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Quantum hashing for finite abelian groups

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Abstract

We propose a generalization of the quantum hashing technique based on the notion of small-bias sets. These sets have proved useful in different areas of computer science, and here their properties give an optimal construction for succinct quantum presentation of elements of any finite abelian group, which can be used in various computational and cryptographic scenarios. We consider two special cases of the proposed quantum hashing which turn out to be the known quantum fingerprinting schemas.

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References

  1. F. M. Ablayev and A. V. Vasiliev, “Cryptographic quantum hashing,” Laser Physics Letters 11 (2), 025202 (2014).

    Article  MathSciNet  MATH  Google Scholar 

  2. D. Gottesman and I. Chuang, Quantum Digital Signatures. arXiv: quant-ph/0105032, 2001.

    Google Scholar 

  3. F. Ablayev and A. Vasiliev, “Computing Boolean functions via quantum hashing,” Computing with New Resources, Lecture Notes in Computer Science 8808, 149–160 (2014).

    Article  MathSciNet  MATH  Google Scholar 

  4. A. Vasiliev, “Quantum communications based on quantum hashing,” International Journal of Applied Engineering Research 10 (12), 31415–31426 (2015).

    Google Scholar 

  5. D. R. Stinson, “On the connections between universal hashing, combinatorial designs and error-correcting codes,” Proc. Congressus Numerantium 114, 7–27 (1996).

    MathSciNet  MATH  Google Scholar 

  6. J. Naor and M. Naor, “Small-bias probability spaces: Efficient constructions and applications,” Proceedings of the Twenty-second Annual ACM Symposium on Theory of Computing (ACM, New York, 1990), pp. 213–223.

    Google Scholar 

  7. N. Alon, O. Goldreich, J. Hastad, and R. Peralta, “Simple constructions of almost k-wise independent random variables,” Random Structures & Algorithms 3 (3), 289–304 (1992).

    Article  MathSciNet  MATH  Google Scholar 

  8. A. Ben-Aroya and A. Ta-Shma, “Constructing small-bias sets from algebraic-geometric codes,” 50th Annual IEEE Symposium on Foundations of Computer Science (Atlanta, GA, 2009), pp. 191–197.

    Google Scholar 

  9. H. Buhrman, R. Cleve, J. Watrous, and R. de Wolf, “Quantum fingerprinting,” Phys. Rev. Lett. 87 (16), 167902 (2001).

    Article  Google Scholar 

  10. F. Ablayev and A. Vasiliev, “Algorithms for quantum branching programs based on fingerprinting,” Electronic Proceedings in Theoretical Computer Science 9, 1–11 (2009).

    Article  Google Scholar 

  11. A. S. Holevo, “Some estimates of the information transmitted by quantum communication channel,” Probl. Pered. Inform. 9 (3), 3–11 (1973).

    MathSciNet  MATH  Google Scholar 

  12. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, 2000).

    MATH  Google Scholar 

  13. S. Chen, C. Moore, and A. Russell, “Small-bias sets for nonabelian groups,” Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, Lecture Notes in Computer Science 8096, 436–451 (2013).

    Article  MathSciNet  MATH  Google Scholar 

  14. N. Alon and Y. Roichman, “Random Cayley graphs and expanders,” Random Structures & Algorithms 5 (2), 271–284 (1994).

    Article  MathSciNet  MATH  Google Scholar 

  15. R. de Wolf, Quantum Computing and Communication Complexity, PhD Thesis (Univ. of Amsterdam, Amsterdam, 2001).

    Google Scholar 

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Authors and Affiliations

  1. Institute of Computational Mathematics and Information Technologies, Kazan (Volga Region) Federal University, Kremlevskaya ul. 35, Kazan, 420008, Tatarstan, Russia

    A. Vasiliev

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  1. A. Vasiliev
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Correspondence to A. Vasiliev.

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Submitted by F. M. Ablayev

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Vasiliev, A. Quantum hashing for finite abelian groups. Lobachevskii J Math 37, 753–757 (2016). https://doi.org/10.1134/S1995080216060184

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  • DOI: https://doi.org/10.1134/S1995080216060184

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