A Limit Theorem in Cryptography.

Author

Kevin Lynch, East Tennessee State University

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 Λ_π(Δx, Δy) which is a count of how many ways a permutation satisfies a certain property. According to Hawkes and O'Connor, the distribution of Λ_π(Δx, Δy) tends to a Poisson distribution with parameter ½ as m → ∞ for all Δx,Δy ∈ (Z/qZ)^m - 0. We give a proof of this theorem using the Stein-Chen method: As q^m approaches infinity, the distribution of Λ_π(Δx, Δy) is approximately Poisson with parameter ½. Error bounds for this approximation are provided.

Document Type

Thesis - unrestricted

Recommended Citation

Lynch, Kevin, "A Limit Theorem in Cryptography." (2005). Electronic Theses and Dissertations. Paper 1042. https://dc.etsu.edu/etd/1042

Copyright

Copyright by the authors.