生成适用于双线性对的椭圆曲线中的多项式构造

在构造适用于双线性对的椭圆曲线的方法中,通常将椭圆曲线的参数表示成有理多项式,为有效地生成椭圆曲线,要求复乘方程的次数应小于3。通过将椭圆曲线参数看作数域元素,提出了一种构造合适的有理多项式的方法,使得复乘方程的次数小于3。给出一些例子,特别给出了嵌入次数为8的例子,一般认为嵌入次数为8时,次数小于3的复乘方程不存在。

Constructing Polynomials for Generating Pairing-friendly Elliptic Curves

In constructing pairing friendly ellitpic curves, the curve parameters are often represented by polynomials with rational coefficients. For efficiently generating the curves parameters, the degree of the complex multipliction polynomial must be less than 3. A method is proposed to constructed suitable polynomials which will make the degree of the complex multipliction polynomial less than 3. Some examples are given, especially when embedding degree is 8. It is generally believed that when embedding degree is 8 the complex multipliction polynomial whose degree is less than 3 does not exist.