Almost perfect nonlinear functions

Creator: 

Arikushi, Karin

Date: 

2008

Abstract: 

Almost perfect nonlinear (APN) functions, or differentially 2-uniform functions, are optimally resistant to differential cryptanalysis. As such, the study of APN functions particularly over fields of characteristic two, has important applications in cryptography. We cover the known results on APN functions over both odd and even characteristic fields. We also explore differentially 1-uniform functions, or perfect nonlinear (PN) functions over odd characteristic fields, and almost bent (AB) functions over even characteristic fields. AB functions are a subset of APN functions that have high nonlinearity, making them resistant to linear cryptanalysis. In addition, we explore equivalence classes of APN functions, and what it means for a class of APN functions to be "new", or inequivalent to previously known classes. Finally, we present some new examples of APN functions over the field F53.

Subject: 

Cryptography.
Data encription (Computer science) -- Standards.
Vector valued functions.
Binomial distribution.

Language: 

English

Publisher: 

Carleton University

Thesis Degree Name: 

Master of Science: 
M.Sc.

Thesis Degree Level: 

Master's

Thesis Degree Discipline: 

Mathematics and Statistics

Parent Collection: 

Theses and Dissertations

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