[英]Point zero on an elliptic curve
I am working on a library that allows me to work with elliptic curves. 我正在使用允许使用椭圆曲线的库。 It is still at embryonic state, and so far it only consists of two classes, EllipticCurve and Point .
它仍然处于萌芽状态,到目前为止,它仅由EllipticCurve和Point两类组成。
Right now I'm implementing the basic operations of existence, belonging, sum, reflection, etc. 现在,我正在实现存在,所有,求和,反射等基本操作。
Unfortunately, I'm stuck now that I have to implement the concept of zero, ie, the point of the elliptic curve E crossing the line through P and -P, where P = (x,y) and -P = (x,-y). 不幸的是,我现在不得不实施零概念,即椭圆曲线E的点穿过P和-P的直线,其中P =(x,y)和-P =(x, -y)。 So, my question could be rephrased as "how do I implement a point at infinity?"
因此,我的问题可以改写为“如何实现无穷远点?”
Here's part of the Point class so far: 到目前为止,这是Point类的一部分:
public class Point implements Comparable<Point> {
private static final BigDecimal MINUSONE = new BigDecimal(-1);
private BigDecimal x;
private BigDecimal y;
private EllipticCurve e;
public Point(BigDecimal x, BigDecimal y, EllipticCurve e) {
if(x != null && y != null && e != null) {
if(liesOn(x,y,e)) {
this.x = x;
this.y = y;
this.e = e;
}
}
}
public Point reflect() {
return new Point(x,y.multiply(MINUSONE),e);
}
public Point add(Point o) {
if(this.e == o.getE()) {
if(this == o) {
return this.multiply(2);
}
if(o == this.reflect()) {
return /*THE INFAMOUS ZERO POINT*/;
}
BigDecimal a;
BigDecimal b;
/*
* computation I still haven't implemented
*/
return new Point(a,b,e);
}
}
/*
* other methods
*/
}
PS: I am aware of the existence of java.security.spec.EllipticCurve, but since I'm going to use this class mostly for mathematical purposes, I felt the need to create my personal library ex novo . PS:我知道java.security.spec.EllipticCurve的存在,但是由于我主要是出于数学目的使用此类,所以我觉得有必要从头创建我的个人库。
There is no way to represent infinity per se using BigDecimal
. 使用
BigDecimal
本身无法表示无穷大。 The only way in Java I know is: 我知道的Java唯一方法是:
Double.POSITIVE_INFINITY;
or Integer
, Float
etc. You also can't take valueOf
from the above, since it will throw a NumberFormatException
. 或
Integer
, Float
等。您也不能从上面获取valueOf
,因为它将抛出NumberFormatException
。
You can use a workaround, ie a very large value that you know will always be larger than any other. 您可以使用一种解决方法,即您知道一个非常大的值将始终大于其他任何值。
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