这里我用Java编写的代码但签名生成和验证过程给出了不同的结果。
请有人帮忙解决这个问题。我非常感谢你的支持。
package ecdsa.draft;
import java.math.BigInteger;
import java.security.MessageDigest;
import java.security.SecureRandom;
public class ECDSADraft {
public static void main(String[] args) throws Exception {
ECDSA a=new ECDSA();
a.key_Gen();
a.signature_gen();
a.signature_veri();
//Point p=new Point(new BigInteger("16"),new BigInteger("5"));
//Point q=new Point(new BigInteger("9"),new BigInteger("7"));
//Point r=p.scalarMul(new BigInteger("9"));
//r.showPoint();
//BigInteger k=new BigInteger(160, random);
// TODO code application logic here
}
}
class ECDSA
{
private BigInteger order_n = new BigInteger("6277101735386680763835789423176059013767194773182842284081");
public Point public_key=new Point();
public BigInteger private_key;
public BigInteger r=null;
public BigInteger s=null;
public BigInteger basex = new BigInteger("602046282375688656758213480587526111916698976636884684818");
public BigInteger basey = new BigInteger("174050332293622031404857552280219410364023488927386650641");
Point Base=new Point(basex, basey);
public SecureRandom random=new SecureRandom();
public void key_Gen(){
System.out.println("\n*****Key Generation Process******");
//Private key generation
private_key=new BigInteger(160, random);
//Public key generation Pb=k*G
public_key=Base.scalarMul(private_key);
//Display keys
System.out.println("Private key is:"+private_key);
System.out.println("public key is:");
public_key.showPoint();
}
public void signature_gen() throws Exception
{
//SecureRandom rand=new SecureRandom();
BigInteger k=new BigInteger(160, random);
if(k.compareTo(order_n)>=0)
signature_gen();
//BigInteger m=new BigInteger("1234567891");
BigInteger e, inversek;
Point p=Base.scalarMul(k);
BigInteger x=p.getx();
r=x.mod(order_n); //signature
if(r.equals(BigInteger.ZERO))
signature_gen();
else
{
SHA1 h=new SHA1();
e=h.hash("12345678");
System.out.println("the hash in generation"+e);
// inversek=k.modInverse(order_n);
s=((e.add(private_key.multiply(r))).divide(k)).mod(order_n);
}
if(s.equals(BigInteger.ZERO))
signature_gen();
//System.out.println("the signature r is "+r);
// System.out.println("the signature s is "+s);
}
public void signature_veri() throws Exception
{
System.out.println("The value of r and s in verification");
System.out.println("the signature r is "+r);
System.out.println("the signature s is "+s);
if(r.compareTo(order_n)>=0 && s.compareTo(order_n)>=0)
{
System.out.println("the r and s are out of range");
System.out.println("reject Signature");
}
else
{
SHA1 h=new SHA1();
BigInteger e=h.hash("12345678");
System.out.print("the hash in veri"+e);
BigInteger w= (BigInteger.ONE.divide(s)).mod(order_n);
BigInteger u1=e.multiply(w).mod(order_n);
BigInteger u2=r.multiply(w).mod(order_n);
Point p=Base.scalarMul(u1);
Point X=public_key.scalarMul(u2);
p.pointAdd(X);
BigInteger x1=X.getx();
BigInteger v=(x1).mod(order_n);
System.out.println("the value of v is"+v);
if(v.equals(r.mod(order_n)))
{
System.out.println("signature accepted");
}
else
{
BigInteger two=new BigInteger("2");
// System.out.println("mod inverse of 2 is "+two.modInverse(new BigInteger("5")));
System.out.println("Signature Rejected");
}
}
}
}
class Point{
private BigInteger x;
private BigInteger y;
private BigInteger p = new BigInteger("6277101735386680763835789423207666416083908700390324961279");
private BigInteger a=new BigInteger("-3");
private BigInteger two=new BigInteger("2");
private BigInteger three=new BigInteger("3");
//Constructor with default arguments....
Point(){
x=BigInteger.ZERO;
y=BigInteger.ZERO;
}
//Constructor with arguments for the object of point
Point(BigInteger a, BigInteger b){
x=a;
y=b;
}
//Module for displaying the point
public void showPoint(){
System.out.println("("+x+","+y+")");
}
public BigInteger getx()
{
return x;
}
public BigInteger gety()
{
return y;
}
//Routine for doubling the point
public Point doublePoint(){
Point R=new Point();
BigInteger lambda,u,v;
// u =((three.multiply(x.pow(2))).add(a));
// v =(two.multiply(y)).modInverse(p);
lambda = (((three.multiply(x.pow(2))).add(a)).divide(two.multiply(y))).mod(p);
// System.out.println("the value of lemda is"+lambda);
R.x = ((lambda.pow(2)).subtract(two.multiply(x))).mod(p);
R.y = ((lambda.multiply(x.subtract(R.x))).subtract(y)).mod(p);
return R;
}
//Routine for point addition
public Point pointAdd(Point Q){
Point R=new Point();
BigInteger u,v,lambda;
// u = (Q.y).subtract(y);
// v = ((Q.x).subtract(x)).modInverse(p);
lambda = (((Q.y).subtract(y)).divide((Q.x).subtract(x))).mod(p);
R.x = ((lambda.pow(2)).subtract(x).subtract(Q.x)).mod(p);
R.y = ((lambda.multiply(x.subtract(R.x))).subtract(y)).mod(p);
// System.out.println("The addition");
// R.showPoint();
return R;
}
// Routine for negating point
public Point negatePoint(){
Point R= new Point();
R.x=x;
R.y=y.negate();
return R;
}
public Point scalarMul(BigInteger k){
Point P=new Point(x,y);
System.out.println("x and y"+x+" "+y);
Point R=new Point();
String str=k.toString(2); //convert into string
Point Q=new Point();
R=P;
BigInteger l1,l2;
l1=P.x;
l2=P.y;
for(int i=1;i<str.length();i++)
{
P=P.doublePoint();
l1=P.x;
l2=P.y;
if(str.charAt(i)=='1')
{
Q=R.pointAdd(new Point(l1,l2));
l1=Q.x;
l2=Q.y;
}
}
// for(int i=str.length()-2;i>=0;i--){
// P=P.doublePoint();
// if(str.charAt(i)=='1')
// Q=Q.pointAdd(P);
Q=new Point(l1,l2);
return Q;
}
}
class SHA1 {
public BigInteger hash(String s) throws Exception
{
// Create a Message Digest from a Factory method
MessageDigest md = MessageDigest.getInstance("SHA1");
byte[] dataBytes = s.getBytes();
md.update(dataBytes);
byte[] mdbytes = md.digest();
// //convert the byte to hex format method 1
// StringBuffer sb = new StringBuffer();
// for (int i = 0; i < mdbytes.length; i++) {
// sb.append(Integer.toString((mdbytes[i] & 0xff) + 0x100, 16).substring(1));
// }
// System.out.println("Hex format : " + sb.toString());
//convert the byte to hex format method 2
StringBuffer hexString = new StringBuffer();
for (int i=0;i<mdbytes.length;i++) {
hexString.append(Integer.toHexString(0xFF & mdbytes[i]));
}
//System.out.println("Hex format : " + hexString.toString());
return (new BigInteger(hexString.toString(),16));
}
}
答案 0 :(得分：3)
在您的实现中，添加一些规则来判断该点是否为无穷大（INF）。检查是否应首先返回INF然后应用添加公式。
这个想法如下：
public Point pointAdd(Point Q){
if(Q.x.compareTo(x) == 0)
return INF;
Point R=new Point();
BigInteger lambda;
lambda = (((Q.y).subtract(y)).divide((Q.x).subtract(x))).mod(p);
R.x = ((lambda.pow(2)).subtract(x).subtract(Q.x)).mod(p);
R.y = ((lambda.multiply(x.subtract(R.x))).subtract(y)).mod(p);
I
return R;
}
public Point doublePoint(){
if (y.comparesTo(ZERO) == 0)
return INF;
Point R=new Point();
BigInteger lambda,u,v;
lambda = (((three.multiply(x.pow(2))).add(a)).divide(two.multiply(y))).mod(p);
R.x = ((lambda.pow(2)).subtract(two.multiply(x))).mod(p);
R.y = ((lambda.multiply(x.subtract(R.x))).subtract(y)).mod(p);
return R;
}
另请注意，任何点加INF都等于点本身。