Random Mappings with Restricted Preimages

  • Andrew MacFie
  • Daniel Panario
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7533)


In this paper we refer to finite endofunctions where each image has at most r preimages as r-mappings. Probabilistic analysis of these mappings provides heuristics for problems arising in cryptography which involve similar but more complicated classes of mappings. We give asymptotic probabilities and expectations related to the joint distribution of some pairs of mapping parameters for these mappings, extending work done previously for general, unrestricted mappings. We give an elementary derivation of the expected value of the maximum of tail length and cycle length of a random node in a random r-mapping, which is a useful component in the heuristic analysis of Pollard’s rho algorithm. All distributions considered are uniform.


Random mappings preimages asymptotic probabilities 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Andrew MacFie
    • 1
  • Daniel Panario
    • 1
  1. 1.School of Mathematics and StatisticsCarleton UniversityOttawaCanada

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