| Elliptic curve cryptography is built on the basis of the difficulty of the elliptic curve discrete logarithm problem in a finite field, and it is one of the most popular public-key cryptosystems. This paper studies the fast algorithms of elliptic curve cryptography and its software implementation of a binary field, puts forward new and efficient binary inversion algorithms and new scalar multiplications. In addition, by using ECC, we make a UKey management software.The paper is composed of five chapters.In chapter one, we will review the development of ECC history, introduce the advantages and disadvantages of the ECC and the research actuality, and also we tell the prospects of ECC.In chapter two, we introduce the math foundation of ECC, including the basic concepts and operations, enumerate kinds of enumerate kinds of attack algorithms to ECDLP.In chapter three, we discuss the fast and efficient realization of the elliptic curve cryptography; indicate and realize the new binary inversion algorithms and new scalar multiplications by Delphi.In chapter four, we make a UKey management software using ECC and UKey, and use the software to build a secure network system.Chapter five is the summary and outlook. |
