Secure Elliptic Curve Selection Algorithm And Its Application

At present, the Elliptic Curve Cryptography has the most secure private key when compared with other Public-Key Cryptography systems. Under similar secure conditions, the ECC has the advantages such as: less computation amounts, shorter length of private key, smaller storing and bandwidth. Moreover, it has been regarded as the most universal public key system for the next generation and has been adopted as a new security standard by many international standard institutions, such as IEEE P1363, ANSI X 9.62 and ANSI X 9.63.In this paper we generalize and analyze the advantages and present research of Elliptic Curve Cryptography, and study the basic theory of the ECC first. And main contributions of our work are as follows:(1) An algorithm which generates the secure elliptic curves of prime order defined over the finite field is described, and the secure elliptic curve choosing module is realized. We implement the algorithm by both the polynomials pre-process and bogus random method on this platform. Implementation results show that our algorithm is faster than other common algorithms with the same security. The results are useful and can be put into the elliptic curve cryptography.(2) Based on elliptic curve cryptosystem, a multi-keys sharing scheme which using the interpolation polynomial and which can detect cheaters is presented. The scheme is introduced and analyzed from aspects of follow: production of the sub-secure keys, check of the participants'sub-secure keys, resumption of the master key, addition or deletion of a sub-secure key, renewal of the master key. The scheme reduces the communication between Center of Authentic (CA) and participants. Furthermore, it is able to check the validity of the sub-secret keys easily and then avoid cheat from either CA or participants efficiently. Security of this scheme is based on the elliptic curve discrete logarithm problem (ECDLP).(3) Based on properties of polynomials over elliptic curve, we design a dynamic secret sharing scheme based on polynomials. This scheme is also introduced and analyzed from aspects of follow: production of the sub-secure keys, check of the participants'sub-secure keys, resumption of the master key, addition or deletion of a sub-secure key, renewal of the master key. Security of this scheme is based on the...