素数域上椭圆曲线快速实现技术研究

Study on Fast Implementation of Prime-field ECC

随着椭圆曲线公钥密码的广泛应用,怎样快速实现椭圆曲线密码一直是业界关注的重点,在一些应用场景下,如移动、无线领域的应用,对椭圆曲线的实现速度要求较高,目前有许多快速实现椭圆曲线的算法,其性能各有差异。文章全面地研究素数域上的椭圆曲线快速实现技术,如Mersenne素数运算、Fermat定理、Euclidean方法等,并分析了这些方法。在此基础上,给出了详细的素数域上的椭圆曲线完整的实现细节及其关键技术的详细分析和实现方法。用该方法,能快速实现素数域上的椭圆曲线。

With the extensive use of ECC, how to speedily implement ECC is always the focus of crypto industry. In certain applications such as mobile and wireless scenes, the speed is very important. Nowadays, there are various ways to implement ECC. This paper disusses in detail the fast implementation of prime-field ECC, and analyzes such key techniques as Mersenne prime algorithm, Fermat theorem, Euclidean theory, and so on. By this way, the fast implemention of prime-field ECC could be done.