From the exciting history of its development in ancient times to the present day Introduction to Cryptography with Mathematical Foundations and Computer Implementations provides a focused tour of the central concepts of cryptography. Rather than present an encyclopedic treatment of topics in cryptography it delineates cryptographic concepts in chronological order developing the mathematics as needed. Written in an engaging yet rigorous style each chapter introduces important concepts with clear definitions and theorems. Numerous examples explain key points while figures and tables help illustrate more difficult or subtle concepts. Each chapter is punctuated with Exercises for the Reader; complete solutions for these are included in an appendix. Carefully crafted exercise sets are also provided at the end of each chapter and detailed solutions to most odd-numbered exercises can be found in a designated appendix. The computer implementation section at the end of every chapter guides students through the process of writing their own programs. A supporting website provides an extensive set of sample programs as well as downloadable platform-independent applet pages for some core programs and algorithms. As the reliance on cryptography by business government and industry continues and new technologies for transferring data become available cryptography plays a permanent important role in day-to-day operations. This self-contained sophomore-level text traces the evolution of the field from its origins through present-day cryptosystems including public key cryptography and elliptic curve cryptography.