Endomorphisms for Faster Elliptic Curve Cryptography on a Large Class of Curves
Endomorphisms for Faster Elliptic Curve Cryptography on a Large Class of Curves
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DOI：
10.1007/s00145-010-9065-y
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发表时间：
2011-07-01
影响因子：
3
通讯作者：
Scott, Michael
中科院分区：
文献类型：
--
作者：
Galbraith, Steven D.;Lin, Xibin;Scott, Michael
高效可计算的同态允许使用 Gallant-Lambert-Vanstone (GLV) 方法加速椭圆曲线点乘。 Iijima、Matsuo、Chao 和 Tsujii 通过研究给出了一大类椭圆曲线的同态。我们扩展了他们的结果并证明它们可以应用于 GLV 方法。一般来说，我们预计我们的方法需要的时间约为以前最佳方法的 0.75 倍（子域曲线除外，可以使用 Frobenius 展开）。我们给出了详细的实现结果，表明该方法的运行时间比之前一般曲线上椭圆曲线点乘的最佳方法的时间要短 0.70 到 0.83 倍。
Efficiently computable homomorphisms allow elliptic curve point multiplication to be accelerated using the Gallant-Lambert-Vanstone (GLV) method. Iijima, Matsuo, Chao and Tsujii gave such homomorphisms for a large class of elliptic curves by working over We extend their results and demonstrate that they can be applied to the GLV method.In general we expect our method to require about 0.75 the time of previous best methods (except for subfield curves, for which Frobenius expansions can be used). We give detailed implementation results which show that the method runs in between 0.70 and 0.83 the time of the previous best methods for elliptic curve point multiplication on general curves.