这是对@SkateScout 答案的改进。我在另一个上下文中使用了标量例程，在 SO (Derive EC public key from private key string in native Java for curve secp256k1) 上发布了它们，并得到了@President James Moveon Polk 的“错误”评论：
"该代码不正确，您从中获取的代码也是如此。这一行 BigInteger k = kin.mod(p); 是错误的，错误的，错误的。标量倍数应该取 mod 的顺序该组，这不是定义该字段的素数。您没有被该错误咬伤的唯一原因是因为您从未使用> = p的亲属对其进行测试。这就是您不进行加密的原因手动。但无论如何，您的问题的答案是否定的。如果您只使用 Java 8（或者可能是 7），您可以找到一个内部 sun。 执行标量乘法的类和方法，但不能超出此范围。 * "
我稍微修改了源代码，这是最终代码（完整示例）：
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));
}
}
享受吧！