Cryptography has been employed in war and diplomacy from the time of Julius Caesar. In our Internet age cryptography s most widespread application may be for commerce from protecting the security of electronic transfers to guarding communication from industrial espionage. This accessible introduction for undergraduates explains the cryptographic protocols for achieving privacy of communication and the use of digital signatures for certifying the validity integrity and origin of a message document or program. Rather than offering a how-to on configuring web browsers and e-mail programs the author provides a guide to the principles and elementary mathematics underlying modern cryptography giving readers a look under the hood for security techniques and the reasons they are thought to be secure.