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Quantum Commitments from Complexity Assumptions

  • André Chailloux
  • Iordanis Kerenidis
  • Bill Rosgen
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6755)

Abstract

We study worst-case complexity assumptions that imply quantum bit-commitment schemes. First we show that QSZK \(\not\subseteq\) QMA implies a computationally hiding and statistically binding auxiliary-input quantum commitment scheme. We then extend our result to show that the much weaker assumption QIP \(\not\subseteq\) QMA (which is weaker than PSPACE \(\not\subseteq\) PP) implies the existence of auxiliary-input commitment schemes with quantum advice. Finally, to strengthen the plausibility of the separation QSZK \(\not\subseteq\) QMA we find a quantum oracle relative to which honest-verifier QSZK is not contained in QCMA.

Keywords

Quantum Circuit Security Parameter Commitment Scheme Auxiliary Input Negligible Function 
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.
    Aaronson, S.: Impossibility of succinct quantum proofs for collision-freeness. arxiv1101.0403 (2011)Google Scholar
  2. 2.
    Aaronson, S., Kuperberg, G.: Quantum versus classical proofs and advice. Theory of Computing 3(7), 129–157 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Ben-Or, M., Goldreich, O., Goldwasser, S., Håstad, J., Kilian, J., Micali, S., Rogaway, P.: Everything provable is provable in zero-knowledge. In: Goldwasser, S. (ed.) CRYPTO 1988. LNCS, vol. 403, pp. 37–56. Springer, Heidelberg (1990)CrossRefGoogle Scholar
  4. 4.
    Crépeau, C., Légaré, F., Salvail, L.: How to convert the flavor of a quantum bit commitment. In: Pfitzmann, B. (ed.) EUROCRYPT 2001. LNCS, vol. 2045, pp. 60–77. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  5. 5.
    Fuchs, C.A., van de Graaf, J.: Cryptographic distinguishability measures for quantum-mechanical states. IEEE Trans. Inf. Theory 45(4), 1216–1227 (1999)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Goldreich, O., Micali, S., Wigderson, A.: Proofs that yield nothing but their validity or all languages in NP have zero-knowledge proof systems. J. ACM 38(3) (1991)Google Scholar
  7. 7.
    Haitner, I., Nguyen, M.H., Ong, S.J., Reingold, O., Vadhan, S.: Statistically hiding commitments and statistical zero-knowledge arguments from any one-way function. SIAM J. Comput. 39(3), 1153–1218 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Håstad, J., Impagliazzo, R., Levin, L.A., Luby, M.: A pseudorandom generator from any one-way function. SIAM J. Comput. 28(4), 1364–1396 (1999)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Helstrom, C.W.: Detection theory and quantum mechanics. Inform. Control 10(3) (1967)Google Scholar
  10. 10.
    Impagliazzo, R., Luby, M.: One-way functions are essential for complexity based cryptography. In: IEEE Symp. Found. Comput. Sci. (FOCS), pp. 230–235 (1989)Google Scholar
  11. 11.
    Jain, R., Ji, Z., Upadhyay, S., Watrous, J.: QIP = PSPACE. In: ACM STOC (2010)Google Scholar
  12. 12.
    Jozsa, R.: Fidelity for mixed quantum states. J. Mod. Opt. 41(12), 2315–2323 (1994)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Kitaev, A.Y., Shen, A.H., Vyalyi, M.N.: Classical and Quantum Computation. Graduate Studies in Mathematics, vol. 47. American Mathematical Society, Providence (2002)zbMATHGoogle Scholar
  14. 14.
    Kitaev, A., Watrous, J.: Parallelization, amplification, and exponential time simulation of quantum interactive proof systems. In: ACM STOC, pp. 608–617 (2000)Google Scholar
  15. 15.
    Lo, H.K., Chau, H.F.: Is quantum bit commitment really possible? Phys. Rev. Lett. 78, 3410 (1997)CrossRefGoogle Scholar
  16. 16.
    Marriott, C., Watrous, J.: Quantum Arthur-Merlin games. Comput. Complex. 14(2) (2005)Google Scholar
  17. 17.
    Mayers, D.: Unconditionally secure quantum bit commitment is impossible. Phys. Rev. Lett. 78, 3414 (1997)CrossRefGoogle Scholar
  18. 18.
    Naor, M.: Bit commitment using pseudorandomness. J. of Cryptology 4(2), 151–158 (1991)CrossRefzbMATHGoogle Scholar
  19. 19.
    Nayak, A., Shor, P.: Bit-commitment-based quantum coin flipping. Phys. Rev. A 67(1), 012304 (2003)CrossRefGoogle Scholar
  20. 20.
    Ostrovsky, R., Wigderson, A.: One-way functions are essential for non-trivial zero-knowledge. In: 2nd Israel Symposium on Theory and Computing Systems, pp. 3–17 (1993)Google Scholar
  21. 21.
    Rosgen, B., Watrous, J.: On the hardness of distinguishing mixed-state quantum computations. In: Conf. Comput. Compl. (CCC), pp. 344–354 (2005)Google Scholar
  22. 22.
    Shor, P.W.: Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM J. Comput. 26(5), 1484–1509 (1997)MathSciNetCrossRefzbMATHGoogle Scholar
  23. 23.
    Spekkens, R.W., Rudolph, T.: Degrees of concealment and bindingness in quantum bit commitment protocols. Phys. Rev. A 65(1), 012310 (2001)CrossRefGoogle Scholar
  24. 24.
    Vadhan, S.: An unconditional study of computational zero knowledge. SIAM J. Comput. 36(4), 1160–1214 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  25. 25.
    Watrous, J.: Succinct quantum proofs for properties of finite groups. In: FOCS 2000 (2000)Google Scholar
  26. 26.
    Watrous, J.: Limits on the power of quantum statistical zero-knowledge. In: FOCS 2002 (2002)Google Scholar
  27. 27.
    Watrous, J.: PSPACE has constant-round quantum interactive proof systems. Theor. Comput. Sci. 292(3), 575–588 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  28. 28.
    Watrous, J.: Zero-knowledge against quantum attacks. SIAM J. Comput. 39(1), 25–58 (2009)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • André Chailloux
    • 1
  • Iordanis Kerenidis
    • 2
    • 3
  • Bill Rosgen
    • 3
  1. 1.Laboratoire de Recherche en InformatiqueUniversité Paris-SudFrance
  2. 2.LIAFAUniversité Paris Diderot and CNRSFrance
  3. 3.Centre for Quantum TechnologiesNational University of SingaporeSingapore

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