The Research And Application Based On Elliptic Curve Cryptosystems

With the rapid development of computers network, people more focus on the security of the information in networks. The research and application of cryptology is one of the core domains of the information security technique. Elliptic Curve Cryptosystems (ECC) is researched widely in the field of cryptology in recent yeas, Researchers at home and broad have paid widely attention to ECC.People started to research elliptic curve in more than 100 years ago, Elliptic Curve Public-Key Cryptosystem was put forward independently by Neal Koblitz and Victor Miller in 1985. ElliPtic Curve Cryptosystems is a kind of public-key cryptosystems with high security. Compared with other public-key cryptosystems, ECC has shorter key, this means higher speed, fewer memory and bandwidth. So it has already become a hotspot of cryptology.In Elliptic Curve Cryptosystems, scalar multiplication (point multiplication) and multiple scalar multiplication are the core operation, which is crucial to rapid realization of ECC. Width-w non-adjacent-form (w-NAF) algorithm is usually used to speed up the operation of the point multiplication on Elliptic Curve Cryptosystems. Some improvements are done to make it more effective in this paper. Furthermore,a new simple algorithm of double scalar multiplication is put forward combine with the subsection and parallel method. This paper gives a detailed analysis and precise measure of the new algorithm. The analysis and result of test show that the efficiency of improved algorithm can be increased by about 23%. The new algorithm of double scalar multiplication can be increased by about 60% in efficiency. The research of this paper is well practical value on elliptic curve scalar multiplication.The systems have been implemented with VC++6.0.Function blocks have excellencies such as well independence and expandability. The system adopt visualized interface,so it's easy to operate. The system implements the encryption and signature of file and ECDH has been used to instead of DH in IPSec.