一种改进的椭圆曲线密码实现算法

An Improved Implementation Method on Elliptic Curve Cryptography

椭圆曲线密码系统(ECC)与其他公钥体制相比, 是迄今为止每比特具有最高安全强度的密码系统。椭圆曲线密码的算法研究的一个方向是进一步减少算法的运算量,以便于该算法在实际环境中应用。椭圆曲线上的倍点和数乘运算是椭圆曲线中核心运算,该文通过对计算过程的深入研究,推导了直接计算2m P,m ≥1的公式,并从理论上分析直接计算所节省的计算量。进而对椭圆曲线密码的快速实现算法进行了相应的改进,所提出的新算法的性能随着直接计算2m P,m ≥1中 m 的增大而提高,在极限情况下性能可比原算法提高 30%, 具有较大的应用价值。

Compared with previous public key schemes, this improved Elliptic Curve Cryptography has the highest secure strength-per-bit. One of the major research fields of the Elliptic Curve Cryptography is to reduce its complexity so as to be conveniently applied. Since multiplication of points and scalar multiplication of points are key operations in elliptic curve cryptography, this paper deduces through in-depth researches into the calculating process a formula to calculate 2mP, m≥1 directly and analyzes in theory the amount of operation saved by using this method. Furthermore, the new algorithm for calculating 2mP, m≥ 1 directly can effectively improve the calculating performance with the increase of m. Therefore, the performance of the new algorithm can be improved by 30% at most to the original one, thus making it a desirable algorithm of great value.