This text provides a rigorous yet accessible treatment of modern cryptography, focusing on formal definitions, assumptions, and rigorous proofs of security. The first half of the book gives an extensive treatment of private-key cryptography, including encryption, message authentication, and design principles for block ciphers such as the DES and the AES. The second half focuses on public-key cryptography, beginning with a self-contained introduction to the number theory needed for the RSA, Diffie-Hellman, El Gamal, and other cryptosystems. After exploring public-key encryption and digital signatures, the book concludes with a discussion of the random oracle model and its applications.