Examples with ECFieldElement com.github.zhenwei.core.math.ec.ECFieldElement used on opensource projects

Example 1 with ECFieldElement

use of com.github.zhenwei.core.math.ec.ECFieldElement in project LinLong-Java by zhenwei1108.

the class DSTU4145PointEncoder method decodePoint.

public static ECPoint decodePoint(ECCurve curve, byte[] bytes) {
    /*byte[] bp_enc=new byte[bytes.length+1];
          if (0==(bytes[bytes.length-1]&0x1))
              bp_enc[0]=0x02;
          else
              bp_enc[0]=0x03;
          System.arraycopy(bytes, 0, bp_enc, 1, bytes.length);
          if (!trace(curve.fromBigInteger(new BigInteger(1, bytes))).equals(curve.getA().toBigInteger()))
              bp_enc[bp_enc.length-1]^=0x01;

          return curve.decodePoint(bp_enc);*/
    ECFieldElement k = curve.fromBigInteger(BigInteger.valueOf(bytes[bytes.length - 1] & 0x1));
    ECFieldElement xp = curve.fromBigInteger(new BigInteger(1, bytes));
    if (!trace(xp).equals(curve.getA())) {
        xp = xp.addOne();
    }
    ECFieldElement yp = null;
    if (xp.isZero()) {
        yp = curve.getB().sqrt();
    } else {
        ECFieldElement beta = xp.square().invert().multiply(curve.getB()).add(curve.getA()).add(xp);
        ECFieldElement z = solveQuadraticEquation(curve, beta);
        if (z != null) {
            if (!trace(z).equals(k)) {
                z = z.addOne();
            }
            yp = xp.multiply(z);
        }
    }
    if (yp == null) {
        throw new IllegalArgumentException("Invalid point compression");
    }
    return curve.validatePoint(xp.toBigInteger(), yp.toBigInteger());
}

Example 2 with ECFieldElement

use of com.github.zhenwei.core.math.ec.ECFieldElement in project LinLong-Java by zhenwei1108.

the class DSTU4145PointEncoder method solveQuadraticEquation.

/**
 * Solves a quadratic equation <code>z<sup>2</sup> + z = beta</code>(X9.62 D.1.6) The other
 * solution is <code>z + 1</code>.
 *
 * @param beta The value to solve the quadratic equation for.
 * @return the solution for <code>z<sup>2</sup> + z = beta</code> or
 * <code>null</code> if no solution exists.
 */
private static ECFieldElement solveQuadraticEquation(ECCurve curve, ECFieldElement beta) {
    if (beta.isZero()) {
        return beta;
    }
    ECFieldElement zeroElement = curve.fromBigInteger(ECConstants.ZERO);
    ECFieldElement z = null;
    ECFieldElement gamma = null;
    Random rand = new Random();
    int m = beta.getFieldSize();
    do {
        ECFieldElement t = curve.fromBigInteger(new BigInteger(m, rand));
        z = zeroElement;
        ECFieldElement w = beta;
        for (int i = 1; i <= m - 1; i++) {
            ECFieldElement w2 = w.square();
            z = z.square().add(w2.multiply(t));
            w = w2.add(beta);
        }
        if (!w.isZero()) {
            return null;
        }
        gamma = z.square().add(z);
    } while (gamma.isZero());
    return z;
}

Example 3 with ECFieldElement

use of com.github.zhenwei.core.math.ec.ECFieldElement in project LinLong-Java by zhenwei1108.

the class ECDSASigner method verifySignature.

// 5.4 pg 29
/**
 * return true if the value r and s represent a DSA signature for the passed in message (for
 * standard DSA the message should be a SHA-1 hash of the real message to be verified).
 */
public boolean verifySignature(byte[] message, BigInteger r, BigInteger s) {
    ECDomainParameters ec = key.getParameters();
    BigInteger n = ec.getN();
    BigInteger e = calculateE(n, message);
    // r in the range [1,n-1]
    if (r.compareTo(ONE) < 0 || r.compareTo(n) >= 0) {
        return false;
    }
    // s in the range [1,n-1]
    if (s.compareTo(ONE) < 0 || s.compareTo(n) >= 0) {
        return false;
    }
    BigInteger c = BigIntegers.modOddInverseVar(n, s);
    BigInteger u1 = e.multiply(c).mod(n);
    BigInteger u2 = r.multiply(c).mod(n);
    ECPoint G = ec.getG();
    ECPoint Q = ((ECPublicKeyParameters) key).getQ();
    ECPoint point = ECAlgorithms.sumOfTwoMultiplies(G, u1, Q, u2);
    // components must be bogus.
    if (point.isInfinity()) {
        return false;
    }
    /*
     * If possible, avoid normalizing the point (to save a modular inversion in the curve field).
     *
     * There are ~cofactor elements of the curve field that reduce (modulo the group order) to 'r'.
     * If the cofactor is known and small, we generate those possible field values and project each
     * of them to the same "denominator" (depending on the particular projective coordinates in use)
     * as the calculated point.X. If any of the projected values matches point.X, then we have:
     *     (point.X / Denominator mod p) mod n == r
     * as required, and verification succeeds.
     *
     * Based on an original idea by Gregory Maxwell (https://github.com/gmaxwell), as implemented in
     * the libsecp256k1 project (https://github.com/bitcoin/secp256k1).
     */
    ECCurve curve = point.getCurve();
    if (curve != null) {
        BigInteger cofactor = curve.getCofactor();
        if (cofactor != null && cofactor.compareTo(EIGHT) <= 0) {
            ECFieldElement D = getDenominator(curve.getCoordinateSystem(), point);
            if (D != null && !D.isZero()) {
                ECFieldElement X = point.getXCoord();
                while (curve.isValidFieldElement(r)) {
                    ECFieldElement R = curve.fromBigInteger(r).multiply(D);
                    if (R.equals(X)) {
                        return true;
                    }
                    r = r.add(n);
                }
                return false;
            }
        }
    }
    BigInteger v = point.normalize().getAffineXCoord().toBigInteger().mod(n);
    return v.equals(r);
}

Example 4 with ECFieldElement

use of com.github.zhenwei.core.math.ec.ECFieldElement in project LinLong-Java by zhenwei1108.

the class SecT409K1Point method negate.

public ECPoint negate() {
    if (this.isInfinity()) {
        return this;
    }
    ECFieldElement X = this.x;
    if (X.isZero()) {
        return this;
    }
    // L is actually Lambda (X + Y/X) here
    ECFieldElement L = this.y, Z = this.zs[0];
    return new SecT409K1Point(curve, X, L.add(Z), new ECFieldElement[] { Z });
}

Example 5 with ECFieldElement

use of com.github.zhenwei.core.math.ec.ECFieldElement in project LinLong-Java by zhenwei1108.

the class SecT409K1Point method add.

public ECPoint add(ECPoint b) {
    if (this.isInfinity()) {
        return b;
    }
    if (b.isInfinity()) {
        return this;
    }
    ECCurve curve = this.getCurve();
    ECFieldElement X1 = this.x;
    ECFieldElement X2 = b.getRawXCoord();
    if (X1.isZero()) {
        if (X2.isZero()) {
            return curve.getInfinity();
        }
        return b.add(this);
    }
    ECFieldElement L1 = this.y, Z1 = this.zs[0];
    ECFieldElement L2 = b.getRawYCoord(), Z2 = b.getZCoord(0);
    boolean Z1IsOne = Z1.isOne();
    ECFieldElement U2 = X2, S2 = L2;
    if (!Z1IsOne) {
        U2 = U2.multiply(Z1);
        S2 = S2.multiply(Z1);
    }
    boolean Z2IsOne = Z2.isOne();
    ECFieldElement U1 = X1, S1 = L1;
    if (!Z2IsOne) {
        U1 = U1.multiply(Z2);
        S1 = S1.multiply(Z2);
    }
    ECFieldElement A = S1.add(S2);
    ECFieldElement B = U1.add(U2);
    if (B.isZero()) {
        if (A.isZero()) {
            return twice();
        }
        return curve.getInfinity();
    }
    ECFieldElement X3, L3, Z3;
    if (X2.isZero()) {
        // TODO This can probably be optimized quite a bit
        ECPoint p = this.normalize();
        X1 = p.getXCoord();
        ECFieldElement Y1 = p.getYCoord();
        ECFieldElement Y2 = L2;
        ECFieldElement L = Y1.add(Y2).divide(X1);
        X3 = L.square().add(L).add(X1);
        if (X3.isZero()) {
            return new SecT409K1Point(curve, X3, curve.getB());
        }
        ECFieldElement Y3 = L.multiply(X1.add(X3)).add(X3).add(Y1);
        L3 = Y3.divide(X3).add(X3);
        Z3 = curve.fromBigInteger(ECConstants.ONE);
    } else {
        B = B.square();
        ECFieldElement AU1 = A.multiply(U1);
        ECFieldElement AU2 = A.multiply(U2);
        X3 = AU1.multiply(AU2);
        if (X3.isZero()) {
            return new SecT409K1Point(curve, X3, curve.getB());
        }
        ECFieldElement ABZ2 = A.multiply(B);
        if (!Z2IsOne) {
            ABZ2 = ABZ2.multiply(Z2);
        }
        L3 = AU2.add(B).squarePlusProduct(ABZ2, L1.add(Z1));
        Z3 = ABZ2;
        if (!Z1IsOne) {
            Z3 = Z3.multiply(Z1);
        }
    }
    return new SecT409K1Point(curve, X3, L3, new ECFieldElement[] { Z3 });
}