Discrete Mathematics With Cryptographic Applications

This book covers discrete mathematics both as it has been established after its emergence since the middle of the last century and as its elementary applications to cryptography. It can be used by any individual studying discrete mathematics, finite mathematics, and similar subjects. Any necessary prerequisites are explained and illustrated in the book. As a background of cryptography, the textbook gives an introduction into number theory, coding theory, information theory, that obviously have discrete nature. Designed in a “self-teaching” format, the book includes about 600 problems (with and without solutions) and numerous, practical examples of cryptography.


FEATURES: 

Designed in a “self-teaching” format, the book includes about 600 problems (with and without solutions) and numerous examples of cryptography 

Provides an introduction into number theory, game theory, coding theory, and information theory as background for the coverage of cryptography

Covers cryptography topics such as CRT, affine ciphers, hashing functions, substitution ciphers, unbreakable ciphers, Discrete Logarithm Problem (DLP), and more.



1: Elementary Functions

2: Propositional Algebra

3: Naïve and Formal (Axiomatic) Set Theory

4: Mappings; Groups, Rings, and Fields; Matrices and Determinants

5: Predicates and Quantifiers

6: Binary Relations and Relational Databases

7: Combinatorics

8. Number Theory

9: Boolean Functions

10: Hashing Functions and Cryptographic Maps

11: Generating Polynomials and Inversion Formulas

12: Systems of Representatives

13: Boolean Algebras

14: Combinatorial Circuits

15: Complete Systems of Boolean Functions

16: Graph Theory

17: Trees and Digraphs

18: Computations and Algorithms

19: Finite Automata

20: Game Theory

21: Information Theory and Coding

22: Probability Theory with a Finite Sample Space

23: Turing Machines, P, NP Classes and Other Models

24: Answers and Solutions to Selected Exercises

Index