Math in Network Security: A Crash Course
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Math in Network Security: A Crash Course
Changyu
Dong
<cd04 at doc.ic.ac.uk>
Table of Contents
1. Math and Security
2. Unique-Prime-Factorisation Theorem
3. Modular Arithmetic
4. Finite Fields
Groups, Modular Arithmetic and Finite Fields
Galois' Theorem and Polynomial Arithmetic
GF
(
p
^{m}
)
GF
(
2
^{m}
)
5. Elementary Number Theory
Fermat's little theorem
Euler's Totient Function and Euler's Theorem
6. Discrete Logarithms
Cyclic Groups and Generators
Discrete Logarithm Problem
List of Tables
3.1.
Multiplication modulo 6
3.2.
Multiplication modulo 5
4.1.
Addition modulo
x
^{2}
+1
4.2.
Multiplication modulo
x
^{2}
+1