Quantum One-Time Programs

(Extended Abstract)
  • Anne Broadbent
  • Gus Gutoski
  • Douglas Stebila
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8043)

Abstract

A one-time program is a hypothetical device by which a user may evaluate a circuit on exactly one input of his choice, before the device self-destructs. One-time programs cannot be achieved by software alone, as any software can be copied and re-run. However, it is known that every circuit can be compiled into a one-time program using a very basic hypothetical hardware device called a one-time memory. At first glance it may seem that quantum information, which cannot be copied, might also allow for one-time programs. But it is not hard to see that this intuition is false: one-time programs for classical or quantum circuits based solely on quantum information do not exist, even with computational assumptions.

This observation raises the question, “what assumptions are required to achieve one-time programs for quantum circuits?” Our main result is that any quantum circuit can be compiled into a one-time program assuming only the same basic one-time memory devices used for classical circuits. Moreover, these quantum one-time programs achieve statistical universal composability (UC-security) against any malicious user. Our construction employs methods for computation on authenticated quantum data, and we present a new quantum authentication scheme called the trap scheme for this purpose. As a corollary, we establish UC-security of a recent protocol for delegated quantum computation.

Keywords

Quantum Channel Authentication Scheme Quantum Circuit Full Version Ideal Functionality 
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.

References

  1. 1.
    Goldwasser, S., Kalai, Y., Rothblum, G.: One-time programs. In: Wagner, D. (ed.) CRYPTO 2008. LNCS, vol. 5157, pp. 39–56. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  2. 2.
    Bellare, M., Hoang, V.T., Rogaway, P.: Adaptively secure garbling with applications to one-time programs and secure outsourcing. In: Wang, X., Sako, K. (eds.) ASIACRYPT 2012. LNCS, vol. 7658, pp. 134–153. Springer, Heidelberg (2012), Full version available at http://eprint.iacr.org/2012/564CrossRefGoogle Scholar
  3. 3.
    Goyal, V., Ishai, Y., Sahai, A., Venkatesan, R., Wadia, A.: Founding cryptography on tamper-proof hardware tokens. In: Micciancio, D. (ed.) TCC 2010. LNCS, vol. 5978, pp. 308–326. Springer, Heidelberg (2010), Full version available at http://eprint.iacr.org/2010/153CrossRefGoogle Scholar
  4. 4.
    Aaronson, S.: Quantum copy-protection and quantum money. In: Proc. 24th IEEE Conference on Computational Complexity, CCC 2009, pp. 229–242 (2009)Google Scholar
  5. 5.
    Mosca, M., Stebila, D.: Quantum coins. In: Error-Correcting Codes, Finite Geometries and Cryptography. Contemporary Mathematics, vol. 523, pp. 35–47. American Mathematical Society (2010)Google Scholar
  6. 6.
    Barak, B., Goldreich, O., Impagliazzo, R., Rudich, S., Sahai, A., Vadhan, S., Yang, K.: On the (im)possibility of obfuscating programs. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 1–18. Springer, Heidelberg (2001), Full version available at http://www.wisdom.weizmann.ac.il/~oded/p_obfuscate.htmlCrossRefGoogle Scholar
  7. 7.
    Aharonov, D., Ben-Or, M., Eban, E.: Interactive proofs for quantum computations. In: Proc. Innovations in Computer Science (ICS) 2010, pp. 453–469 (2010)Google Scholar
  8. 8.
    Dunjko, V., Fitzsimons, J.F., Portmann, C., Renner, R.: Composable security of delegated quantum computation (2013), arXiv.org/abs/1301.3662 (quant-ph)Google Scholar
  9. 9.
    Aaronson, S., Christiano, P.: Quantum money from hidden subspaces. In: Proc. 44th Symposium on Theory of Computing (STOC) 2012, pp. 41–60 (2012), Full version available as arXiv:1203.4740 (quant-ph)Google Scholar
  10. 10.
    Ben-Or, M., Crépeau, C., Gottesman, D., Hassidim, A., Smith, A.: Secure multiparty quantum computation with (only) a strict honest majority. In: FOCS 2006, pp. 249–260 (2006)Google Scholar
  11. 11.
    Dupuis, F., Nielsen, J.B., Salvail, L.: Actively secure two-party evaluation of any quantum operation. In: Safavi-Naini, R., Canetti, R. (eds.) CRYPTO 2012. LNCS, vol. 7417, pp. 794–811. Springer, Heidelberg (2012)Google Scholar
  12. 12.
    Broadbent, A., Gutoski, G., Stebila, D.: Quantum one-time programs (2013), (full version) arXiv:1211.1080 (quant-ph)Google Scholar
  13. 13.
    Unruh, D.: Universally composable quantum multi-party computation. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 486–505. Springer, Heidelberg (2010), Full version available as arXiv:0910.2912 (quant-ph)Google Scholar
  14. 14.
    Bera, D., Fenner, S., Green, F., Homer, S.: Efficient universal quantum circuits. Quantum Information and Computation 10(1), 16–28 (2010)MathSciNetMATHGoogle Scholar
  15. 15.
    Nielsen, M.A., Chuang, I.L.: Programmable quantum gate arrays. Physical Review Letters 79, 321–324 (1997)MathSciNetCrossRefMATHGoogle Scholar
  16. 16.
    de Sousa, P.B., Ramos, R.V.: Universal quantum circuit for N-qubit quantum gate: a programmable quantum gate. Quantum Information and Computation 7(3), 228–242 (2007)MathSciNetMATHGoogle Scholar
  17. 17.
    Barnum, H., Crépeau, C., Gottesman, D., Smith, A., Tapp, A.: Authentication of quantum messages. In: FOCS 2002, pp. 449–458 (2002), Full version available as arXiv:quant-ph/0205128Google Scholar
  18. 18.
    Shor, P., Preskill, J.: Simple proof of security of the BB84 quantum key distribution protocol. Physical Review Letters 85, 441–444 (2000)CrossRefGoogle Scholar
  19. 19.
    Broadbent, A., Fitzsimons, J., Kashefi, E.: Universal blind quantum computation. In: FOCS 2009, pp. 517–526. IEEE (2009)Google Scholar
  20. 20.
    Buhrman, H., Christandl, M., Schaffner, C.: Complete insecurity of quantum protocols for classical two-party computation. Physical Review Letters 109, 160501 (2012)CrossRefGoogle Scholar
  21. 21.
    Childs, A.: Secure assisted quantum computation. Quantum Information and Computation 5, 456–466 (2005)MathSciNetMATHGoogle Scholar

Copyright information

© International Association for Cryptologic Research 2013

Authors and Affiliations

  • Anne Broadbent
    • 1
  • Gus Gutoski
    • 2
  • Douglas Stebila
    • 3
  1. 1.Institute for Quantum Computing and, Department of Combinatorics and OptimizationUniversity of WaterlooWaterlooCanada
  2. 2.Institute for Quantum Computing and School of Computer ScienceUniversity of WaterlooWaterlooCanada
  3. 3.School of Electrical Engineering and Computer Science and, School of Mathematical Sciences, Science and Engineering FacultyQueensland University of TechnologyBrisbaneAustralia

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