Cryptological Mathematics introduces the reader to
elementary yet rigorous mathematics from several different
branches of the subject including number theory, abstract
algebra, matrix algebra, probability, and statistics, all
of which play a role in enciphering and deciphering secret
messages. And it does so in a light-hearted fashion, thanks
to the carryings-on of the book's three main characters,
Beth, Stephanie and Molly.
The book can be used at several different levels. Those
interested in learning how to encipher messages using a
variety of symmetric and asymmetric schemes will learn
those techniques in this volume. Those interested in
learning the mathematical foundations of these techniques
will learn how and why the enciphering schemes actually
work. And those who arc looking for some challenging
computer programming exercises will also find material in
this book to keep them busy. So the book may be used
profitably by amateur cryptographers, motivated liberal
arts students, and mathematics or computer
Whether readers are interested in cryptology,
mathematics, or computer science, they will discover
engaging and delightful material in this volume.
Contents
1- Monoalphabetic
Substitution Ciphers
- Well-Ordering Axiom, Principle of Mathematical
Induction
- Prime Numbers, Division Algorithm, Greatest Common
Divisor
- Relatively Prime Integers, Fundamental Theorem of
Arithmetic
- Modular Arithmetic
- Simple Ciphers
- Cryptanalysis of Monoalphabetic Substitution
Ciphers
- Personalities
2- Polyalphabetic Substitution Ciphers
- The Multiplication Principle
- Permutations and Combinations
- Probability
- Independent Events and Expected Number
- Disguising the Frequencies
- Personalities
3- Polygraphic Substitution Ciphers
- Elementary Polygraphic Substitution Ciphers
- Elementary Matrix Theory
- Hill's System
- Personalities
4- Public Key Cryptography
- More Number Theory
- The RSA Algorithm
- Two Examples
- Other Illustrations of Public Key Cryptography
- Personalities