Application of Montgomery's Trick to Scalar Multiplication for Elliptic and Hyperelliptic Curves Using a Fixed Base Point
Application of Montgomery's Trick to Scalar Multiplication for Elliptic and Hyperelliptic Curves Using a Fixed Base Point
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蒙哥马利技巧在使用固定基点的椭圆和超椭圆曲线标量乘法中的应用
DOI：
10.1007/978-3-540-24632-9_4
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发表时间：
2004
期刊：
影响因子：
--
通讯作者：
P. Sarkar
中科院分区：
文献类型：
--
作者：
P. Mishra;P. Sarkar
我们提出了一种用于椭圆和超椭圆曲线密码系统的标量乘法算法，该算法使用仿射算法并且能够抵抗简单的幂攻击。此外，使用已知技术的修改，可以使算法免受差分功率攻击。该算法使用蒙哥马利技巧和由基点的倍数组成的预先计算表。因此，该算法在基点固定的场景中非常有用，例如 Elgamal 加密或签名生成。在这种情况下，对于超椭圆曲线，该算法在所有领域都优于其他已知算法。对于椭圆曲线，在相似的情况下，该算法在素数域上的表现优于其他算法。速度的提高是由于正确应用了蒙哥马利技巧来有效地执行多个场元素的同时反演。
We propose a scalar multiplication algorithm for elliptic and hyperelliptic curve cryptosystems, which uses affine arithmetic and is resistant against simple power attacks. Also, using a modification of known techniques the algorithm can be made immune against differential power attacks. The algorithm uses Montgomery’s trick and a precomputed table consisting of multiples of the base point. Consequently, the algorithm is useful in a scenario where the base point is fixed, like Elgamal encryption or signature generation. Under such circumstances, for hyperelliptic curves, the algorithm compares favourably with other known algorithms over all fields. For elliptic curves, under similar circumstances, the algorithm performs better than other algorithms over prime fields. The increase in speed is due to a proper application of Montgomery’s trick to efficiently perform the simultaneous inversion of several field elements.