Based on the research experience of the authors, this book provides a theoretical structure of fundamental number theory and algebra knowledge supporting public-key cryptography. The authors integrate the results and thinking from more than 20 years of research and teaching, bridging the gap between math theory and crypto practice. It can be used in courses for junior/senior undergraduate students and first-year graduate students. Cryptography researchers and engineers can also benefit from this manuscript to build a more rigorous and effective way of thinking.

Divisibility of Integers. Congruences. Congruence Equations. Exponents and Primitive Roots. Some Elementary Results for Prime Distribution. Simple Continued Fractions. Basic Concepts. Group Theory. Rings and Fields. Some Mathematical Problems in Public Key Cryptography. Basics of Lattices. References. Further Reading. Index.

Dr. Xiaoyun Wang is a professor at the Institute of Advanced Study, Tsinghua University, China. She is also the director of the Center for Cryptology Study at Tsinghua University and an adjunct professor in the Key Lab of Cryptographic Technology and Information Security at Shandong University, China.
Dr. Guangwu Xu is an associate professor in the Department of Electrical Engineering and Computer Science, University of Wisconsin-Milwaukee. Dr. Xu's research concerns the efficiency, security, and reliability of information processing. He is interested in the fundamental problems of these aspects.

Dr. Mingqiang Wang

earned his PhD degree in 2004 from Shandong University, China where he serves as a professor now. Dr. Wang is a member of the Chinese Association for Cryptologic Research, his research focuses on number theory and analysis and design of public key algorithms.

Dr. Xianmeng Meng

earned her bachelor's and master's degrees from Jilin University in 1993 and 1996 respectively, then graduated with a PhD degree from Shandong University, China. She is a member of the Chinese Association for Cryptologic Research and is currently a professor in Shandong University of Finance and Economics, her main research interest is number theory and cryptography.