用替换标量加速椭圆曲线点乘的研究

在优化有限域上椭圆曲线点乘的研究中，寻找标量的等价表示形式以减少点加和倍点运算的数量一直是关注的热点。因为点乘运算在一个H阶有限群中，利用有限群的性质，Q=kP=（n-k）（-P）。对于椭圆曲线，n-k和-P容易计算，于是计算点乘的标量k可以替换为n-k。因此，计算点乘时可通过选取代价更小的标量来减少计算量。理论和实验研究表明，替换标量可在微小的开销下使通常的重复倍加点算法的点加次数平均减少约5％。

Accelerating Elliptic Curve Point Multiplication Using Alternative Scalar

In the acceleration of elliptic curve point multiplication, significant research is focused on finding equivalent and efficient representation of the scalar. Because point multiplication occurs within a finite group of order n, and based on this property, Q=kP=（n-k）（-P）, where n-k and -P could be easily computed. Thus two alternative scalars k and n-k are left. By choosing the scalar that involves less computation, current methods of point multiplication could be further accelerated. The theory and practice shows that by using alternative scalar, the number of point additions in repeated double-and-add algorithm could be reduced by 5% on average.