Elliptic and Hyperelliptic Curve Public Key Cryptography: Theory and Implementation

Author: Wang Xueli, Pei Dingyi
Publisher:
Publish Date: 2006-12-01
Features: This book discusses the basic theory and implementation of elliptic and hyperelliptic curve public-key cryptography, including: an introduction to elliptic curve public-key cryptography, the basic theory of elliptic and hyperelliptic curves, the counting of rational points on finite fields over elliptic and hyperelliptic curves, the discrete logarithm on elliptic and hyperelliptic curves, elementary attack methods, index attack methods, algebraic geometry attack methods, and algebraic number theory attack methods for the discrete logarithm on elliptic and hyperelliptic curves. One of the features of this book is its broad coverage, which includes necessary prerequisites and relatively complete mathematical proofs within a limited space, striving to form a coherent system. Another feature is the systematic and unified summary of most effective counting methods for rational points on finite fields over elliptic and hyperelliptic curves. A third feature is the systematic mathematical presentation of the main effective attack methods for the discrete logarithm on elliptic and hyperelliptic curves. A fourth feature is that we always discuss from the perspective of algorithmic number theory, and for each important theoretical result, we strive to provide its programmable practical algorithm. Some of the more elementary content in this book has been used as graduate teaching material in the Key Laboratory of Information Security, Graduate School of the Chinese Academy of Sciences, as well as in Guangzhou University and Hunan University. This book can serve as a reference for researchers in information security, number theory, and related fields, as well as for university teachers and advanced students. Some of its content can also be used as teaching material for graduate students in information security and number theory.