Quantum Hashing. Group approach


In this paper we consider a generalization of quantum hash functions for arbitrary groups. We show that quantum hash function exists for arbitrary abelian group. We construct a set of “good” automorphisms—a key component of quantum hash funciton. We prove some restrictions on Hilbert space dimension and group used in quantum hash function.

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  1. 1.

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

    Article  Google Scholar 

  2. 2.

    F. Ablayev and A. Vasiliev, Electronic Proceedings in Theoretical Computer Science 9, 1–11 (2009).

    Article  Google Scholar 

  3. 3.

    F. Ablayev and A. Vasiliev, Laser Physics Letters 11 (2), 5202 (2014).

    MathSciNet  Article  Google Scholar 

  4. 4.

    C. McDiarmid, Surveys in Combinatorics 141 (1), 148–188 (1989).

    MathSciNet  Google Scholar 

  5. 5.

    G. C. Shephard, Canadian J. Math. 5 (3), 363–383 (1953).

    MathSciNet  Google Scholar 

  6. 6.

    G. C. Shephard and J. A. Todd, Canadian J. Math. 6 (2), 274–304 (1954).

    MathSciNet  Article  Google Scholar 

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Correspondence to M. Ziiatdinov.

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Submitted by F. M. Ablayev

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Ziiatdinov, M. Quantum Hashing. Group approach. Lobachevskii J Math 37, 222–226 (2016). https://doi.org/10.1134/S1995080216020165

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Keywords and phrases

  • Quantum hash function
  • quantum fingerprinting