Example usage for java.math BigInteger gcd

List of usage examples for java.math BigInteger gcd

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Introduction

In this page you can find the example usage for java.math BigInteger gcd.

Prototype

public BigInteger gcd(BigInteger val)

Source Link

Document

Returns a BigInteger whose value is the greatest common divisor of abs(this) and abs(val) .

Usage

From source file:Main.java

public static void main(String[] args) {

    // assign values to bi1, bi2
    BigInteger bi1 = new BigInteger("18");
    BigInteger bi2 = new BigInteger("24");

    // assign gcd of bi1, bi2 to bi3
    BigInteger bi3 = bi1.gcd(bi2);

    System.out.println(bi3);/*from   w  w  w  . j a v a2  s  .  c om*/
}

From source file:cc.redberry.core.number.Exponentiation.java

public static Complex findIntegerRoot(Complex base, BigInteger power) {
    BigInteger rDenominator = ((Rational) base.getReal()).getDenominator();
    BigInteger iDenominator = ((Rational) base.getImaginary()).getDenominator();

    BigInteger lcm = rDenominator.gcd(iDenominator);
    lcm = rDenominator.divide(lcm);/*from   w  w  w  .  j a  va2 s  .c o m*/
    lcm = lcm.multiply(iDenominator);

    BigInteger lcmRoot = findIntegerRoot(lcm, power);

    if (lcm == null)
        return null;

    base = base.multiply(lcm);

    Complex numericValue = base.pow(1.0 / power.doubleValue());
    double real = numericValue.getReal().doubleValue();
    double imaginary = numericValue.getImaginary().doubleValue();

    int ceilReal = (int) Math.ceil(real), floorReal = (int) Math.floor(real),
            ceilImaginary = (int) Math.ceil(imaginary), floorImaginary = (int) Math.floor(imaginary);

    Complex candidate;
    if ((candidate = new Complex(ceilReal, ceilImaginary)).pow(power).equals(base))
        return candidate.divide(lcmRoot);
    if ((candidate = new Complex(floorReal, ceilImaginary)).pow(power).equals(base))
        return candidate.divide(lcmRoot);
    if ((candidate = new Complex(ceilReal, floorImaginary)).pow(power).equals(base))
        return candidate.divide(lcmRoot);
    if ((candidate = new Complex(floorReal, floorImaginary)).pow(power).equals(base))
        return candidate.divide(lcmRoot);
    return null;
}

From source file:RSA.java

/** Generate a new public and private key set. */
public synchronized void generateKeys() {
    SecureRandom r = new SecureRandom();
    BigInteger p = new BigInteger(bitlen / 2, 100, r);
    BigInteger q = new BigInteger(bitlen / 2, 100, r);
    n = p.multiply(q);/*from ww  w  .  j a v a 2s  .c o  m*/
    BigInteger m = (p.subtract(BigInteger.ONE)).multiply(q.subtract(BigInteger.ONE));
    e = new BigInteger("3");
    while (m.gcd(e).intValue() > 1) {
        e = e.add(new BigInteger("2"));
    }
    d = e.modInverse(m);
}

From source file:RSA.java

/** Create an instance that can both encrypt and decrypt. */
public RSA(int bits) {
    bitlen = bits;// www .j av  a 2 s.c o  m
    SecureRandom r = new SecureRandom();
    BigInteger p = new BigInteger(bitlen / 2, 100, r);
    BigInteger q = new BigInteger(bitlen / 2, 100, r);
    n = p.multiply(q);
    BigInteger m = (p.subtract(BigInteger.ONE)).multiply(q.subtract(BigInteger.ONE));
    e = new BigInteger("3");
    while (m.gcd(e).intValue() > 1) {
        e = e.add(new BigInteger("2"));
    }
    d = e.modInverse(m);
}

From source file:net.pms.util.Rational.java

/**
 * Returns an instance that represents the value of {@code value}.
 *
 * @param value the value./* w ww.  ja  v a2 s. co m*/
 * @return An instance that represents the value of {@code value}.
 */
@Nullable
public static Rational valueOf(@Nullable BigDecimal value) {
    if (value == null) {
        return null;
    }
    BigInteger numerator;
    BigInteger denominator;
    if (value.signum() == 0) {
        return ZERO;
    }
    if (BigDecimal.ONE.equals(value)) {
        return ONE;
    }
    if (value.scale() > 0) {
        BigInteger unscaled = value.unscaledValue();
        BigInteger tmpDenominator = BigInteger.TEN.pow(value.scale());
        BigInteger tmpGreatestCommonDivisor = unscaled.gcd(tmpDenominator);
        numerator = unscaled.divide(tmpGreatestCommonDivisor);
        denominator = tmpDenominator.divide(tmpGreatestCommonDivisor);
    } else {
        numerator = value.toBigIntegerExact();
        denominator = BigInteger.ONE;
    }
    return new Rational(numerator, denominator, BigInteger.ONE, numerator, denominator);
}

From source file:net.pms.util.Rational.java

/**
 * Calculates the greatest common divisor for two {@link BigInteger}s using
 * {@link BigInteger#gcd}.//from w w  w.  j  a  va 2 s. c o  m
 *
 * @param u the first number.
 * @param v the second number.
 * @return The GDC, always 1 or greater.
 */
@Nullable
public static BigInteger calculateGreatestCommonDivisor(@Nullable BigInteger u, @Nullable BigInteger v) {
    if (u == null || v == null) {
        return null;
    }
    if (u.abs().compareTo(BigInteger.ONE) <= 0 || v.abs().compareTo(BigInteger.ONE) <= 0) {
        return BigInteger.ONE;
    }
    return u.gcd(v);
}

From source file:net.pms.util.Rational.java

/**
 * Returns a {@link Rational} whose value is {@code (this * value)}.
 *
 * @param value the value to be multiplied by this {@link Rational}.
 * @return The multiplication result.//from w w  w.  j a  v a2s . com
 */
@Nullable
public Rational multiply(@Nullable Rational value) {
    if (value == null) {
        return null;
    }
    if (isNaN() || value.isNaN()) {
        return NaN;
    }
    if (isInfinite() || value.isInfinite()) {
        if (signum() == 0 || value.signum() == 0) {
            return NaN; // Infinity by zero
        }
        return numerator.signum() == value.signum() ? POSITIVE_INFINITY : NEGATIVE_INFINITY;
    }
    if (value.signum() == 0) {
        return ZERO;
    }

    if (value.numerator.abs().equals(value.denominator)) {
        return value.signum() < 0 ? this.negate() : this;
    }

    BigInteger newNumerator = reducedNumerator.multiply(value.reducedNumerator);
    BigInteger newDenominator = reducedDenominator.multiply(value.reducedDenominator);
    BigInteger gcd = newNumerator.gcd(newDenominator);
    return valueOf(newNumerator.divide(gcd), newDenominator.divide(gcd));
}

From source file:org.jbpm.formModeler.core.processing.formRendering.FormRenderingFormatter.java

protected BigInteger calculateMCM(List colspans) {
    if (colspans == null || colspans.isEmpty()) {
        return new BigInteger("1");
    } else if (colspans.size() == 1) {
        return (BigInteger) colspans.get(0);
    } else if (colspans.size() == 2) {
        BigInteger b1 = (BigInteger) colspans.get(0);
        BigInteger b2 = (BigInteger) colspans.get(1);
        return b1.multiply(b2).divide(b1.gcd(b2));
    } else { //Size > 2
        int halfLength = colspans.size() / 2;
        List firstHalf = colspans.subList(0, halfLength);
        List secondHalf = colspans.subList(halfLength, colspans.size());
        BigInteger b1 = calculateMCM(firstHalf);
        BigInteger b2 = calculateMCM(secondHalf);
        return b1.multiply(b2).divide(b1.gcd(b2));
    }// w  w w . ja  va 2s.  c o m
}

From source file:test.be.fedict.eid.applet.RSATest.java

@Test
public void testManualEncryption() throws Exception {
    while (true) {
        KeyPairGenerator keyPairGenerator = KeyPairGenerator.getInstance("RSA",
                BouncyCastleProvider.PROVIDER_NAME);
        SecureRandom random = new SecureRandom();
        int keySize = 128;
        keyPairGenerator.initialize(new RSAKeyGenParameterSpec(keySize, RSAKeyGenParameterSpec.F0), random);
        KeyPair keyPair = keyPairGenerator.generateKeyPair();
        PrivateKey privateKey = keyPair.getPrivate();
        PublicKey publicKey = keyPair.getPublic();
        RSAPrivateCrtKey rsaPrivateKey = (RSAPrivateCrtKey) privateKey;
        LOG.debug("private key modulus: " + rsaPrivateKey.getModulus());
        RSAPublicKey rsaPublicKey = (RSAPublicKey) publicKey;
        LOG.debug("public key modulus: " + rsaPublicKey.getModulus());
        LOG.debug("public key exponent: " + rsaPublicKey.getPublicExponent());
        LOG.debug("modulus size: " + rsaPublicKey.getModulus().toByteArray().length);

        Cipher cipher = Cipher.getInstance("RSA/ECB/PKCS1Padding");
        cipher.init(Cipher.ENCRYPT_MODE, privateKey);

        int dataSize = keySize / 8 - 11;
        byte[] data1 = new byte[dataSize];
        for (int i = 0; i < data1.length; i++) {
            data1[i] = 0x00;/* w  ww  .j a v  a  2  s.  co m*/
        }
        byte[] data2 = new byte[dataSize];
        for (int i = 0; i < data2.length; i++) {
            data2[i] = 0x00;
        }
        data2[data2.length - 1] = 0x07;

        byte[] signatureValue1 = cipher.doFinal(data1);

        LOG.debug("signature size: " + signatureValue1.length);

        cipher = Cipher.getInstance("RSA/ECB/PKCS1Padding");
        cipher.init(Cipher.ENCRYPT_MODE, privateKey);
        byte[] signatureValue2 = cipher.doFinal(data2);

        BigInteger sigBigInt1 = new BigInteger(signatureValue1);
        BigInteger sigBigInt2 = new BigInteger(signatureValue2);
        BigInteger msgBigInt1 = sigBigInt1.modPow(rsaPublicKey.getPublicExponent(), rsaPublicKey.getModulus());
        BigInteger msgBigInt2 = sigBigInt2.modPow(rsaPublicKey.getPublicExponent(), rsaPublicKey.getModulus());
        LOG.debug("msg big int: " + msgBigInt1);
        byte[] msgBytes1 = msgBigInt1.toByteArray();
        LOG.debug("original message size: " + msgBytes1.length);
        LOG.debug("original message1: " + new String(Hex.encodeHex(msgBytes1)));
        LOG.debug("original message2: " + new String(Hex.encodeHex(msgBigInt2.toByteArray())));

        LOG.debug("msg1 prime: " + msgBigInt1.isProbablePrime(100));
        LOG.debug("msg2 prime: " + msgBigInt2.isProbablePrime(100));

        // BigInteger.pow offers a very naive implementation
        LOG.debug("calculating s1^e...");
        BigInteger s1_e = sigBigInt1.pow(rsaPublicKey.getPublicExponent().intValue());
        LOG.debug("s1^e: " + s1_e);
        LOG.debug("calculating s2^e...");
        BigInteger s2_e = sigBigInt2.pow(rsaPublicKey.getPublicExponent().intValue());
        LOG.debug("s2^e: " + s2_e);

        LOG.debug("calculating GCD...");
        LOG.debug("msg1: " + msgBigInt1);
        LOG.debug("msg2: " + msgBigInt2);
        BigInteger a = s1_e.subtract(msgBigInt1);
        BigInteger b = s2_e.subtract(msgBigInt2);
        LOG.debug("a: " + a);
        LOG.debug("b: " + b);
        BigInteger candidateModulus = a.gcd(b);
        LOG.debug("candidate modulus: " + candidateModulus);
        LOG.debug("candidate modulus size: " + candidateModulus.toByteArray().length);
        BigInteger s_e = s1_e.multiply(s2_e);
        BigInteger m = msgBigInt1.multiply(msgBigInt2);
        while (false == rsaPublicKey.getModulus().equals(candidateModulus)) {
            LOG.error("incorrect candidate modulus");
            LOG.debug("modulus | candidate modulus: "
                    + candidateModulus.remainder(rsaPublicKey.getModulus()).equals(BigInteger.ZERO));
            s_e = s_e.multiply(s1_e);
            m = m.multiply(msgBigInt1);
            BigInteger n1 = s_e.subtract(m).gcd(a);
            BigInteger n2 = s_e.subtract(m).gcd(b);
            candidateModulus = n1.gcd(n2);
            // try / 2
            LOG.debug("new modulus:       " + n1);
            LOG.debug("new modulus:       " + n2);
            LOG.debug("candidate modulus: " + candidateModulus);
            LOG.debug("actual mod:        " + rsaPublicKey.getModulus());
        }
    }
}