ph/9908010
  8. 8.
    Gutoski, G., Watrous, J.: Quantum interactive proofs with competing provers. In: Diekert, V., Durand, B. (eds.) STACS 2005. LNCS, vol. 3404, pp. 605–616. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  9. 9.
    Kilian, J.: Founding cryptography on oblivious transfer. In: 20th Annual ACM Symposium on Theory of Computing (STOC), pp. 20–31 (1988)Google Scholar
  10. 10.
    Lo, H.-K.: Insecurity of quantum secure computations. Physical Review A 56(2), 1154–1162 (1997)CrossRefGoogle Scholar
  11. 11.
    Lo, H.-K., Chau, H.F.: Is quantum bit commitment really possible? Physical Review Letters 78, 3410–3413 (1997)CrossRefGoogle Scholar
  12. 12.
    Mayers, D.: Unconditionally secure quantum bit commitment is impossible. Physical Review Letters 78, 3414–3417 (1997)CrossRefGoogle Scholar
  13. 13.
    Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)MATHGoogle Scholar
  14. 14.
    Popescu, S., Rohrlich, D.: Quantum nonlocality as an axiom. Foundations of Physics 24(3), 379–385 (1994)CrossRefMathSciNetGoogle Scholar
  15. 15.
    Popescu, S., Rohrlich, D.: Causality and nonlocality as axioms for quantum mechanics. In: Symposium on Causality and Locality in Modern Physics and Astronomy: Open Questions and Possible Solutions (1997), http://arxiv.org/abs/quant-ph/9709026
  16. 16.
    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
  17. 17.
    Salvail, L., Sotáková, M., Schaffner, C.: On the power of two-party quantum cryptography. In: Matsui, M. (ed.) ASIACRYPT 2009. LNCS, vol. 5912, pp. 70–87. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  18. 18.
    Shor, P.W.: Fault-tolerant quantum computation. In: 37th Annual IEEE Symposium on Foundations of Computer Science (FOCS), pp. 56–65 (1996)Google Scholar
  19. 19.
    Smith, A.: Techniques for secure distributed computing with quantum data. Presented at the Field’s institute Quantum Cryptography and Computing Workshop (October 2006)Google Scholar
  20. 20.
    Watrous, J.: Limits on the power of quantum statistical zero-knowledge. In: 43rd Annual IEEE Symposium on Foundations of Computer Science (FOCS), pp. 459–468 (2002)Google Scholar
  21. 21.
    Wolf, S., Wullschleger, J.: Oblivious transfer and quantum non-locality. In: International Symposium on Information Theory (ISIT 2005), pp. 1745–1748 (2005)Google Scholar
  22. 22.
    Yao, A.: How to generate and exchange secrets. In: 27th Annual IEEE Symposium on Foundations of Computer Science (FOCS) (1986)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Frédéric Dupuis
    • 1
  • Jesper Buus Nielsen
    • 2
  • Louis Salvail
    • 3
  1. 1.Institute for Theoretical PhysicsETH ZurichSwitzerland
  2. 2.DAIMIAarhus UniversityDenmark
  3. 3.Université de Montréal (DIRO)Canada

Personalised recommendations