Elliptic Curve Cryptographic Algorithms And Their Applications

Elliptic curve cryptography(ECC) is an important subject in the field of public key cryptography. It provides higher security, shorter key size, less computation, faster process speed, less memory space and lower bandwidth, so it has wide application prospect in information security field.In this paper, the author primarily introduces how elliptic curves have been applied to public key cryptography from algebra and number theory, analyzes the advantage and security of ECC. The work the author has done is:(1) study the arithmetic of ECC on the encryption/decryption, digital signature and key exchange schemes and analyze their security performance;(2) propose a new ID-based group signature with existed ID-based digital signature and discuss its application in digital cash;(3) realize the electronic auction system and key authentication system with ECC.