Boolean functions are the main building blocks of most cipher systems.
Various aspects of their cryptological characteristics are examined and investigated
by many researchers from different fields. This thesis has no claim to
obtain original results but consists in an attempt at giving a unified survey of
the main results of the subject. In this thesis, the theory of boolean functions
is presented in details, emphasizing some important cryptological properties
such as balance, nonlinearity, strict avalanche criterion and propagation criterion.
After presenting many results about these criteria with detailed proofs,
two upper bounds and two lower bounds on the nonlinearity of a boolean
function due to Zhang and Zheng are proved. Because of their importance in
the theory of boolean functions, construction of Sylvester-Hadamard matrices
are shown and most of their properties used in cryptography are proved. The
Walsh transform is investigated in detail by proving many properties. By using
a property of Sylvester-Hadamard matrices, the fast Walsh transform is
presented and its application in finding the nonlinearity of a boolean function
is demonstrated. One of the most important classes of boolean functions, so
called bent functions, are presented with many properties and by giving several
examples, from the paper of Rothaus. By using bent functions, relations
between balance, nonlinearity and propagation criterion are presented and it
is shown that not all these criteria can be simultaneously satisfied completely.
For this reason, several constructions of functions optimizing these criteria
which are due to Seberry, Zhang and Zheng are presented.
| Identifer | oai:union.ndltd.org:METU/oai:etd.lib.metu.edu.tr:http://etd.lib.metu.edu.tr/upload/1082403/index.pdf |
| Date | 01 January 2003 |
| Creators | Sagdicoglu, Serhat |
| Contributors | Doganaksoy, Ali |
| Publisher | METU |
| Source Sets | Middle East Technical Univ. |
| Language | English |
| Detected Language | English |
| Type | M.S. Thesis |
| Format | text/pdf |
| Rights | To liberate the content for public access |
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