Skip to main content
SpringerLink
Log in

On estimation of the probability of absence of collisions of some random mappings

  • Published:
Cybernetics and Systems Analysis Aims and scope

Abstract

Let X and Y be finite sets and φ: (X,Y) →Y be a mapping. Consider a random mapping i → φ(xi,yi), where xi are arbitrarily chosen from the set X, whereas (yi) is a random sample from Y without replacement. A two-sided bound is derived for the probability of absence of collisions of this mapping. A case of mapping, defined as φ(x, y)=x+ y modulo n, is considered in particular. The results may be used in the selection of identification codes.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. C. Cooper, R. Gilchrist, I. N. Kovalenko, and D. Novakovic, “Estimation of the number of “good” permutations, with applications to cryptography,” Kibern. Sist. Anal., No. 5, 10–16 (1999).

  2. R. Konheim, Cryptography. A Primer, J. Wiley and Sons, Chichester (1991).

    Google Scholar 

  3. J. Denes and A. D. Keedwell, Latin Squares and Their Applications, English Univ. Press, London (1974).

    MATH  Google Scholar 

  4. V. F. Kolchin, Random Mappings [in Russian], Nauka, Moscow (1984).

    Google Scholar 

  5. A. A. Levitskaya, “A combinatorial problem in a class of permutations above a ringZn of odd modulon residues,” Probl. Upravl. Informat., No. 5, 99–108 (1996).

Download references

Author information

Authors and Affiliations

  1. Research Center STORM, North London University, Great Britain

    R. Gilchrist

  2. Cybernetics Institute, National Academy of Sciences of Ukraine, Kiev, Ukraine

    I. N. Kovalenko

Authors
  1. R. Gilchrist
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. I. N. Kovalenko
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Kibernetika i Sistemnyi Analiz, No. 1, pp. 132–137, January–February, 2000.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gilchrist, R., Kovalenko, I.N. On estimation of the probability of absence of collisions of some random mappings. Cybern Syst Anal 36, 102–107 (2000). https://doi.org/10.1007/BF02733305

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02733305

Keywords

Search

Navigation