The Mathematics of Encryption

How quickly can you compute the remainder when dividing     by 120143? Why would you even want to compute this? And what does this have to do with cryptography?

Modern
cryptography lies at the intersection of mathematics and computer
sciences, involving number theory, algebra, computational complexity,
fast algorithms, and even quantum mechanics. Many people think of codes
in terms of spies, but in the information age, highly mathematical
codes are used every day by almost everyone, whether at the bank ATM,
at the grocery checkout, or at the keyboard when you access your email
or purchase products online.

This book provides a historical and
mathematical tour of cryptography, from classical ciphers to quantum
cryptography. The authors introduce just enough mathematics to explore
modern encryption methods, with nothing more than basic algebra and
some elementary number theory being necessary. Complete expositions are
given of the classical ciphers and the attacks on them, along with a
detailed description of the famous Enigma system. The public-key system
RSA is described, including a complete mathematical proof that it
works. Numerous related topics are covered, such as efficiencies of
algorithms, detecting and correcting errors, primality testing and
digital signatures. The topics and exposition are carefully chosen to
highlight mathematical thinking and problem solving. Each chapter ends
with a collection of problems, ranging from straightforward
applications to more challenging problems that introduce advanced
topics. Unlike many books in the field, this book is aimed at a general
liberal arts student, but without losing mathematical completeness.