path: root/libjava/classpath/gnu/java/security/util/Prime2.java

/* Prime2.java -- 
   Copyright (C) 2001, 2002, 2003, 2006 Free Software Foundation, Inc.

This file is a part of GNU Classpath.

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it under the terms of the GNU General Public License as published by
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Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301
USA

Linking this library statically or dynamically with other modules is
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package gnu.java.security.util;

import java.io.PrintWriter;
import java.lang.ref.WeakReference;
import java.math.BigInteger;
import java.util.Map;
import java.util.WeakHashMap;

/**
 * <p>A collection of prime number related utilities used in this library.</p>
 */
public class Prime2
{

  // Debugging methods and variables
  // -------------------------------------------------------------------------

  private static final String NAME = "prime";

  private static final boolean DEBUG = false;

  private static final int debuglevel = 5;

  private static final PrintWriter err = new PrintWriter(System.out, true);

  private static void debug(String s)
  {
    err.println(">>> " + NAME + ": " + s);
  }

  // Constants and variables
  // -------------------------------------------------------------------------

  private static final int DEFAULT_CERTAINTY = 20; // XXX is this a good value?

  private static final BigInteger ZERO = BigInteger.ZERO;

  private static final BigInteger ONE = BigInteger.ONE;

  private static final BigInteger TWO = BigInteger.valueOf(2L);

  /**
   * The first SMALL_PRIME primes: Algorithm P, section 1.3.2, The Art of
   * Computer Programming, Donald E. Knuth.
   */
  private static final int SMALL_PRIME_COUNT = 1000;

  private static final BigInteger[] SMALL_PRIME = new BigInteger[SMALL_PRIME_COUNT];
  static
    {
      long time = -System.currentTimeMillis();
      SMALL_PRIME[0] = TWO;
      int N = 3;
      int J = 0;
      int prime;
      P2: while (true)
        {
          SMALL_PRIME[++J] = BigInteger.valueOf(N);
          if (J >= 999)
            {
              break P2;
            }
          P4: while (true)
            {
              N += 2;
              P6: for (int K = 1; true; K++)
                {
                  prime = SMALL_PRIME[K].intValue();
                  if ((N % prime) == 0)
                    {
                      continue P4;
                    }
                  else if ((N / prime) <= prime)
                    {
                      continue P2;
                    }
                }
            }
        }
      time += System.currentTimeMillis();
      if (DEBUG && debuglevel > 8)
        {
          StringBuffer sb;
          for (int i = 0; i < (SMALL_PRIME_COUNT / 10); i++)
            {
              sb = new StringBuffer();
              for (int j = 0; j < 10; j++)
                {
                  sb.append(String.valueOf(SMALL_PRIME[i * 10 + j])).append(" ");
                }
              debug(sb.toString());
            }
        }
      if (DEBUG && debuglevel > 4)
        {
          debug("Generating first " + String.valueOf(SMALL_PRIME_COUNT)
                + " primes took: " + String.valueOf(time) + " ms.");
        }
    }

  private static final Map knownPrimes = new WeakHashMap();

  // Constructor(s)
  // -------------------------------------------------------------------------

  /** Trivial constructor to enforce Singleton pattern. */
  private Prime2()
  {
    super();
  }

  // Class methods
  // -------------------------------------------------------------------------

  /**
   * <p>Trial division for the first 1000 small primes.</p>
   *
   * <p>Returns <code>true</code> if at least one small prime, among the first
   * 1000 ones, was found to divide the designated number. Retuens <code>false</code>
   * otherwise.</p>
   *
   * @param w the number to test.
   * @return <code>true</code> if at least one small prime was found to divide
   * the designated number.
   */
  public static boolean hasSmallPrimeDivisor(BigInteger w)
  {
    BigInteger prime;
    for (int i = 0; i < SMALL_PRIME_COUNT; i++)
      {
        prime = SMALL_PRIME[i];
        if (w.mod(prime).equals(ZERO))
          {
            if (DEBUG && debuglevel > 4)
              {
                debug(prime.toString(16) + " | " + w.toString(16) + "...");
              }
            return true;
          }
      }
    if (DEBUG && debuglevel > 4)
      {
        debug(w.toString(16) + " has no small prime divisors...");
      }
    return false;
  }

  /**
   * <p>Java port of Colin Plumb primality test (Euler Criterion)
   * implementation for a base of 2 --from bnlib-1.1 release, function
   * primeTest() in prime.c. this is his comments.</p>
   *
   * <p>"Now, check that bn is prime. If it passes to the base 2, it's prime
   * beyond all reasonable doubt, and everything else is just gravy, but it
   * gives people warm fuzzies to do it.</p>
   *
   * <p>This starts with verifying Euler's criterion for a base of 2. This is
   * the fastest pseudoprimality test that I know of, saving a modular squaring
   * over a Fermat test, as well as being stronger. 7/8 of the time, it's as
   * strong as a strong pseudoprimality test, too. (The exception being when
   * <code>bn == 1 mod 8</code> and <code>2</code> is a quartic residue, i.e.
   * <code>bn</code> is of the form <code>a^2 + (8*b)^2</code>.) The precise
   * series of tricks used here is not documented anywhere, so here's an
   * explanation. Euler's criterion states that if <code>p</code> is prime
   * then <code>a^((p-1)/2)</code> is congruent to <code>Jacobi(a,p)</code>,
   * modulo <code>p</code>. <code>Jacobi(a, p)</code> is a function which is
   * <code>+1</code> if a is a square modulo <code>p</code>, and <code>-1</code>
   * if it is not. For <code>a = 2</code>, this is particularly simple. It's
   * <code>+1</code> if <code>p == +/-1 (mod 8)</code>, and <code>-1</code> if
   * <code>m == +/-3 (mod 8)</code>. If <code>p == 3 (mod 4)</code>, then all
   * a strong test does is compute <code>2^((p-1)/2)</code>. and see if it's
   * <code>+1</code> or <code>-1</code>. (Euler's criterion says <i>which</i>
   * it should be.) If <code>p == 5 (mod 8)</code>, then <code>2^((p-1)/2)</code>
   * is <code>-1</code>, so the initial step in a strong test, looking at
   * <code>2^((p-1)/4)</code>, is wasted --you're not going to find a
   * <code>+/-1</code> before then if it <b>is</b> prime, and it shouldn't
   * have either of those values if it isn't. So don't bother.</p>
   *
   * <p>The remaining case is <code>p == 1 (mod 8)</code>. In this case, we
   * expect <code>2^((p-1)/2) == 1 (mod p)</code>, so we expect that the
   * square root of this, <code>2^((p-1)/4)</code>, will be <code>+/-1 (mod p)
   * </code>. Evaluating this saves us a modular squaring 1/4 of the time. If
   * it's <code>-1</code>, a strong pseudoprimality test would call <code>p</code>
   * prime as well. Only if the result is <code>+1</code>, indicating that
   * <code>2</code> is not only a quadratic residue, but a quartic one as well,
   * does a strong pseudoprimality test verify more things than this test does.
   * Good enough.</p>
   *
   * <p>We could back that down another step, looking at <code>2^((p-1)/8)</code>
   * if there was a cheap way to determine if <code>2</code> were expected to
   * be a quartic residue or not. Dirichlet proved that <code>2</code> is a
   * quadratic residue iff <code>p</code> is of the form <code>a^2 + (8*b^2)</code>.
   * All primes <code>== 1 (mod 4)</code> can be expressed as <code>a^2 +
   * (2*b)^2</code>, but I see no cheap way to evaluate this condition."</p>
   *
   * @param bn the number to test.
   * @return <code>true</code> iff the designated number passes Euler criterion
   * as implemented by Colin Plumb in his <i>bnlib</i> version 1.1.
   */
  public static boolean passEulerCriterion(final BigInteger bn)
  {
    BigInteger bn_minus_one = bn.subtract(ONE);
    BigInteger e = bn_minus_one;
    // l is the 3 least-significant bits of e
    int l = e.and(BigInteger.valueOf(7L)).intValue();
    int j = 1; // Where to start in prime array for strong prime tests
    BigInteger a;
    int k;

    if (l != 0)
      {
        e = e.shiftRight(1);
        a = TWO.modPow(e, bn);
        if (l == 6) // bn == 7 mod 8, expect +1
          {
            if (a.bitLength() != 1)
              {
                debugBI("Fails Euler criterion #1", bn);
                return false; // Not prime
              }
            k = 1;
          }
        else // bn == 3 or 5 mod 8, expect -1 == bn-1
          {
            a = a.add(ONE);
            if (a.compareTo(bn) != 0)
              {
                debugBI("Fails Euler criterion #2", bn);
                return false; // Not prime
              }
            k = 1;
            if ((l & 4) != 0) // bn == 5 mod 8, make odd for strong tests
              {
                e = e.shiftRight(1);
                k = 2;
              }
          }
      }
    else // bn == 1 mod 8, expect 2^((bn-1)/4) == +/-1 mod bn
      {
        e = e.shiftRight(2);
        a = TWO.modPow(e, bn);
        if (a.bitLength() == 1)
          j = 0; // Re-do strong prime test to base 2
        else
          {
            a = a.add(ONE);
            if (a.compareTo(bn) != 0)
              {
                debugBI("Fails Euler criterion #3", bn);
                return false; // Not prime
              }
          }
        // bnMakeOdd(n) = d * 2^s. Replaces n with d and returns s.
        k = e.getLowestSetBit();
        e = e.shiftRight(k);
        k += 2;
      }
    // It's prime!  Now go on to confirmation tests

    // Now, e = (bn-1)/2^k is odd.  k >= 1, and has a given value with
    // probability 2^-k, so its expected value is 2.  j = 1 in the usual case
    // when the previous test was as good as a strong prime test, but 1/8 of
    // the time, j = 0 because the strong prime test to the base 2 needs to
    // be re-done.
    for (int i = j; i < 7; i++) // try only the first 7 primes
      {
        a = SMALL_PRIME[i];
        a = a.modPow(e, bn);
        if (a.bitLength() == 1)
          continue; // Passed this test

        l = k;
        while (true)
          {
//            a = a.add(ONE);
//            if (a.compareTo(w) == 0) { // Was result bn-1?
            if (a.compareTo(bn_minus_one) == 0) // Was result bn-1?
              break; // Prime

            if (--l == 0) // Reached end, not -1? luck?
              {
                debugBI("Fails Euler criterion #4", bn);
                return false; // Failed, not prime
              }
            // This portion is executed, on average, once
//            a = a.subtract(ONE); // Put a back where it was
            a = a.modPow(TWO, bn);
            if (a.bitLength() == 1)
              {
                debugBI("Fails Euler criterion #5", bn);
                return false; // Failed, not prime
              }
          }
        // It worked (to the base primes[i])
      }
    debugBI("Passes Euler criterion", bn);
    return true;
  }

  public static boolean isProbablePrime(BigInteger w)
  {
    return isProbablePrime(w, DEFAULT_CERTAINTY);
  }

  /**
   * Wrapper around {@link BigInteger#isProbablePrime(int)} with few pre-checks.
   *
   * @param w the integer to test.
   * @param certainty the certainty with which to compute the test.
   */
  public static boolean isProbablePrime(BigInteger w, int certainty)
  {
    // Nonnumbers are not prime.
    if (w == null)
        return false;

    // eliminate trivial cases when w == 0 or 1
    if (w.equals(ZERO) || w.equals(ONE))
        return false;

    // Test if w is a known small prime.
    for (int i = 0; i < SMALL_PRIME_COUNT; i++)
        if (w.equals(SMALL_PRIME[i]))
          {
            if (DEBUG && debuglevel > 4)
                debug(w.toString(16) + " is a small prime");
            return true;
          }

    // Check if it's already a known prime
    WeakReference obj = (WeakReference) knownPrimes.get(w);
    if (obj != null && w.equals(obj.get()))
      {
        if (DEBUG && debuglevel > 4)
            debug("found in known primes");
        return true;
      }

    // trial division with first 1000 primes
    if (hasSmallPrimeDivisor(w))
      {
        if (DEBUG && debuglevel > 4)
            debug(w.toString(16) + " has a small prime divisor. Rejected...");
        return false;
      }

//     Euler's criterion.
//           if (passEulerCriterion(w)) {
//              if (DEBUG && debuglevel > 4) {
//                 debug(w.toString(16)+" passes Euler's criterion...");
//              }
//           } else {
//              if (DEBUG && debuglevel > 4) {
//                 debug(w.toString(16)+" fails Euler's criterion. Rejected...");
//              }
//              return false;
//           }
//
//    if (DEBUG && debuglevel > 4)
//      {
//        debug(w.toString(16) + " is probable prime. Accepted...");
//      }

    boolean result = w.isProbablePrime(certainty);
    if (result && certainty > 0) // store it in the known primes weak hash-map
      knownPrimes.put(w, new WeakReference(w));

    return result;
  }

  // helper methods -----------------------------------------------------------

  private static final void debugBI(String msg, BigInteger bn)
  {
    if (DEBUG && debuglevel > 4)
      debug("*** " + msg + ": 0x" + bn.toString(16));
  }
}