Research Of Elliptic Curve Password System And Its Applications

Since computers and applications of communication net inflenced people's daily life and work with develoments of the computer science technology, the communication, the microelectronic technology development, pepople need more and more safier information.The password technology is the key technologies of information security, the crypto-algorithm is the core password technology, along with the high speed development of information technology, at the present, public key cryptographic system has not faced people's demand.The elliptic curve password system has the high safety performance, the small computation; the quick processing speed, the slightly storage space, the width band requests, and easy realization, so these characteristics has caused it to suit especially in the weak environment of computation ability. In particular in correspondence terminal product like mobile pheone, PAD, WAP, smart card and so on. This high secure meets to the people in the life.The elliptic curve password system production background and mathematics theory in elliptic curve password finite field have been introduced in this thesis simply. And has given two kinds of elliptic curves under different coordinate system equation and algorithm; According to the advantages of elliptic curve, we can use it in digital signatures. Those main results have obtained:(1) Under affine coordinate system, standard projection coordinate system, the Yak compares coordinate system, the LD projection coordinate system equation; the different elliptic curves have been given in this thesis.(2) Under the affine coordinate system, the standard projection coordinate system, the Yak compares coordinate system, the coordinate system; LD projection coordinate system, spot Canada operation and time of spot operation have been given Basis elliptic curve calculated in detail under the affine coordinate system the LD projection coordinate system spot Canada operation and time of spot operation.(3) Acording to different coordinate system spot Canada operation and time of spot operation, I has maded the simple estimate to their operation order of complexity, and has given several kinds of operation order of complexity comparison, which kind of coordinate system is adopted in suitable situation, in order to more fast.(4) We can apply it in the digital signature using elliptic curve password system's merits and the nature.