The Orders of Elliptic Curves y(2) = x(3) + b, b ∈ F(* q)
The Orders of Elliptic Curves y(2) = x(3) + b, b ∈ F(* q)
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椭圆曲线的阶数 y(2) = x(3) + b, b ∈ F(* q)
DOI：
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发表时间：
2006
期刊：
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通讯作者：
Y. Morikawa
中科院分区：
文献类型：
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作者：
Y. Nogami;Y. Morikawa
本文特别研究了E(x, y) = y(2)−x(3)−b = 0, b∈F（* q）的椭圆曲线，其中3除q−1。在本文中，我们将众所周知的捻法称为x捻法，并提出y捻法。结合x-捻和y-捻考虑6条椭圆曲线，本文提出了一种只计算其中一个阶数就能求出这6条曲线阶数的方法。
This paper particularly deals with elliptic curves in the form of E(x, y) = y(2) − x(3) −b = 0, b ∈ F(* q) , where 3 divides q−1. In this paper, we refer to the well-known twist technique as x-twist and propose y-twist. By combining x-twist and y-twist, we can consider six elliptic curves and this paper proposes a method to obtain the orders of these six curves by counting only one order among the six curves.