Discrete Mathematics with Cryptographic Applications
- 6h 21m
- Alexander I. Kheyfits PhD
- Mercury Learning
- 2021
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.
FEATURES:
- Designed in a “self-teaching” format, the book includes about 600 problems (with and without solutions) and numerous examples of cryptography
- Covers cryptography topics such as CRT, affine ciphers, hashing functions, substitution ciphers, unbreakable ciphers, Discrete Logarithm Problem (DLP), and more.
In this Book
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A Brief Survey of Elementary Functions
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Propositional Algebra
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Naïve and Formal (Axiomatic) Set Theory
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Groups, Rings, and Fields
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Predicates and Quantifiers—Algebraic Theory
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Binary Relations and Relational Databases
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Combinatorics
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Elements of Number Theory
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Boolean Functions
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Hashing Functions and Cryptographic Maps
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Generating Polynomials and Inversion Formulas
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Systems of Representatives
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Boolean Algebras
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Combinatorial Circuits
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Complete Systems of Boolean Functions and Bases
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Introductory Graph Theory, Euler's Formula, and Unbreakable Ciphers
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Trees and Digraphs
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Computations and Algorithms
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Finite Automata
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Introduction to Game Theory
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Information Theory and Coding
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Probability Theory with a Finite Sample Space and the Birthday Problem
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Turing Machines, P and NP Classes, and Other Models of Computation
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Answers and Solutions to Selected Exercises
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Bibliography
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