Explaining the mathematics of cryptography

The Mathematics of Secrets takes readers on a fascinating tour of the mathematics behind cryptography―the science of sending secret messages. Using a wide range of historical anecdotes and real-world examples, Joshua Holden shows how mathematical principles underpin the ways that different codes and ciphers work. He focuses on both code making and code breaking and discusses most of the ancient and modern ciphers that are currently known. He begins by looking at substitution ciphers, and then discusses how to introduce flexibility and additional notation. Holden goes on to explore polyalphabetic substitution ciphers, transposition ciphers, connections between ciphers and computer encryption, stream ciphers, public-key ciphers, and ciphers involving exponentiation. He concludes by looking at the future of ciphers and where cryptography might be headed. The Mathematics of Secrets reveals the mathematics working stealthily in the science of coded messages.

Table of Contents

1 Introduction to Ciphers and Substitution

2 Polyalphabetic Substitution Ciphers

3 Transposition Ciphers

4 Ciphers and Computers

5 Stream Ciphers

6 Ciphers Involving Exponentiation

7 Public-Key Ciphers

8 Other Public-Key Systems

9 The Future of Cryptography

List of Symbols

Review

"Complete in surveying cryptography. . . . This is a marvelous way of illustrating the use of simple mathematics in an important application that has triggered the wit of the designers and the ingenuity of the attackers since antiquity." --Adhemar Bultheel, European Mathematical Society

"In The Mathematics of Secrets, Joshua Holden takes the reader on a chronological journey from Julius Caesar's substitution cipher to modern day public-key algorithms and beyond. . . . Written for anyone with an interest in cryptography." --Noel-Ann Bradshaw, Times Higher Education

"The best book I have seen on this subject." --Phil Dyke, Leonardo Reviews

"This is a fascinating tour of the mathematics behind cryptography, showing how its principles underpin the ways that different codes and ciphers operate. . . . While it's all about maths, the book is accessible--basic high school algebra is all that's needed to understand and enjoy it." --Cosmos Magazine

"In The Mathematics of Secrets, Joshua Holden takes the reader on a chronological journey from Julius Caesar’s substitution cipher to modern day public-key algorithms and beyond. . . . Written for anyone with an interest in cryptography." ―Noel-Ann Bradshaw, Times Higher Education

"Complete in surveying cryptography. . . . This is a marvelous way of illustrating the use of simple mathematics in an important application that has triggered the wit of the designers and the ingenuity of the attackers since antiquity." ―Adhemar Bultheel, European Mathematical Society

"The best book I have seen on this subject." ―Phil Dyke, Leonardo Reviews

"This is a fascinating tour of the mathematics behind cryptography, showing how its principles underpin the ways that different codes and ciphers operate. . . . While it’s all about maths, the book is accessible―basic high school algebra is all that’s needed to understand and enjoy it." ―Cosmos Magazine

About the Author

Joshua Holden is professor of mathematics at the Rose-Hulman Institute of Technology.