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Refining the asymptotic approximation of the group size in the birthday paradox

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Abstract

Two theorems on the asymptotic behavior of the group size in the birthday paradox are proved. Theorem 1 gives asymptotically unimprovable estimates for the group size if particles are arranged in cells uniformly and independently. Theorem 2 gives asymptotically unimprovable estimates for the group size if two equal sets of particles are arranged in cells uniformly and independently. The results may be applied in cryptography to estimate the complexity of finding collisions of hash functions.

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Authors and Affiliations

  1. National Technical University “Kyiv Polytechnic Institute”, Kyiv, Ukraine

    P. A. Endovitskii

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  1. P. A. Endovitskii
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Correspondence to P. A. Endovitskii.

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Translated from Kibernetika i Sistemnyi Analiz, No. 3, pp. 185–188, May–June 2010.

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Endovitskii, P.A. Refining the asymptotic approximation of the group size in the birthday paradox. Cybern Syst Anal 46, 516–520 (2010). https://doi.org/10.1007/s10559-010-9228-8

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  • DOI: https://doi.org/10.1007/s10559-010-9228-8

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