我需要使用jdk 1.7实现ECC（Elliptic Curve Cryptography）算法。我尝试使用充气城堡，sunEC，但他们都给出了错误和错误。我的目标是使用私钥生成椭圆曲线，我将被提供给系统。
因此，我需要使用jdk1.7获取使用给定私钥生成公钥的准确代码。我使用的IDE是ecllipse。我需要知道，除了私钥之外，我应该给出的其他参数是什么？仅仅提供一个曲线点和私钥就足够了吗？
有人可以帮我从私钥生成公钥吗？我可以管理其余的实施。
任何知道使用java实现Elliptic Curve Cryptography密钥的人，请告诉我这段代码是否正确？
public class ECCrypt {
private ECPoint curve_point;
public ECCrypt(ECPoint curve_point) {
this.curve_point = curve_point;
}
public BigInteger makePublicKey(BigInteger privateKey) {
ECPoint ecPublicKey = new ECPoint(curve_point);
ecPublicKey.mult(privateKey);
return ecPublicKey.pack();
}
public static void main(String[] argv) throws Exception {
java.util.Random rnd = new java.util.Random();
ECPoint cp = new ECPoint();
cp.random(rnd);
ECCrypt ec = new ECCrypt(cp);
BigInteger priv = new BigInteger(255,rnd);
BigInteger pub = ec.makePublicKey(priv);
}
谢谢！
答案 0 :(得分：8)
我写了一个输出以下内容的示例程序：
FL261:java jvah$ javac -cp bcprov-ext-jdk15on-149.jar ECTest.java
FL261:java jvah$ java -cp bcprov-ext-jdk15on-149.jar:. ECTest
Private key: 7ba78909571fbc336b2b94054dfb745a6b0776ff36a8fa98a598dc32cb83cc8e
Public key: 035b9e4a6148c9f9b08b573871ac66a832e6e9f63cf117545523a45b8017b7c43f
Calculated public key: 035b9e4a6148c9f9b08b573871ac66a832e6e9f63cf117545523a45b8017b7c43f
Congratulations, public keys match!
FL261:java jvah$
代码应该足够清晰，以便您可以了解这里所做的事情。请注意，您必须知道为您的私钥生成哪条曲线，否则无法生成匹配的公钥。示例代码使用secp256r1曲线，这是很常用的。
import java.math.BigInteger;
import java.security.SecureRandom;
import org.bouncycastle.asn1.x9.X9ECParameters;
import org.bouncycastle.asn1.sec.SECNamedCurves;
import org.bouncycastle.crypto.AsymmetricCipherKeyPair;
import org.bouncycastle.crypto.params.ECDomainParameters;
import org.bouncycastle.crypto.params.ECKeyGenerationParameters;
import org.bouncycastle.crypto.params.ECPrivateKeyParameters;
import org.bouncycastle.crypto.params.ECPublicKeyParameters;
import org.bouncycastle.crypto.generators.ECKeyPairGenerator;
import org.bouncycastle.math.ec.ECPoint;
class ECTest {
public static String toHex(byte[] data) {
StringBuilder sb = new StringBuilder();
for (byte b: data) {
sb.append(String.format("%02x", b&0xff));
}
return sb.toString();
}
public static void main(String[] argv) {
// Get domain parameters for example curve secp256r1
X9ECParameters ecp = SECNamedCurves.getByName("secp256r1");
ECDomainParameters domainParams = new ECDomainParameters(ecp.getCurve(),
ecp.getG(), ecp.getN(), ecp.getH(),
ecp.getSeed());
// Generate a private key and a public key
AsymmetricCipherKeyPair keyPair;
ECKeyGenerationParameters keyGenParams = new ECKeyGenerationParameters(domainParams, new SecureRandom());
ECKeyPairGenerator generator = new ECKeyPairGenerator();
generator.init(keyGenParams);
keyPair = generator.generateKeyPair();
ECPrivateKeyParameters privateKey = (ECPrivateKeyParameters) keyPair.getPrivate();
ECPublicKeyParameters publicKey = (ECPublicKeyParameters) keyPair.getPublic();
byte[] privateKeyBytes = privateKey.getD().toByteArray();
// First print our generated private key and public key
System.out.println("Private key: " + toHex(privateKeyBytes));
System.out.println("Public key: " + toHex(publicKey.getQ().getEncoded(true)));
// Then calculate the public key only using domainParams.getG() and private key
ECPoint Q = domainParams.getG().multiply(new BigInteger(privateKeyBytes));
System.out.println("Calculated public key: " + toHex(Q.getEncoded(true)));
// The calculated public key and generated public key should always match
if (!toHex(publicKey.getQ().getEncoded(true)).equals(toHex(Q.getEncoded(true)))) {
System.out.println("ERROR: Public keys do not match!");
} else {
System.out.println("Congratulations, public keys match!");
}
}
}
答案 1 :(得分：2)
我使用此方法从ECPrivateKey恢复ECPublicKey。 最后，主要的Routine证明它有效。很明白 没有任何外部库的java。
public final class MULT {
private static ECPoint doublePoint(final BigInteger p, final BigInteger a, final ECPoint R) {
if (R.equals(ECPoint.POINT_INFINITY)) return R;
BigInteger slope = (R.getAffineX().pow(2)).multiply(FieldP._3);
slope = slope.add(a);
slope = slope.multiply((R.getAffineY().multiply(FieldP._2)).modInverse(p));
final BigInteger Xout = slope.pow(2).subtract(R.getAffineX().multiply(FieldP._2)).mod(p);
final BigInteger Yout = (R.getAffineY().negate()).add(slope.multiply(R.getAffineX().subtract(Xout))).mod(p);
return new ECPoint(Xout, Yout);
}
private static ECPoint addPoint (final BigInteger p, final BigInteger a, final ECPoint r, final ECPoint g) {
if (r.equals(ECPoint.POINT_INFINITY)) return g;
if (g.equals(ECPoint.POINT_INFINITY)) return r;
if (r==g || r.equals(g)) return doublePoint(p, a, r);
final BigInteger gX = g.getAffineX();
final BigInteger sY = g.getAffineY();
final BigInteger rX = r.getAffineX();
final BigInteger rY = r.getAffineY();
final BigInteger slope = (rY.subtract(sY)).multiply(rX.subtract(gX).modInverse(p)).mod(p);
final BigInteger Xout = (slope.modPow(FieldP._2, p).subtract(rX)).subtract(gX).mod(p);
BigInteger Yout = sY.negate().mod(p);
Yout = Yout.add(slope.multiply(gX.subtract(Xout))).mod(p);
return new ECPoint(Xout, Yout);
}
public static ECPoint scalmult (final EllipticCurve curve, final ECPoint g, final BigInteger kin) {
final ECField field = curve.getField();
if(!(field instanceof ECFieldFp)) throw new UnsupportedOperationException(field.getClass().getCanonicalName());
final BigInteger p = ((ECFieldFp)field).getP();
final BigInteger a = curve.getA();
ECPoint R = ECPoint.POINT_INFINITY;
BigInteger k = kin.mod(p);
final int length = k.bitLength();
final byte[] binarray = new byte[length];
for(int i=0;i<=length-1;i++){
binarray[i] = k.mod(FieldP._2).byteValue();
k = k.shiftRight(1);
}
for(int i = length-1;i >= 0;i--){
R = doublePoint(p, a, R);
if(binarray[i]== 1) R = addPoint(p, a, R, g);
}
return R;
}
public static ECPublicKey getPublicKey(final ECPrivateKey pk) throws GeneralSecurityException {
final ECParameterSpec params = pk.getParams();
final ECPoint w = scalmult(params.getCurve(), pk.getParams().getGenerator(), pk.getS());
final KeyFactory kg = KeyFactory.getInstance("EC");
return (ECPublicKey)kg.generatePublic (new ECPublicKeySpec (w, params));
}
}
答案 2 :(得分：0)
对@markw上的Generate ECPublicKey from ECPrivateKey的答案有更多改进，并扩展了@bas-goossen从此处开始的曲线名称检测：How to find the matching curve name from an ECPublicKey
public static ECPublicKey publicFromPrivate(final ECPrivateKey privateKey) throws Exception {
ECParameterSpec params = privateKey.getParams();
org.bouncycastle.jce.spec.ECParameterSpec bcSpec = org.bouncycastle.jcajce.provider.asymmetric.util.EC5Util
.convertSpec(params, false);
org.bouncycastle.math.ec.ECPoint q = bcSpec.getG().multiply(privateKey.getS());
org.bouncycastle.math.ec.ECPoint bcW = bcSpec.getCurve().decodePoint(q.getEncoded(false));
ECPoint w = new ECPoint(
bcW.getAffineXCoord().toBigInteger(),
bcW.getAffineYCoord().toBigInteger());
ECPublicKeySpec keySpec = new ECPublicKeySpec(w, tryFindNamedCurveSpec(params));
return (ECPublicKey) KeyFactory
.getInstance("EC", org.bouncycastle.jce.provider.BouncyCastleProvider.PROVIDER_NAME)
.generatePublic(keySpec);
}
@SuppressWarnings("unchecked")
public static ECParameterSpec tryFindNamedCurveSpec(ECParameterSpec params) {
org.bouncycastle.jce.spec.ECParameterSpec bcSpec
= org.bouncycastle.jcajce.provider.asymmetric.util.EC5Util.convertSpec(params, false);
for (Object name : Collections.list(org.bouncycastle.jce.ECNamedCurveTable.getNames())) {
org.bouncycastle.jce.spec.ECNamedCurveParameterSpec bcNamedSpec
= org.bouncycastle.jce.ECNamedCurveTable.getParameterSpec((String) name);
if (bcNamedSpec.getN().equals(bcSpec.getN())
&& bcNamedSpec.getH().equals(bcSpec.getH())
&& bcNamedSpec.getCurve().equals(bcSpec.getCurve())
&& bcNamedSpec.getG().equals(bcSpec.getG())) {
return new org.bouncycastle.jce.spec.ECNamedCurveSpec(
bcNamedSpec.getName(),
bcNamedSpec.getCurve(),
bcNamedSpec.getG(),
bcNamedSpec.getN(),
bcNamedSpec.getH(),
bcNamedSpec.getSeed());
}
}
return params;
}
答案 3 :(得分：0)
这是对@SkateScout答案的改进。我在其他情况下使用了标量例程，并在此处（Derive EC public key from private key string in native Java for curve secp256k1）上发布了它们，并从@President James Moveon Polk得到了“错误”评论：
“ 该代码是不正确的，就像您从中获取的代码一样。此行BigInteger k = kin.mod（p）;是错误的，错误的，错误的。标量倍数应按以下顺序获取：该组，而不是定义该字段的主要对象，没有被该错误咬住的唯一原因是，因为您从未用过> = p的亲戚对其进行过测试，这就是为什么您不进行加密但是无论如何，您的问题的答案是否定的。如果您仅使用Java 8（或7），则可以找到内部的sun。类和方法可以进行标量乘法，但不能超出此范围。 *“
我稍微更改了源代码，这是最终代码（完整的示例）：
import org.bouncycastle.jce.ECNamedCurveTable;
import org.bouncycastle.jce.spec.ECNamedCurveParameterSpec;
import java.math.BigInteger;
import java.security.GeneralSecurityException;
import java.security.KeyFactory;
import java.security.PrivateKey;
import java.security.interfaces.ECPrivateKey;
import java.security.interfaces.ECPublicKey;
import java.security.spec.*;
public class DerivePublicKeyFromPrivateKeyCurveSecp256k1Final {
// sourcecode available https://github.com/java-crypto/Stackoverflow/tree/master/DervicePublicKeyFromPrivateKeyCurveSecp256k1
// get bouncycastle here: https://mvnrepository.com/artifact/org.bouncycastle/bcprov-jdk15on/1.65
// tested with version 15 1.65
// java open jdk 11.0.5
final static BigInteger FieldP_2 = BigInteger.TWO; // constant for scalar operations
final static BigInteger FieldP_3 = BigInteger.valueOf(3); // constant for scalar operations
public static void main(String[] args) throws GeneralSecurityException {
System.out.println("Generate ECPublicKey from PrivateKey (String) for curve secp256k1 (final)");
System.out.println("Check keys with https://gobittest.appspot.com/Address");
// https://gobittest.appspot.com/Address
String privateKey = "D12D2FACA9AD92828D89683778CB8DFCCDBD6C9E92F6AB7D6065E8AACC1FF6D6";
String publicKeyExpected = "04661BA57FED0D115222E30FE7E9509325EE30E7E284D3641E6FB5E67368C2DB185ADA8EFC5DC43AF6BF474A41ED6237573DC4ED693D49102C42FFC88510500799";
System.out.println("\nprivatekey given : " + privateKey);
System.out.println("publicKeyExpected: " + publicKeyExpected);
// routine with bouncy castle
System.out.println("\nGenerate PublicKey from PrivateKey with BouncyCastle");
ECNamedCurveParameterSpec spec = ECNamedCurveTable.getParameterSpec("secp256k1"); // this ec curve is used for bitcoin operations
org.bouncycastle.math.ec.ECPoint pointQ = spec.getG().multiply(new BigInteger(1, hexStringToByteArray(privateKey)));
byte[] publickKeyByte = pointQ.getEncoded(false);
String publicKeyBc = byteArrayToHexString(publickKeyByte);
System.out.println("publicKeyExpected: " + publicKeyExpected);
System.out.println("publicKey BC : " + publicKeyBc);
System.out.println("publicKeys match : " + publicKeyBc.contentEquals(publicKeyExpected));
// regeneration of ECPublicKey with java native starts here
System.out.println("\nGenerate PublicKey from PrivateKey with Java native routines");
// the preset "303E.." only works for elliptic curve secp256k1
// see answer by user dave_thompson_085
// https://stackoverflow.com/questions/48832170/generate-ec-public-key-from-byte-array-private-key-in-native-java-7
String privateKeyFull = "303E020100301006072A8648CE3D020106052B8104000A042730250201010420" +
privateKey;
byte[] privateKeyFullByte = hexStringToByteArray(privateKeyFull);
System.out.println("privateKey full : " + privateKeyFull);
KeyFactory keyFactory = KeyFactory.getInstance("EC");
PrivateKey privateKeyNative = keyFactory.generatePrivate(new PKCS8EncodedKeySpec(privateKeyFullByte));
ECPrivateKey ecPrivateKeyNative = (ECPrivateKey) privateKeyNative;
ECPublicKey ecPublicKeyNative = getPublicKey(ecPrivateKeyNative);
byte[] ecPublicKeyNativeByte = ecPublicKeyNative.getEncoded();
String publicKeyNativeFull = byteArrayToHexString(ecPublicKeyNativeByte);
String publicKeyNativeHeader = publicKeyNativeFull.substring(0, 46);
String publicKeyNativeKey = publicKeyNativeFull.substring(46, 176);
System.out.println("ecPublicKeyFull : " + publicKeyNativeFull);
System.out.println("ecPublicKeyHeader: " + publicKeyNativeHeader);
System.out.println("ecPublicKeyKey : " + publicKeyNativeKey);
System.out.println("publicKeyExpected: " + publicKeyExpected);
System.out.println("publicKeys match : " + publicKeyNativeKey.contentEquals(publicKeyExpected));
}
private static String byteArrayToHexString(byte[] a) {
StringBuilder sb = new StringBuilder(a.length * 2);
for (byte b : a)
sb.append(String.format("%02X", b));
return sb.toString();
}
public static byte[] hexStringToByteArray(String s) {
int len = s.length();
byte[] data = new byte[len / 2];
for (int i = 0; i < len; i += 2) {
data[i / 2] = (byte) ((Character.digit(s.charAt(i), 16) << 4)
+ Character.digit(s.charAt(i + 1), 16));
}
return data;
}
// scalar operations for native java
// see https://stackoverflow.com/a/42797410/8166854
// written by author: SkateScout
private static ECPoint doublePoint(final BigInteger p, final BigInteger a, final ECPoint R) {
if (R.equals(ECPoint.POINT_INFINITY)) return R;
BigInteger slope = (R.getAffineX().pow(2)).multiply(FieldP_3);
slope = slope.add(a);
slope = slope.multiply((R.getAffineY().multiply(FieldP_2)).modInverse(p));
final BigInteger Xout = slope.pow(2).subtract(R.getAffineX().multiply(FieldP_2)).mod(p);
final BigInteger Yout = (R.getAffineY().negate()).add(slope.multiply(R.getAffineX().subtract(Xout))).mod(p);
return new ECPoint(Xout, Yout);
}
private static ECPoint addPoint(final BigInteger p, final BigInteger a, final ECPoint r, final ECPoint g) {
if (r.equals(ECPoint.POINT_INFINITY)) return g;
if (g.equals(ECPoint.POINT_INFINITY)) return r;
if (r == g || r.equals(g)) return doublePoint(p, a, r);
final BigInteger gX = g.getAffineX();
final BigInteger sY = g.getAffineY();
final BigInteger rX = r.getAffineX();
final BigInteger rY = r.getAffineY();
final BigInteger slope = (rY.subtract(sY)).multiply(rX.subtract(gX).modInverse(p)).mod(p);
final BigInteger Xout = (slope.modPow(FieldP_2, p).subtract(rX)).subtract(gX).mod(p);
BigInteger Yout = sY.negate().mod(p);
Yout = Yout.add(slope.multiply(gX.subtract(Xout))).mod(p);
return new ECPoint(Xout, Yout);
}
public static ECPoint scalmultNew(final ECParameterSpec params, final ECPoint g, final BigInteger kin) {
EllipticCurve curve = params.getCurve();
final ECField field = curve.getField();
if (!(field instanceof ECFieldFp)) throw new UnsupportedOperationException(field.getClass().getCanonicalName());
final BigInteger p = ((ECFieldFp) field).getP();
final BigInteger a = curve.getA();
ECPoint R = ECPoint.POINT_INFINITY;
// value only valid for curve secp256k1, code taken from https://www.secg.org/sec2-v2.pdf,
// see "Finally the order n of G and the cofactor are: n = "FF.."
BigInteger SECP256K1_Q = params.getOrder();
//BigInteger SECP256K1_Q = new BigInteger("00FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141",16);
BigInteger k = kin.mod(SECP256K1_Q); // uses this !
// BigInteger k = kin.mod(p); // do not use this ! wrong as per comment from President James Moveon Polk
final int length = k.bitLength();
final byte[] binarray = new byte[length];
for (int i = 0; i <= length - 1; i++) {
binarray[i] = k.mod(FieldP_2).byteValue();
k = k.shiftRight(1);
}
for (int i = length - 1; i >= 0; i--) {
R = doublePoint(p, a, R);
if (binarray[i] == 1) R = addPoint(p, a, R, g);
}
return R;
}
public static ECPoint scalmultOrg(final EllipticCurve curve, final ECPoint g, final BigInteger kin) {
final ECField field = curve.getField();
if (!(field instanceof ECFieldFp)) throw new UnsupportedOperationException(field.getClass().getCanonicalName());
final BigInteger p = ((ECFieldFp) field).getP();
final BigInteger a = curve.getA();
ECPoint R = ECPoint.POINT_INFINITY;
// value only valid for curve secp256k1, code taken from https://www.secg.org/sec2-v2.pdf,
// see "Finally the order n of G and the cofactor are: n = "FF.."
BigInteger SECP256K1_Q = new BigInteger("00FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141",16);
BigInteger k = kin.mod(SECP256K1_Q); // uses this !
// wrong as per comment from President James Moveon Polk
// BigInteger k = kin.mod(p); // do not use this !
System.out.println(" SECP256K1_Q: " + SECP256K1_Q);
System.out.println(" p: " + p);
System.out.println("curve: " + curve.toString());
final int length = k.bitLength();
final byte[] binarray = new byte[length];
for (int i = 0; i <= length - 1; i++) {
binarray[i] = k.mod(FieldP_2).byteValue();
k = k.shiftRight(1);
}
for (int i = length - 1; i >= 0; i--) {
R = doublePoint(p, a, R);
if (binarray[i] == 1) R = addPoint(p, a, R, g);
}
return R;
}
public static ECPublicKey getPublicKey(final ECPrivateKey pk) throws GeneralSecurityException {
final ECParameterSpec params = pk.getParams();
final ECPoint w = scalmultNew(params, pk.getParams().getGenerator(), pk.getS());
//final ECPoint w = scalmult(params.getCurve(), pk.getParams().getGenerator(), pk.getS());
final KeyFactory kg = KeyFactory.getInstance("EC");
return (ECPublicKey) kg.generatePublic(new ECPublicKeySpec(w, params));
}
}
享受！