Researches On Elliptic Curve Public Key Cryptosystems In Network Information Security

This dissertation summarizes the works finished by the author with eight chapters based on the analyses and study of elliptic curve cryptosystems. In the first chapter, with the analysis of the security problems which the network communication is faced, the demand of people are listed. The solution is introduced and the elliptic curve cryptosystems is educed too. In this chapter, the list of the results obtained by the author is also presented. In the second chapter, some necessary and basic background materials about elliptic curve theory are presented. In chapter three, the elliptic curve discrete logarithm problems on the elliptic curve finite group are discussed. And the rules to select the secure elliptic curve are also neatened. In chapter four, the problem about calculating the order of the elliptic curve finite group is researched. Then, on the basis of discussing the security problems about the communication protocols, several efficiency security elliptic curve public key cryptography schemes which are designed by the author are thoroughly investigated and analyzed at chapter five. In chapter six and seven, some key points in the efficient implementation of elliptic curve public key cryptography schemes are thorough studied. The last chapter, chapter eight, summarizes all the dissertation and give a expectation about the future of elliptic curve cryptosystems.In this dissertation, the main works done by the author are listed as follows:(1) A new scheme to make the basis secure keys which named XRNGS are designed. And the reliability about the public-key is discussed.(2) The efficient XKAS key agreement schemes are designed. With dissimilarity demands, several extend schemes are studied.(3) XKDS key distribute schemes are designed. The problem about its application under network meeting condition is discussed.(4) The hybrid data encrypt schemes based on the key share scheme are proposed. These schemes combine the strongpoint of two class cryptography, and have excellent practicability.(5) A unified form about the general digital signature scheme based on the elliptic curve discrete logarithm problems are described as XECDS. An example of XECDS is presented as XECDS-I scheme. The ways about how to educed some common digital signature schemes form XECDS scheme are explained too.(6) About the problem to integrate the encrypt technique and the signature scheme, the author analyzes two type of modes possible, points out the hidden troubles and the solutions are given too.(7) The blind digital signature scheme based on the XECDS-I scheme is designed, and its correctness is proved.(8) On the basis of studying some general and special algorithms for the ellipticcurve discrete logarithm problems (ECDLP Problems), the rules to select the secure elliptic curve are neatened, and several kinds of secure elliptic curve are compared.(9) With the investigation about the SEA Algorithm, an effective decision scheme to colligating some improve algorithms on the SEA algorithm is designed and implemented.(10) Some key problems about the efficient implementation of elliptic curve public key cryptography schemes are thorough studied. The efficient algorithms to select the high-randomicity secure elliptic curve and randomicity base point are devised and implemented.