Application Of Elliptic Curve Cryptosystem

With the rapid development of information technology, the demands for information security rapidly increase. At the same time increasing computing power makes RSA cryptosystem, which has been to occupy the central position in public key cryptosystem, unable to meet the increasing security demands. There are some enviroments of those fields are special such as intelligence card or mobile environment, in which the bindwidth, computation ablity and store ablity are limited, so the traditional public key cryptosystems are not fit for those new fields.With high intensity security and efficient algorithm, elliptic curve cryptosystem meets the high-security needs of information in the future and wins more and more people's attention. Elliptic curve cryptosystem has been widely used and replaces the existing position of RSA soon. After 20 years of research, elliptic curve cryptosystem starts from academic research to practical application. At present, it becomes the most promising public key cryptography system.In a comprehensive study of the basic theory of elliptic curves and the knowledge of elliptic curve cryptosystem, this paper is primarily in-depthed to study the threshold secret sharing and threshold group signature. The details of the research are as follows.①To propose a threshold multiple secret sharing scheme based on the elliptic curve. This scheme should have the following features: the shorter key length and shorter signature length can be used than the scheme based on Factorization and Discrete Logarithm Problem when has the same security. The shares can be repeatedly used for the reconstruction of multiple secrets. The verification is offered to avoid the cheating of dealer and the cheating between participants. At the same time, the less interactive info and less compute by dealer can be used than the last schemes.②Use of existing codes about security hash algorithm, to confirm the feasibility and correctness of the threshold multiple secret sharing scheme. Then contrast to some existing schemes to analyze the advantages of the scheme.③To summarize the weakness of current threshold group signature schemes. To detailed analysis the weakness of one dynamic threshold group signature scheme.④To propose a secure threshold group signature scheme based on the elliptic curve. All the members share the group secret. Any subgroup shares one shadow and the sum of all of the shadows is the group secret. So it can withstand conspiracy attacks effectively.