Research on Elliptic Curve Cryptography Systems

Author: Xiao You'an
Publisher:
Publish Date: 2006-10-01
Features: Elliptic Curve Cryptography (ECC) is one of the research hotspots in the field of information security. Based on an analysis and research of the latest research achievements in elliptic curve cryptography, this book summarizes a series of research works completed by the author in this field over 7 chapters. Chapter 1 starts from the current status of network information security, analyzes the security threats faced, summarizes the security requirements proposed by people, and provides corresponding solutions, leading to the introduction of the Elliptic Curve Public Key Cryptography (ECC) system. Chapter 2 mainly introduces and discusses the basic mathematical theoretical foundations and related background knowledge used in this book for ECC. Chapter 3 introduces the discrete elliptic curves over finite fields and deeply discusses the Elliptic Curve Discrete Logarithm Problem (ECDLP) on elliptic curve finite groups, summarizing the selection criteria for secure elliptic curves. Chapter 4 studies the computation of the order of finite groups in elliptic curve groups and thoroughly investigates the SEA (Square-and-Multiply) number point algorithm. Chapter 5, based on the needs of secure communication, discusses the security issues of communication protocols and researches and analyzes the author-designed secure and efficient cryptographic schemes for ECC, including key generation, key agreement, key distribution, information encryption, and digital signatures. Chapters 6 and 7 deeply study several key technologies in the implementation of ECC systems, providing specific implementation algorithms and experimental results for typical schemes. This book is suitable for doctoral and master students, as well as senior undergraduate students in the fields of information, computer science, and related disciplines. It can also serve as a reference book for researchers and technical professionals in the field of information security.