Advertisement

Quantum Hashing via ε-Universal Hashing Constructions and Freivalds’ Fingerprinting Schemas

  • Farid Ablayev
  • Marat Ablayev
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8614)

Abstract

We define the concept of a quantum hash generator and offer a design, which allows one to build a large number of different quantum hash functions. The construction is based on composition of a classical ε-universal hash family and a given family of functions – quantum hash generators.

In particular, using the relationship between ε-universal hash families and Freivalds’ fingerprinting schemas we present explicit quantum hash function and prove that this construction is optimal with respect to the number of qubits needed for the construction.

Keywords

quantum hashing quantum hash function ε-universal hashing error-correcting codes 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Ablayev, F., Vasiliev, A.: Algorithms for quantum branching programs based on fingerprinting. In: Proceedings Fifth Workshop on Developments in Computational Models–Computational Models From Nature, DCM 2009, Rhodes, Greece, vol. 9, pp. 1–11 (July 11, 2009)Google Scholar
  2. 2.
    Ablayev, F., Vasiliev, A.: Quantum Hashing, arXiv:1310.4922 (quant-ph) (2013)Google Scholar
  3. 3.
    Ablayev, F., Vasiliev, A.: Cryptographic quantum hashing. Laser Physics Letters 11(2), 025202 (2014)Google Scholar
  4. 4.
    Ablayev, F., Ablayev, M.: Quantum Hashing via Classical ε-universal Hashing Constructions, arXiv:1404.1503 (quant-ph) (2014)Google Scholar
  5. 5.
    Bierbrauer, J., Johansson, T., Kabatianskii, G.A., Smeets, B.J.M.: On Families of Hash Functions via Geometric Codes and Concatenation. In: Stinson, D.R. (ed.) Advances in Cryptology - CRYPTO 1993. LNCS, vol. 773, pp. 331–342. Springer, Heidelberg (1994)Google Scholar
  6. 6.
    Buhrman, H., Cleve, R., Watrous, J., de Wolf, R.: Quantum fingerprinting. Phys. Rev. Lett. 87, 167902 (2001)CrossRefGoogle Scholar
  7. 7.
    Carter, J., Wegman, M.: Universal Classes of Hash Functions. J. Computer and System Sciences 18, 143–154 (1979)CrossRefzbMATHMathSciNetGoogle Scholar
  8. 8.
    Gavinsky, D., Ito, T.: Quantum fingerprints that keep secrets. Quantum Information & Computation 13(7-8), 583–606 (2013)MathSciNetGoogle Scholar
  9. 9.
    Gottesman, D., Chuang, I.: Quantum digital signatures, T echnical report (2001), http://arxiv.org/abs/quant-ph/0105032
  10. 10.
    Freivalds, R.: Probabilistic Machines Can Use Less Running Time. In: Proceedings of the IFIP Congress 1977, Toronto, Canada, vol. 1977, pp. 839–842. North-Holland (1977)Google Scholar
  11. 11.
    Montanaro, A., Osborne, T.: Quantum Boolean functions. Chicago Journal of Theoretical Computer Science 1, arXiv:0810.2435 (2010)Google Scholar
  12. 12.
    Razborov, A., Szemeredi, E., Wigderson, A.: Constructing small sets that are uniform in arithmetic progressions. Combinatorics, Probability & Computing 2, 513–518 (1993)CrossRefzbMATHMathSciNetGoogle Scholar
  13. 13.
    Stinson, D.R.: On the connections between universal ε-hashing, combinatorial designs and error-correcting codes. Congressus Numerantium 114, 7–27 (1996)zbMATHMathSciNetGoogle Scholar
  14. 14.
    Stinson, D.R.: Universal hash families and the leftover hash lemma, and applications to cryptography and computing. Journal of Combinatorial Mathematics and Combinatorial Computing 42, 3–31 (2002)zbMATHMathSciNetGoogle Scholar
  15. 15.
    Stinson, D.R.: Cryptography: Theory and Practice, 3rd edn. Discrete Mathematics and Its Applications. CRC Press (2005)Google Scholar
  16. 16.
    Wigderson, A.: Lectures on the Fusion Method and Derandomization. Technical Report SOCS-95. 2, School of Computer Science, McGill University (file/pub/tech-reports/library/reports/95/TR95.2.ps.gz at the anonymousftpsiteftp.cs.mcgill.caGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Farid Ablayev
    • 1
  • Marat Ablayev
    • 1
  1. 1.Kazan Federal UniversityKazanRussia

Personalised recommendations