Refined Computations for Points of the Form 2kP Based on Montgomery Trick
Refined Computations for Points of the Form 2kP Based on Montgomery Trick
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DOI：
10.1093/ietfec/e89-a.1.334
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发表时间：
2006
期刊：
影响因子：
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通讯作者：
D. Adachi;T. Hirata
中科院分区：
文献类型：
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作者：
D. Adachi;T. Hirata
本文重点讨论高效标量乘法的算法。它提出了两种计算仿射坐标中 2kP 形式的点的算法。一种适用于 k = 2，另一种适用于任意自然数 k。这些算法的效率基于域求逆和多个域乘法之间的权衡。蒙哥马利技巧就是用来实现这种权衡的。由于一次域求逆通常比 10 次域乘法更昂贵，因此所提出的算法与现有算法相比更加高效。
This paper focuses on algorithms for an efficient scalar multiplication. It proposes two algorithms for computing points of the form 2kP in affine coordinates. One works for k = 2, and the other works for an arbitrary natural number k. The efficiency of these algorithms is based on a trade-off between a field inversion and several field multiplications. Montgomery trick is used to implement this trade-off. Since a field inversion is usually more expensive than 10 field multiplications, the proposed algorithms are efficient in comparison with existing ones.