Research And Improvement Of Scalar Multiplication Algorithm In Elliptic Curve Cryptography

The establishment of "Capital Network Security Day" in Beijing marked that the network security has become major social concern of government and ECC (Elliptic Curve Cryptography) which is a kind of common public key cryptography plays an important role in security guarantees of information transmitting in networks. As the basic operation in ECC, the speed of scalar multiplication determines the efficiency of encryption system, thus the optimization of scalar multiplication algorithm has become the focus in the research of ECC.This paper made a series of research on traditional scalar multiplication algorithm and proposed improved algorithm. The main research includes as follows:This paper summarized different optimization methods according to the classification of scalar multiplication and analyzed optimization strategy and efficiency of traditional scalar multiplication algorithms. It was founded that the scalar multiplication can be divided into operation of random scalar’s generation and scalar multiplication’s calculation in encryption or signature systems, and the two steps were completed separately. According to the random generation and application of scalar multiplication method, this paper proposed an improved algorithm to combine two processes into the pseudo-random number generator.On the basis of research on generation of random number, this paper chose Fibonacci sequence generator with security, large period and fast speed to generate random scalar and used pre-storage curve points to calculate scalar multiplication with point additions. The paper designed the process of the improved the algorithm and analyzed advantages to resist energy attacks.In experiments, the calculating time and amount of point addition and point doubling in different algorithms are compared and analysed. The experimental results show that the improved algorithm gets rid of point doubling with certain storage and reduces calculation efficiently overall.This paper accomplished scalar multiplications and some usual application protocols of ECC in Mathematica.