Fixed Points of Rational Functions Satisfying the Carlitz Property

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Creator: 

Chubb, Kaitlyn Rose

Date: 

2018

Abstract: 

Recent research within the field of cryptography has suggested that S-boxes should be chosen to contain few fixed points, motivating analysis of the fixed points of permutations. This thesis presents a novel means of obtaining fixed points for all functions satisfying a property put forth by L. Carlitz. We introduce an algorithm which cyclically generates fixed points for three such classes of functions, the most renowned of which are Rédei rational functions. Further, we provide an explicit expression for the fixed points of all Rédei functions over Fq.

Subject: 

Mathematics

Language: 

English

Publisher: 

Carleton University

Thesis Degree Name: 

Master of Science: 
M.Sc.

Thesis Degree Level: 

Master's

Thesis Degree Discipline: 

Mathematics

Parent Collection: 

Theses and Dissertations

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