Elliptic Curve Public Key Cryptography Guide

Author: Zhu Yuefei, Zhang Yajuan
Publisher:
Publish Date: 2006-10-01
Features: Elliptic curves are an ancient and rich branch of mathematics. ECC theory involves many profound aspects of elliptic curve arithmetic theory. To systematically and comprehensively teach ECC theory requires a solid mathematical foundation. The purpose of this book is to systematically elaborate on ECC theory based on commutative algebra, providing a systematic and comprehensive foundational textbook for those who are interested in pursuing research in this field. The book is divided into three parts around the theory and practice of ECC: Part 1 introduces the arithmetic theory of elliptic curves, primarily focusing on the relevant theories of elliptic curves over finite fields; Part 2 covers the cryptographic theory of ECC, emphasizing the algorithms for computing the order of elliptic curves over finite fields, the algorithms for solving the discrete logarithm on elliptic curves, and the elliptic curve public-key cryptography, as well as primality testing and integer factorization algorithms for elliptic curves; Part 3 discusses the effective implementation of elliptic curve public-key cryptography, focusing on the key operators in elliptic curve public-key cryptography, such as the fast implementation of scalar multiplication and double scalar multiplication. This book can serve as a textbook for graduate students in information security and cryptography, and can also be referenced by researchers in related fields.