我在 Stack Overflow 上找到了以下代码用于算术运算，即。椭圆曲线点的加法、加倍和乘法。我尝试运行它并使用以下 NIST 例程文档中给出的测试用例，[NSA 提供的 NIST 椭圆曲线例程] (http://www.nsa.gov/ia/_files/nist-routines.pdf/)。
代码编译并运行，但输出与给定的预测值不匹配。请帮忙。
import java.lang.*;
import java.math.*;
import java.security.spec.*;
import java.util.*;
class ECPointArthimetic{
EllipticCurve ec;
ECFieldFp ef;
private BigInteger x;
private BigInteger y;
private BigInteger z;
private BigInteger zinv;
private BigInteger one = BigInteger.ONE;
private BigInteger zero = BigInteger.ZERO;
private boolean infinity;
public ECPointArthimetic(EllipticCurve ec, BigInteger x, BigInteger y, BigInteger z) {
this.ec = ec;
this.x = x;
this.y = y;
this.ef=(ECFieldFp)ec.getField();
// Projective coordinates: either zinv == null or z * zinv == 1
// z and zinv are just BigIntegers, not fieldElements
if (z == null)
{
this.z = BigInteger.ONE;
}
else
{
this.z = z;
}
this.zinv = null;
infinity = false;
//TODO: compression flag
}
public BigInteger getX()
{
if (this.zinv == null)
{
this.zinv = this.z.modInverse(this.ef.getP());
}
return this.x.multiply(this.zinv).mod(this.ef.getP());
}
public BigInteger getY()
{
if (this.zinv == null)
{
this.zinv = this.z.modInverse(this.ef.getP());
}
return this.y.multiply(this.zinv).mod(this.ef.getP());
}
public boolean pointEquals(ECPointArthimetic other)
{
if (other == this)
{
return true;
}
if (this.isInfinity())
{
return other.isInfinity();
}
if (other.isInfinity())
{
return this.isInfinity();
}
BigInteger u, v;
// u = Y2 * Z1 - Y1 * Z2
u = other.y.multiply(this.z).subtract(this.y.multiply(other.z)).mod(this.ef.getP());
if (!u.equals(BigInteger.ZERO))
{
return false;
}
// v = X2 * Z1 - X1 * Z2
v = other.x.multiply(this.z).subtract(this.x.multiply(other.z)).mod(this.ef.getP());
return v.equals(BigInteger.ZERO);
}
public boolean isInfinity()
{
if ((this.x == zero) && (this.y == zero))
{
return true;
}
return this.z.equals(BigInteger.ZERO) && !this.y.equals(BigInteger.ZERO);
}
public ECPointArthimetic negate()
{
return new ECPointArthimetic(this.ec, this.x, this.y.negate(), this.z);
}
public ECPointArthimetic add(ECPointArthimetic b)
{
if (this.isInfinity())
{
return b;
}
if (b.isInfinity())
{
return this;
}
ECPointArthimetic R = new ECPointArthimetic(this.ec, zero, zero, null);
// u = Y2 * Z1 - Y1 * Z2
BigInteger u = b.y.multiply(this.z).subtract(this.y.multiply(b.z)).mod(this.ef.getP());
// v = X2 * Z1 - X1 * Z2
BigInteger v = b.x.multiply(this.z).subtract(this.x.multiply(b.z)).mod(this.ef.getP());
if (BigInteger.ZERO.equals(v))
{
if (BigInteger.ZERO.equals(u))
{
return this.twice(); // this == b, so double
}
infinity = true; // this = -b, so infinity
return R;
}
BigInteger THREE = new BigInteger("3");
BigInteger x1 = this.x;
BigInteger y1 = this.y;
BigInteger x2 = b.x;
BigInteger y2 = b.y;
BigInteger v2 = v.pow(2);
BigInteger v3 = v2.multiply(v);
BigInteger x1v2 = x1.multiply(v2);
BigInteger zu2 = u.pow(2).multiply(this.z);
// x3 = v * (z2 * (z1 * u^2 - 2 * x1 * v^2) - v^3)
BigInteger x3 = zu2.subtract(x1v2.shiftLeft(1)).multiply(b.z).subtract(v3).multiply(v).mod(this.ef.getP());
// y3 = z2 * (3 * x1 * u * v^2 - y1 * v^3 - z1 * u^3) + u * v^3
BigInteger y3 = x1v2.multiply(THREE).multiply(u).subtract(y1.multiply(v3)).subtract(zu2.multiply(u)).multiply(b.z).add(u.multiply(v3)).mod(this.ef.getP());
// z3 = v^3 * z1 * z2
BigInteger z3 = v3.multiply(this.z).multiply(b.z).mod(this.ef.getP());
return new ECPointArthimetic(this.ec, x3, y3, z3);
}
public ECPointArthimetic twice()
{
if (this.isInfinity())
{
return this;
}
ECPointArthimetic R = new ECPointArthimetic(this.ec, zero, zero, null);
if (this.y.signum() == 0)
{
infinity = true;
return R;
}
BigInteger THREE = new BigInteger("3");
BigInteger x1 = this.x;
BigInteger y1 = this.y;
BigInteger y1z1 = y1.multiply(this.z);
BigInteger y1sqz1 = y1z1.multiply(y1).mod(this.ef.getP());
BigInteger a = this.ec.getA();
// w = 3 * x1^2 + a * z1^2
BigInteger w = x1.pow(2).multiply(THREE);
if (!BigInteger.ZERO.equals(a))
{
w = w.add(this.z.pow(2).multiply(a));
}
w = w.mod(this.ef.getP());
// x3 = 2 * y1 * z1 * (w^2 - 8 * x1 * y1^2 * z1)
BigInteger x3 = w.pow(2).subtract(x1.shiftLeft(3).multiply(y1sqz1)).shiftLeft(1).multiply(y1z1).mod(this.ef.getP());
// y3 = 4 * y1^2 * z1 * (3 * w * x1 - 2 * y1^2 * z1) - w^3
BigInteger y3 = (w.multiply(THREE).multiply(x1).subtract(y1sqz1.shiftLeft(1))).shiftLeft(2).multiply(y1sqz1).subtract(w.pow(2).multiply(w)).mod(this.ef.getP());
// z3 = 8 * (y1 * z1)^3
BigInteger z3 = y1z1.pow(2).multiply(y1z1).shiftLeft(3).mod(this.ef.getP());
return new ECPointArthimetic(this.ec, x3, y3, z3);
}
public ECPointArthimetic multiply(BigInteger k)
{
if (this.isInfinity())
{
return this;
}
ECPointArthimetic R = new ECPointArthimetic(this.ec, zero, zero, null);
if (k.signum() == 0)
{
infinity = true;
return R;
}
BigInteger e = k;
BigInteger h = e.multiply(new BigInteger("3"));
ECPointArthimetic neg = this.negate();
R = this;
int i;
for (i = h.bitLength() - 2; i > 0; --i)
{
R = R.twice();
boolean hBit = h.testBit(i);
boolean eBit = e.testBit(i);
if (hBit != eBit) {
R = R.add(hBit ? this : neg);
}
}
return R;
}
}
class ECMath{
public static void main(String args[])
{
//sx,sy,tx,ty are provided coordinates, and so is d which is a random integer, to be used later as a private key
BigInteger sx = new BigInteger("d458e7d127ae671b0c330266d246769353a012073e97acf8",16);
BigInteger sy = new BigInteger("325930500d851f336bddc050cf7fb11b5673a1645086df3b",16);
BigInteger tx = new BigInteger("f22c4395213e9ebe67ddecdd87fdbd01be16fb059b9753a4",16);
BigInteger ty = new BigInteger("264424096af2b3597796db48f8dfb41fa9cecc97691a9c79",16);
BigInteger d = new BigInteger("2854434767935089551580740784991073913165554873467591589150");
String p192X = "188da80eb03090f67cbf20eb43a18800f4ff0afd82ff1012";
String p192Y = "07192b95ffc8da78631011ed6b24cdd573f977a11e794811";
String p192B = "64210519e59c80e70fa7e9ab72243049feb8deecc146b9b1";
String p192P = "6277101735386680763835789423207666416083908700390324961279";
String p192Order = "6277101735386680763835789423176059013767194773182842284081";
String p192A = "-3";
BigInteger p = new BigInteger(p192P, 16);
BigInteger gx = new BigInteger(p192X, 16);
BigInteger gy = new BigInteger(p192Y, 16);
ECFieldFp ef= new ECFieldFp(p);
EllipticCurve ec = new EllipticCurve(ef,new BigInteger(p192A).mod(p),new BigInteger(p192B, 16));
ECPointArthimetic G = new ECPointArthimetic(ec, new BigInteger(p192X,16), new BigInteger(p192Y,16),null);
BigInteger order = new BigInteger(p192Order, 16);
ECPointArthimetic ga = new ECPointArthimetic(ec,gx,gy,null);
ECPointArthimetic sa = new ECPointArthimetic(ec,sx,sy,null);
ECPointArthimetic ta = new ECPointArthimetic(ec,tx,ty,null);
ECPointArthimetic resAdd = sa.add(ta);
ECPointArthimetic resMul = ga.multiply(d);
System.out.println(resAdd.getX().toString(16));
System.out.println(resAdd.getY().toString(16));
System.out.println(resMul.getX().toString(16));
System.out.println(resMul.getY().toString(16));
}
}