椭圆曲线密码系统(ECC)整体算法设计及优化研究

在安全性差不多的情况下,ECC使用的密钥要比RSA短得多.然而,虽然ECC的数学理论已比较成熟,但其算法要比RSA更难理解,算法实现也比RSA困难得多,往往需要通过专门的硬件来加速算法实现.本文设计了一种ECC整体算法,并对其中的点积、平方剩余判定等关键算法进行优化,提高了算法的效率,使其能够完全通过软件实现.

The Research on Designing and Optimizing of the Algorithm for Elliptic Curve Cryptography (ECC)

ECC uses much shorter key than RSA does in the case of the same security.Although the mathematical theory of ECC has become perfect, understanding and implementing its algorithms is much more difficult than those of RSA.It often needs special ECC chip to speed the algorithm implementing.This paper introduces a kind of entire ECC algorithms we have designed.To raise the efficiency of the ECC implementing,the algorithms for point multiplying and square overplus judging have been optimized,so that the whole ECC algorithms can be implemented through software.