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This is a collection of JAVA libraries that implement Unbound cryptographic classes for JAVA provider, PKCS11 wrapper, cryptoki, and advapi
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package com.unbound.common;

import java.math.BigInteger;

public class Arithmetic
{
  public static final BigInteger ZERO = BigInteger.valueOf(0);
  public static final BigInteger ONE = BigInteger.valueOf(1);
  public static final BigInteger TWO = BigInteger.valueOf(2);
  public static final BigInteger FOUR = BigInteger.valueOf(4);

  private static final int[] jacobiTable = {0, 1, 0, -1, 0, -1, 0, 1};

  public static int jacobi(BigInteger A, BigInteger B)
  {
    BigInteger a, b, v;
    long k = 1;

    k = 1;

    // test trivial cases
    if (B.equals(ZERO))
    {
      a = A.abs();
      return a.equals(ONE) ? 1 : 0;
    }

    if (!A.testBit(0) && !B.testBit(0))
    {
      return 0;
    }

    a = A;
    b = B;

    if (b.signum() == -1)
    { // b < 0
      b = b.negate(); // b = -b
      if (a.signum() == -1)
      {
        k = -1;
      }
    }

    v = ZERO;
    while (!b.testBit(0))
    {
      v = v.add(ONE); // v = v + 1
      b = b.divide(TWO); // b = b/2
    }

    if (v.testBit(0))
    {
      k = k * jacobiTable[a.intValue() & 7];
    }

    if (a.signum() < 0)
    { // a < 0
      if (b.testBit(1))
      {
        k = -k; // k = -k
      }
      a = a.negate(); // a = -a
    }

    // main loop
    while (a.signum() != 0)
    {
      v = ZERO;
      while (!a.testBit(0))
      { // a is even
        v = v.add(ONE);
        a = a.divide(TWO);
      }
      if (v.testBit(0))
      {
        k = k * jacobiTable[b.intValue() & 7];
      }

      if (a.compareTo(b) < 0)
      { // a < b
        // swap and correct intermediate result
        BigInteger x = a;
        a = b;
        b = x;
        if (a.testBit(1) && b.testBit(1))
        {
          k = -k;
        }
      }
      a = a.subtract(b);
    }

    return b.equals(ONE) ? (int) k : 0;
  }

  public static BigInteger sqrtP(BigInteger a, BigInteger p)
          throws IllegalArgumentException
  {

    BigInteger v = null;

    if (a.compareTo(ZERO) < 0)
    {
      a = a.add(p);
    }

    if (a.equals(ZERO))
    {
      return ZERO;
    }

    if (p.equals(TWO))
    {
      return a;
    }

    // p = 3 mod 4
    if (p.testBit(0) && p.testBit(1))
    {
      if (jacobi(a, p) == 1)
      { // a quadr. residue mod p
        v = p.add(ONE); // v = p+1
        v = v.shiftRight(2); // v = v/4
        return a.modPow(v, p); // return a^v mod p
        // return --> a^((p+1)/4) mod p
      }
      throw new IllegalArgumentException("No quadratic residue: " + a + ", " + p);
    }

    long t = 0;

    // initialization
    // compute k and s, where p = 2^s (2k+1) +1

    BigInteger k = p.subtract(ONE); // k = p-1
    long s = 0;
    while (!k.testBit(0))
    { // while k is even
      s++; // s = s+1
      k = k.shiftRight(1); // k = k/2
    }

    k = k.subtract(ONE); // k = k - 1
    k = k.shiftRight(1); // k = k/2

    // initial values
    BigInteger r = a.modPow(k, p); // r = a^k mod p

    BigInteger n = r.multiply(r).remainder(p); // n = r^2 % p
    n = n.multiply(a).remainder(p); // n = n * a % p
    r = r.multiply(a).remainder(p); // r = r * a %p

    if (n.equals(ONE))
    {
      return r;
    }

    // non-quadratic residue
    BigInteger z = TWO; // z = 2
    while (jacobi(z, p) == 1)
    {
      // while z quadratic residue
      z = z.add(ONE); // z = z + 1
    }

    v = k;
    v = v.multiply(TWO); // v = 2k
    v = v.add(ONE); // v = 2k + 1
    BigInteger c = z.modPow(v, p); // c = z^v mod p

    // iteration
    while (n.compareTo(ONE) == 1)
    { // n > 1
      k = n; // k = n
      t = s; // t = s
      s = 0;

      while (!k.equals(ONE))
      { // k != 1
        k = k.multiply(k).mod(p); // k = k^2 % p
        s++; // s = s + 1
      }

      t -= s; // t = t - s
      if (t == 0)
      {
        throw new IllegalArgumentException("No quadratic residue: " + a + ", " + p);
      }

      v = ONE;
      for (long i = 0; i < t - 1; i++)
      {
        v = v.shiftLeft(1); // v = 1 * 2^(t - 1)
      }
      c = c.modPow(v, p); // c = c^v mod p
      r = r.multiply(c).remainder(p); // r = r * c % p
      c = c.multiply(c).remainder(p); // c = c^2 % p
      n = n.multiply(c).mod(p); // n = n * c % p
    }
    return r;
  }

  public static BigInteger subP(BigInteger a, BigInteger b, BigInteger p)
  {
    if (a.compareTo(b)>=0) return a.subtract(b);
    return a.add(p).subtract(b);
  }

  public static BigInteger divP(BigInteger a, BigInteger b, BigInteger p)
  {
    return a.multiply(b.modInverse(p)).mod(p);
  }

}