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Professor’s New Book Solves Cryptic Mysteries

February 1, 2017

Joshua Holden

Secrets Behind Secret Messages: Mathematics professor Joshua Holden’s new book helps others understand the mathematical principles behind ancient and modern cryptic codes and ciphers.

Cryptography may be commmonly associated with computer science and software engineering, but there are numerous mathematics principles behind the centuries-old practice of keeping sensitive messages available for intended recipients.

Mathematics professor Joshua Holden has spent most of his career in number theory unlocking some of the secrets behind cryptography and examining a field that’s becoming a battleground for some of the world’s best mathematicians and computer scientists. The ability to securely store and transfer sensitive information has proved a critical factor in success in war and business.

“Cryptography is all about secrets, and throughout most of its history the whole field has been shrouded in secrecy. The result has been that just knowing about cryptography seems dangerous and even mystical,” he says.

Holden’s new book “The Mathematics of Secrets: Cryptography from Caesar Ciphers to Digital Encryption,” published by Princeton Press, hopes to help others understand the mathematical principles behind ancient and modern cryptic codes and ciphers.

And you don’t need to have a doctoral degree in mathematics to understand the basic concepts, just knowledge of high school algebra and a willingness to think hard through the problem-solving process.

“I intended to write something that someone who enjoys recreational reading could pick up and understand. Also, there’s a lot of storytelling because cryptography has a fascinating history,” said Holden. “Along the way, I didn’t want to teach the reader how to make their computer safer, but to appreciate the math that’s behind this secretive curtain of homeland security, international business and governmental affairs.”

The origin of cryptography dates back to about 2000 BC, with the Egyptian practice of hieroglyphics. These consisted of complex pictograms, the full meaning of which was only known to an elite few. An early use of a modern cipher was by Julius Caesar, who did not trust his messengers when communicating with his governors and officers. For this reason, he created a system—known as the Caesar Cipher—in which each character in his messages was replaced by a character three positions ahead of it in the Roman alphabet. Modern cryptography concerns itself with confidentiality, integrity, non-repudiation and authentication of information.

In his book, Holden reveals the key mathematical idea behind each cryptic code, how such ciphers are made and how they are broken. He also includes several modern-day examples out of today’s media headlines of cryptography usage—and inherent problems with computer security through internationally based hacking missions. Because of the ever-changing nature of the subject matter, Holden was making changes to his book until publication.

“I wanted the book to be authentic and that’s hard in an area that’s practically changing every day,” remarks Holden, who started on the book project seven years ago.

A member of the Rose-Hulman faculty since 2001, Holden specializes in teaching number theory, algebra, calculus, discrete mathematics, and, of course, cryptography. He has led National Science Foundation-funded research projects exploring discrete logarithms, and advised several student projects and theses on discrete mathematics and algebraic number theory. He also has led a campus committee on integrating classroom technology, and now serves as associate head of the Department of Mathematics.