This book offers a comprehensive guide to discrete mathematics and its applications to cryptography. It is designed for students and professionals in fields such as discrete mathematics and finite mathematics, with all necessary prerequisites clearly explained and illustrated. The text introduces key concepts in number theory, coding theory, and information theory, which are essential for understanding cryptography.
Understanding discrete mathematics is crucial for anyone working in cryptography and related fields. The book begins with a survey of elementary functions and moves on to propositional algebra, set theory, and algebraic structures like groups, rings, and fields. It covers binary relations, combinatorics, and elements of number theory, which are fundamental to cryptographic methods.
Readers will explore topics such as Boolean functions, hashing functions, cryptographic maps, combinatorial circuits, and graph theory. The book also delves into advanced areas like finite automata, game theory, and Turing machines. Through numerous examples, problems, and solutions, readers will gain a solid foundation in discrete mathematics and its cryptographic applications.

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Spis treści

Discrete Mathematics With Cryptographic Applications. A Self-Teaching Guide to Unlocking the Power of Advanced Concepts and Computational Techniques eBook -- spis treści

• 1. A Brief Survey of Elementary Functions
• 2. Propositional Algebra
• 3. Naïve and Formal (Axiomatic) Set Theory
• 4. Groups, Rings, and Fields
• 5. Predicates and Quantifiers—Algebraic Theory
• 6. Binary Relations and Relational Databases
• 7. Combinatorics
• 8. Elements of 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 and Bases
• 16. Introductory Graph Theory, Euler's Formula, and Unbreakable Ciphers
• 17. Trees and Digraphs
• 18. Computations and Algorithms
• 19. Finite Automata
• 20. Introduction to Game Theory
• 21. Information Theory and Coding
• 22. Probability Theory with a Finite Sample Space and the Birthday Problem
• 23. Turing Machines, P and NP Classes, and Other Models of Computation
• 24. Answers and Solutions to Selected Exercises