Cryptological Mathematics (Mathematical Association of America Textbooks)

This Is An Introduction To The Mathematics Involved In The Intriguing Field Of Cryptology, The Science Of Writing And Reading Secret Messages Which Are Designed To Be Read Only By Their Intended Recipients. It Is Written At An Elementary Level, Suitable For Beginning Undergraduates, With Careful Explanations Of All The Concepts Used. The Basic Branches Of Mathematics Required, Including Number Theory, Abstract Algebra And Probability, Are Used To Show How To Encipher And Decipher Messages, And Why This Works, Giving A Practical As Well As Theoretical Basis To The Subject. Challenging Computer Programming Exercises Are Also Included. The Book Is Written In An Engaging Style Which Will Appeal To All, And Also Includes Historical Background On Some Of The Founders Of The Subject. It Will Be Of Interest Both To Students Wishing To Learn Cryptology Per Se, And Also To Those Searching For Practical Applications Of Seemingly Abstract Mathematics. Monoalphabetic Substitution Ciphers -- Polyalphabetic Substitutions Ciphers -- Polygraphic Substitution Ciphers -- Public Key Cryptography -- Ascii Code -- Taxonomy Of Cryptology -- Answers To Even-numbered Problems. Robert Edward Lewand. Includes Bibliographical References And Index. Contents 8 Preface 12 1 Monoalphabetic Substitution Ciphers 16 1.1. Well-Ordering Axiom, Principle of Mathematical Induction 17 1.2. Prime Numbers, Division Algorithm, Greatest Common Divisor 22 1.3. Relatively Prime Integers, Fundamental Theorem of Arithmetic 31 1.4 Modular Arithmetic 34 1.5. Simple Ciphers 42 1.6. Cryptanalysis of Monoalphabetic Substitution Ciphers 50 1.7. Personalities 57 2 Polyalphabetic Substitution Ciphers 60 2.1. The Multiplication Principle 61 2.2. Permutations and Combinations 66 2.3. Probability 76 2.4. Independent Events and Expected Number 87 2.5. Disguising the Frequencies 91 2.6. Personalities 114 3 Polygraphic Substitution Ciphers 118 3.1. Elementary Polygraphic Substitution Ciphers 119 3.2. Elementary Matrix Theory 123 3.3. Hill's System 139 3.4. Personalities 153 4 Public Key Cryptography 156 4.1. More Number Theory 157 4.2. The RSA Algorithm 165 4.3. Two Examples 175 4.4. Other Illustrations of Public Key Cryptography 186 4.5. Personalities 193 A ASCII Code 196 B Taxonomy of Cryptology 198 C Answers to Even-Numbered Problems 200 Index 212

This is an introduction to the mathematics involved in the intriguing field of cryptology, the science of writing and reading secret messages which are designed to be read only by their intended recipients. It is written at an elementary level, suitable for beginning undergraduates, with careful explanations of all the concepts used. The basic branches of mathematics required, including number theory, abstract algebra and probability, are used to show how to encipher and decipher messages, and why this works, giving a practical as well as theoretical basis to the subject. Challenging computer programming exercises are also included. The book is written in an engaging style which will appeal to all, and also includes historical background on some of the founders of the subject. It will be of interest both to students wishing to learn cryptology per se, and also to those searching for practical applications of seemingly abstract mathematics.

An elementary introduction to the mathematics involved in cryptology, the science of reading and writing secret messages. The book has an engaging style, and all concepts used are carefully explained. It will be suitable for all students interested in cryptology and those looking for practical applications of seemingly abstract mathematics.