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A Self-Teaching Introduction

Discrete Mathematics With Cryptographic Applications

Frontmatter

Contents

Preface

Chapter 1: A Brief Survey of Elementary Functions

Chapter 2: Propositional Algebra

Chapter 3: Naïve and Formal (Axiomatic) Set Theory

Chapter 4: Groups, Rings, and Fields

Chapter 5: Predicates and Quantifiers—Algebraic Theory

Chapter 6: Binary Relations and Relational Databases

Chapter 7: Combinatorics

Chapter 8: Elements of Number Theory

Chapter 9: Boolean Functions

Chapter 10: Hashing Functions and Cryptographic Maps

Chapter 11: Generating Polynomials and Inversion Formulas

Chapter 12: Systems of Representatives

Chapter 13: Boolean Algebras

Chapter 14: Combinatorial Circuits

Chapter 15: Complete Systems of Boolean Functions and Bases

Chapter 16: Introductory Graph Theory, Euler’s Formula, and Unbreakable Ciphers

Chapter 17: Trees and Digraphs

Chapter 18: Computations and Algorithms

Chapter 19: Finite Automata

Chapter 20: Introduction to Game Theory

Chapter 21: Information Theory and Coding

Chapter 22: Probability Theory with a Finite Sample Space and the Birthday Problem

Chapter 23: Turing Machines, P and NP Classes, and Other Models of Computation

Chapter 24: Answers and Solutions to Selected Exercises

Bibliography

Index

Kheyfits, Alexander I.

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.

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...

Format

Discrete Mathematics With Cryptographic Applications

A Self-Teaching Introduction

Alexander I. Kheyfits

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