Research Of Scalar Multiplication Fast Algorithm On Elliptic Curve Over GF(2~n)

In recent years, with the rapid development of the network, the various industries in various fields use of computer networks to carry data storage, transfer and exchange of information more and more. Security needs become increasingly urgent. Elliptic curve cryptosystem(ECC) has many advantages such as good safety performance, calculation speed, shorter key and key certificate small, limited processing power, storage space, bandwidth, power consumption environment these advantages of excellent to outstanding, making it the research focus in the public-key cryptosystem.Elliptic curve group algorithms are relatively complex, involving add operation, point multiplication, inverse operations, reduction operations and the representation of finite field elements and other issues. Among them, the point multiplication is the basic operations and key to achieve ECC, because it is more time-consuming operation, directly determines the performance of the ECC.This paper applies the idea of the improved m-ary method over ECC scalar multiplication for further improvement of a fast scalar multiplication algorithm, the results show that the improved algorithm reduces the computational of scalar multiplication and the storage space, analyzing computational efficiency and giving the comparison of the two algorithms.