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Discrete Mathematics with Cryptographic Applications
A Self-Teaching Introduction
- This book covers the discrete mathematics as it has been established after its emergence since the middle of the last century and 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
- Alexander I. Kheyfits, Ph.D. taught undergraduate and graduate-level subjects in mathematics and computer science for over thirty years at various CUNY colleges, including the CUNY Graduate Center and Bronx Community College. He has published several books, over forty journal articles, and has been an invited speaker at numerous conferences.
- 1: Elementary Functions 2: Propositional Algebra 3: Naive 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
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