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Efficient Branching Programs for Quantum Hash Functions Generated by Small-Biased Sets

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Abstract

In the paper we consider quantum (δ, ϵ)-hash functions in so called phase form (phase quantum (δ, ϵ)-hash function). It is known that ϵ-biased sets generate phase quantum (δ, ϵ)- hash function. We show that the construction is invertible, that is, phase quantum (δ, ϵ)-hash function defines ϵ-biased sets. Next, we present an efficient (in the sense of time and qubits needed) Branching program construction for phase quantum (δ, ϵ)-hash function.

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Authors and Affiliations

  1. Institute of Computational Mathematics and Information Technologies, Kazan (Volga region) Federal University, ul. Kremlevskaya 18, Kazan, Tatarstan, 420008, Russia

    M. F. Ablayev

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  1. M. F. Ablayev
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Correspondence to M. F. Ablayev.

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Submitted by A. M. Elizarov

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Ablayev, M.F. Efficient Branching Programs for Quantum Hash Functions Generated by Small-Biased Sets. Lobachevskii J Math 39, 961–966 (2018). https://doi.org/10.1134/S199508021807003X

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  • DOI: https://doi.org/10.1134/S199508021807003X

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