Research on Design Principles of Elliptic Curve Public Key Cryptography and Its Implementation

The mathematical theories involved in public key cryptography generally include factors decomposition problem of large numbers and discrete logarithm problem in finite field. In current public key cryptography, factors decomposition problems based on large numbers are commonly used, for example, RSA cryptography. With the development of computer hardware and high-performance computing technology, RSA has encountered some difficulties. In the situations, the cryptography based on elliptic curve discrete logarithm problem appears, whose public key is short, network bandwidth is little and ability to resist to attack is strong. The article analyses the design principles of elliptic curve public key cryptography, the important contents researched in the system, the selection method of secure elliptic curve and its implementation in details.