Research And Application Of Elliptic Curve Algorithm

Elliptic curve cryptosystem (ECC) is a novel public key cryptosystem. Compared with other public key cryptosystems. it has a much smaller key length with the same security level. Thus, it is suitable for wireless system and device with limited storages and calculation speed. It has been adopted by many security standards, and is going to be applied in the not long future.The scalar multiplication algorithm is the key factor of ECC, which can determine the completing speed directly. Elliptic curve cryptosystem rapid achievement quickly became the research focus of many cryptology experts.The main works of the paper can be summarized as follows:First, introduced basic concept and mathematical knowledge of elliptic curve. Basic computing of elliptic curve in finite fields was talking either. From analysis of attack method on elliptic curve discrete logarithm problem, the selected principle of security elliptic curve was taken out.Second, from analysis and comparison of variety of single-scalar algorithms, double-scalar algorithm was introduced. double-scalar is the core of the digital signature of elliptic curve cryptography, which directly determines the efficiency of the signature.JSF is the most popular method of calculating the elliptic curve by double-scalar algorithm.Throug test, found that the computing amount of JSF is not the lowest.The improved algorithm can reduce the times of multiplication, and then reduce the total computing amount of multiplication making operation more efficiency.LiuDuo's multiple-scalar multiplication algorithm is a newly proposed algorithm for computing elliptic curve. Improving multiple-scalar multiplication algorithm by combining fixed window algorithm can improve operational efficiency through precomputation. which acquires little time by increase space.Last, designed an identification scheme based on elliptic curve.Both algorithms before and after improvement of the software have been tested. Analysis of experimental data shows that efficiency of the improved algorithms has heightened actually. The experimental result is consist with theoretical analysis on the efficiency upgrade.