Abstract: In the field with the characteristic different from 2, the elliptic curve was transformed into Edwards curve equivalent to its double rational, and the realization speed of the software and hardware of ECC would be effectively accelerated. First of all, it could simplify doubling point calculation formula on Edwards curve. Then, according to that the coordinates of 2mP(m=2,3,…) have the uniform representation, Consecutive Doubled Algorithm (CDA) for computing 2mP was proposed based on recursive technique. The analytical results of algorithm complexity and instances show that the speed of scalar operation on Edwards curve can be increased by about more than 10 percent.

Key words: elliptic curve cryptosystem, scalar multiplication, Edwards curve, doubling formula, inversion operation

摘要： 在特征不等于2的域上，将椭圆曲线转换为与其双有理等价的Edwards曲线，可以有效提高ECC的软、硬件实现速度。首先简化了Edwards曲线上倍点的计算公式，然后根据连续倍点2mP(m=2,3,…)的坐标具有统一表示形式的特征，基于递归技术提出了一种计算2mP的连续倍点算法(CDA)。通过算法的复杂性分析与实例计算表明：CDA可使Edwards曲线上标量运算的速度提高10%以上。

关键词: 椭圆曲线密码系统, 标量乘法, Edwards曲线, 倍点公式, 求逆运算