Degree Name

MS (Master of Science)

Program

Mathematical Sciences

Date of Award

8-2005

Committee Chair or Co-Chairs

Anant P. Godbole

Committee Members

Debra J. Knisley, James Boland

Abstract

Cryptography is the study of encryptying and decrypting messages and deciphering encrypted messages when the code is unknown. We consider Λπx, Δy) which is a count of how many ways a permutation satisfies a certain property. According to Hawkes and O'Connor, the distribution of Λπx, Δy) tends to a Poisson distribution with parameter ½ as m → ∞ for all Δxy ∈ (Z/qZ)m - 0. We give a proof of this theorem using the Stein-Chen method: As qm approaches infinity, the distribution of Λπx, Δy) is approximately Poisson with parameter ½. Error bounds for this approximation are provided.

Document Type

Thesis - Open Access

Copyright

Copyright by the authors.

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