Physical Sciences and Mathematics Commons^™

A Limit Theorem In Cryptography., Kevin Lynch

Electronic Theses and Dissertations

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 …}