Beispiel #1
0
 protected Address(BigInteger big_int)
 {
   byte[] buffer = ConvertToAddressBuffer(big_int);
   _buffer = MemBlock.Reference(buffer, 0, MemSize);
   if (ClassOf(_buffer) != this.Class) {
     throw new System.
     ArgumentException("Class of address is not my class:  ",
                       this.ToString());
   }
 }
Beispiel #2
0
 /**
  * Static constructor initializes _half and _full
  */
 static Address()
 {
   //Initialize _half
   byte[] tmp = new byte[MemSize];
   for (int i = 1; i < MemSize; i++)
   {
     tmp[i] = 0;
   }
   //Set the first bit to 1, all else to zero :
   tmp[0] = 0x80;
   _half = new BigInteger(tmp);
   _full = _half * 2;
 }
    //***********************************************************************
    // Computes the Jacobi Symbol for a and b.
    // Algorithm adapted from [3] and [4] with some optimizations
    //***********************************************************************

    public static int Jacobi(BigInteger a, BigInteger b)
    {
      // Jacobi defined only for odd integers
      if ((b.data[0] & 0x1) == 0)
        throw(new
              ArgumentException
              ("Jacobi defined only for odd integers."));

      if (a >= b)
        a %= b;
      if (a.dataLength == 1 && a.data[0] == 0)
        return 0;  // a == 0
      if (a.dataLength == 1 && a.data[0] == 1)
        return 1;  // a == 1

      if (a < 0) {
        if ((((b - 1).data[0]) & 0x2) == 0)     //if( (((b-1) >> 1).data[0] & 0x1) == 0)
          return Jacobi(-a, b);
        else
          return -Jacobi(-a, b);
      }

      int e = 0;
      for (int index = 0; index < a.dataLength; index++) {
        uint mask = 0x01;

        for (int i = 0; i < 32; i++) {
          if ((a.data[index] & mask) != 0) {
            index = a.dataLength;       // to break the outer loop
            break;
          }
          mask <<= 1;
          e++;
        }
      }

      BigInteger a1 = a >> e;

      int s = 1;
      if ((e & 0x1) != 0
          && ((b.data[0] & 0x7) == 3 || (b.data[0] & 0x7) == 5))
        s = -1;

      if ((b.data[0] & 0x3) == 3 && (a1.data[0] & 0x3) == 3)
        s = -s;

      if (a1.dataLength == 1 && a1.data[0] == 1)
        return s;
      else
        return (s * Jacobi(b % a1, a1));
    }
Beispiel #4
0
    public void Test14(ref int op) {
      Console.WriteLine("Test 14: Testing 1000 puts and 1 get with 1000 " +
          "results with the same key.  Then we remove the main owner of the " +
          "key.");
      RNGCryptoServiceProvider rng = new RNGCryptoServiceProvider();
      byte[] key = new byte[10];
      byte[] value = new byte[value_size];
      rng.GetBytes(key);
      ArrayList al_results = new ArrayList();
      int count = 60;
      BlockingQueue[] results_queue = new BlockingQueue[count];

      for(int i = 0; i < count; i++) {
        value = new byte[value_size];
        rng.GetBytes(value);
        al_results.Add(value);
        results_queue[i] = new BlockingQueue();
        default_dht.AsyncPut(key, value, 3000, results_queue[i]);
      }
      for (int i = 0; i < count; i++) {
        try {
          bool res = (bool) results_queue[i].Dequeue();
          Console.WriteLine("success in put : " + i);
        }
        catch {
          Console.WriteLine("Failure in put : " + i);
        }
      }
      Console.WriteLine("Insertion done...");
      Console.WriteLine("Disconnecting nodes...");
      MemBlock[] b = default_dht.MapToRing(key);
      BigInteger[] baddrs = new BigInteger[default_dht.DEGREE];
      BigInteger[] addrs = new BigInteger[default_dht.DEGREE];
      bool first_run = true;
      foreach(DictionaryEntry de in nodes) {
        Address addr = (Address) de.Key;
        for(int j = 0; j < b.Length; j++) {
          if(first_run) {
            addrs[j] = addr.ToBigInteger();
            baddrs[j] = (new AHAddress(b[j])).ToBigInteger();
          }
          else {
            BigInteger caddr = addr.ToBigInteger();
            BigInteger new_diff = baddrs[j] - caddr;
            if(new_diff < 0) {
              new_diff *= -1;
            }
            BigInteger c_diff = baddrs[j] - addrs[j];
            if(c_diff < 0) {
              c_diff *= -1;
            }
            if(c_diff > new_diff) {
              addrs[j] = caddr;
            }
          }
        }
        first_run = false;
      }

      for(int i = 0; i < addrs.Length; i++) {
        Console.WriteLine(new AHAddress(baddrs[i]) + " " + new AHAddress(addrs[i]));
        Address laddr = new AHAddress(addrs[i]);
        Node node = (Node) nodes[laddr];
        node.Disconnect();
        nodes.Remove(laddr);
        tables.Remove(laddr);
        network_size--;
      }

      default_dht = new Dht((Node) nodes.GetByIndex(0), degree);

      // Checking the ring every 5 seconds..
      do  { Thread.Sleep(5000);}
      while(!CheckAllConnections());
      Console.WriteLine("Going to sleep now...");
      Thread.Sleep(15000);
      Console.WriteLine("Timeout done.... now attempting gets");
      this.SerialAsyncGet(key, (byte[][]) al_results.ToArray(typeof(byte[])), op++);
      Thread.Sleep(5000);
      Console.WriteLine("This checks to make sure our follow up Puts succeeded");
      this.SerialAsyncGet(key, (byte[][]) al_results.ToArray(typeof(byte[])), op++);
      Console.WriteLine("If no error messages successful up to: " + (op - 1));
      foreach(TableServer ts in tables.Values) {
        Console.WriteLine("Count ... " + ts.Count);
      }
    }
Beispiel #5
0
 /**
  * Return a byte[] of length MemSize, which holds the integer % Full
  * as a buffer which is a binary representation of an Address
  */
 static public byte[] ConvertToAddressBuffer(BigInteger num)
 {
   byte[] bi_buf;
   
   BigInteger val = num % Full;
   if( val < 0 ) {
     val = val + Full;
   }
   bi_buf = val.getBytes();
   int missing = (MemSize - bi_buf.Length);
   if( missing > 0 ) {
     //Missing some bytes at the beginning, pad with zero :
     byte[] tmp_bi = new byte[Address.MemSize];
     for (int i = 0; i < missing; i++) {
       tmp_bi[i] = (byte) 0;
     }
     System.Array.Copy(bi_buf, 0, tmp_bi, missing,
                       bi_buf.Length);
     bi_buf = tmp_bi;
   }
   else if (missing < 0) {
     throw new System.ArgumentException(
       "Integer too large to fit in 160 bits: " + num.ToString());
   }
   return bi_buf;
 }
    //***********************************************************************
    // Overloading of the NOT operator (1's complement)
    //***********************************************************************

    public static BigInteger operator ~(BigInteger bi1)
    {
      BigInteger result = new BigInteger(bi1);

      for (int i = 0; i < maxLength; i++)
        result.data[i] = (uint) (~(bi1.data[i]));

      result.dataLength = maxLength;

      while (result.dataLength > 1
             && result.data[result.dataLength - 1] == 0)
        result.dataLength--;

      return result;
    }
    //***********************************************************************
    // Overloading of unary << operators
    //***********************************************************************

    public static BigInteger operator <<(BigInteger bi1, int shiftVal)
    {
      BigInteger result = new BigInteger(bi1);
      result.dataLength = shiftLeft(result.data, shiftVal);

      return result;
    }
    //***********************************************************************
    // Overloading of the unary -- operator
    //***********************************************************************

    public static BigInteger operator --(BigInteger bi1)
    {
      BigInteger result = new BigInteger(bi1);

      long val;
      bool carryIn = true;
      int index = 0;

      while (carryIn && index < maxLength) {
        val = (long) (result.data[index]);
        val--;

        result.data[index] = (uint) (val & 0xFFFFFFFF);

        if (val >= 0)
          carryIn = false;

        index++;
      }

      if (index > result.dataLength)
        result.dataLength = index;

      while (result.dataLength > 1
             && result.data[result.dataLength - 1] == 0)
        result.dataLength--;

      // overflow check
      int lastPos = maxLength - 1;

      // overflow if initial value was -ve but -- caused a sign
      // change to positive.

      if ((bi1.data[lastPos] & 0x80000000) != 0 &&
          (result.data[lastPos] & 0x80000000) !=
          (bi1.data[lastPos] & 0x80000000)) {
        throw(new ArithmeticException("Underflow in --."));
      }

      return result;
    }
    //***********************************************************************
    // Tests the correct implementation of the /, %, * and + operators
    //***********************************************************************

    public static void MulDivTest(int rounds)
    {
      Random rand = new Random();
      byte[] val = new byte[64];
      byte[] val2 = new byte[64];

      for (int count = 0; count < rounds; count++) {
        // generate 2 numbers of random length
        int t1 = 0;
        while (t1 == 0)
          t1 = (int) (rand.NextDouble() * 65);

        int t2 = 0;
        while (t2 == 0)
          t2 = (int) (rand.NextDouble() * 65);

        bool done = false;
        while (!done) {
          for (int i = 0; i < 64; i++) {
            if (i < t1)
              val[i] = (byte) (rand.NextDouble() * 256);
            else
              val[i] = 0;

            if (val[i] != 0)
              done = true;
          }
        }

        done = false;
        while (!done) {
          for (int i = 0; i < 64; i++) {
            if (i < t2)
              val2[i] = (byte) (rand.NextDouble() * 256);
            else
              val2[i] = 0;

            if (val2[i] != 0)
              done = true;
          }
        }

        while (val[0] == 0)
          val[0] = (byte) (rand.NextDouble() * 256);
        while (val2[0] == 0)
          val2[0] = (byte) (rand.NextDouble() * 256);

        Console.Error.WriteLine(count);
        BigInteger bn1 = new BigInteger(val, t1);
        BigInteger bn2 = new BigInteger(val2, t2);


        // Determine the quotient and remainder by dividing
        // the first number by the second.

        BigInteger bn3 = bn1 / bn2;
        BigInteger bn4 = bn1 % bn2;

        // Recalculate the number
        BigInteger bn5 = (bn3 * bn2) + bn4;

        // Make sure they're the same
        if (bn5 != bn1) {
          Console.Error.WriteLine("Error at " + count);
          Console.Error.WriteLine(bn1 + "\n");
          Console.Error.WriteLine(bn2 + "\n");
          Console.Error.WriteLine(bn3 + "\n");
          Console.Error.WriteLine(bn4 + "\n");
          Console.Error.WriteLine(bn5 + "\n");
          return;
        }
      }
    }
    //***********************************************************************
    // Performs the calculation of the kth term in the Lucas Sequence.
    // For details of the algorithm, see reference [9].
    //
    // k must be odd.  i.e LSB == 1
    //***********************************************************************

    private static BigInteger[]  LucasSequenceHelper(BigInteger P,
        BigInteger Q,
        BigInteger k,
        BigInteger n,
        BigInteger
        constant, int s)
    {
      BigInteger[] result = new BigInteger[3];

      if ((k.data[0] & 0x00000001) == 0)
        throw(new ArgumentException("Argument k must be odd."));

      int numbits = k.bitCount();
      uint mask = (uint) 0x1 << ((numbits & 0x1F) - 1);

      // v = v0, v1 = v1, u1 = u1, Q_k = Q^0

      BigInteger v = 2 % n, Q_k = 1 % n, v1 = P % n, u1 = Q_k;
      bool flag = true;

      for (int i = k.dataLength - 1; i >= 0; i--)       // iterate on the binary expansion of k
      {
        //Console.Error.WriteLine("round");
        while (mask != 0) {
          if (i == 0 && mask == 0x00000001)     // last bit
            break;

          if ((k.data[i] & mask) != 0)  // bit is set
          {
            // index doubling with addition

            u1 = (u1 * v1) % n;

            v = ((v * v1) - (P * Q_k)) % n;
            v1 = n.BarrettReduction(v1 * v1, n, constant);
            v1 = (v1 - ((Q_k * Q) << 1)) % n;

            if (flag)
              flag = false;
            else
              Q_k = n.BarrettReduction(Q_k * Q_k, n, constant);

            Q_k = (Q_k * Q) % n;
          }
          else {
            // index doubling
            u1 = ((u1 * v) - Q_k) % n;

            v1 = ((v * v1) - (P * Q_k)) % n;
            v = n.BarrettReduction(v * v, n, constant);
            v = (v - (Q_k << 1)) % n;

            if (flag) {
              Q_k = Q % n;
              flag = false;
            }
            else
              Q_k = n.BarrettReduction(Q_k * Q_k, n, constant);
          }

          mask >>= 1;
        }
        mask = 0x80000000;
      }

      // at this point u1 = u(n+1) and v = v(n)
      // since the last bit always 1, we need to transform u1 to u(2n+1) and v to v(2n+1)

      u1 = ((u1 * v) - Q_k) % n;
      v = ((v * v1) - (P * Q_k)) % n;
      if (flag)
        flag = false;
      else
        Q_k = n.BarrettReduction(Q_k * Q_k, n, constant);

      Q_k = (Q_k * Q) % n;


      for (int i = 0; i < s; i++) {
        // index doubling
        u1 = (u1 * v) % n;
        v = ((v * v) - (Q_k << 1)) % n;

        if (flag) {
          Q_k = Q % n;
          flag = false;
        }
        else
          Q_k = n.BarrettReduction(Q_k * Q_k, n, constant);
      }

      result[0] = u1;
      result[1] = v;
      result[2] = Q_k;

      return result;
    }
    //***********************************************************************
    // Returns the k_th number in the Lucas Sequence reduced modulo n.
    //
    // Uses index doubling to speed up the process.  For example, to calculate V(k),
    // we maintain two numbers in the sequence V(n) and V(n+1).
    //
    // To obtain V(2n), we use the identity
    //      V(2n) = (V(n) * V(n)) - (2 * Q^n)
    // To obtain V(2n+1), we first write it as
    //      V(2n+1) = V((n+1) + n)
    // and use the identity
    //      V(m+n) = V(m) * V(n) - Q * V(m-n)
    // Hence,
    //      V((n+1) + n) = V(n+1) * V(n) - Q^n * V((n+1) - n)
    //                   = V(n+1) * V(n) - Q^n * V(1)
    //                   = V(n+1) * V(n) - Q^n * P
    //
    // We use k in its binary expansion and perform index doubling for each
    // bit position.  For each bit position that is set, we perform an
    // index doubling followed by an index addition.  This means that for V(n),
    // we need to update it to V(2n+1).  For V(n+1), we need to update it to
    // V((2n+1)+1) = V(2*(n+1))
    //
    // This function returns
    // [0] = U(k)
    // [1] = V(k)
    // [2] = Q^n
    //
    // Where U(0) = 0 % n, U(1) = 1 % n
    //       V(0) = 2 % n, V(1) = P % n
    //***********************************************************************

    public static BigInteger[]  LucasSequence(BigInteger P,
        BigInteger Q,
        BigInteger k,
        BigInteger n)
    {
      if (k.dataLength == 1 && k.data[0] == 0) {
        BigInteger[] result = new BigInteger[3];

        result[0] = 0;
        result[1] = 2 % n;
        result[2] = 1 % n;
        return result;
      }

      // calculate constant = b^(2k) / m
      // for Barrett Reduction
      BigInteger constant = new BigInteger();

      int nLen = n.dataLength << 1;
      constant.data[nLen] = 0x00000001;
      constant.dataLength = nLen + 1;

      constant = constant / n;

      // calculate values of s and t
      int s = 0;

      for (int index = 0; index < k.dataLength; index++) {
        uint mask = 0x01;

        for (int i = 0; i < 32; i++) {
          if ((k.data[index] & mask) != 0) {
            index = k.dataLength;       // to break the outer loop
            break;
          }
          mask <<= 1;
          s++;
        }
      }

      BigInteger t = k >> s;

      //Console.Error.WriteLine("s = " + s + " t = " + t);
      return LucasSequenceHelper(P, Q, t, n, constant, s);
    }
    //***********************************************************************
    // Returns a value that is equivalent to the integer square root
    // of the BigInteger.
    //
    // The integer square root of "this" is defined as the largest integer n
    // such that (n * n) <= this
    //
    //***********************************************************************

    public BigInteger sqrt()
    {
      uint numBits = (uint) this.bitCount();

      if ((numBits & 0x1) != 0) // odd number of bits
        numBits = (numBits >> 1) + 1;
      else
        numBits = (numBits >> 1);

      uint bytePos = numBits >> 5;
      byte bitPos = (byte) (numBits & 0x1F);

      uint mask;

      BigInteger result = new BigInteger();
      if (bitPos == 0)
        mask = 0x80000000;
      else {
        mask = (uint) 1 << bitPos;
        bytePos++;
      }
      result.dataLength = (int) bytePos;

      for (int i = (int)bytePos - 1; i >= 0; i--) {
        while (mask != 0) {
          // guess
          result.data[i] ^= mask;

          // undo the guess if its square is larger than this
          if ((result * result) > this)
            result.data[i] ^= mask;

          mask >>= 1;
        }
        mask = 0x80000000;
      }
      return result;
    }
    //***********************************************************************
    // Returns the modulo inverse of this.  Throws ArithmeticException if
    // the inverse does not exist.  (i.e. gcd(this, modulus) != 1)
    //***********************************************************************

    public BigInteger modInverse(BigInteger modulus)
    {
      BigInteger[] p = {
                         0, 1};
      BigInteger[] q = new BigInteger[2];        // quotients
      BigInteger[] r = {
                         0, 0};       // remainders

      int step = 0;

      BigInteger a = modulus;
      BigInteger b = this;

      while (b.dataLength > 1
             || (b.dataLength == 1 && b.data[0] != 0)) {
        BigInteger quotient = new BigInteger();
        BigInteger remainder = new BigInteger();

        if (step > 1) {
          BigInteger pval = (p[0] - (p[1] * q[0])) % modulus;
          p[0] = p[1];
          p[1] = pval;
        }

        if (b.dataLength == 1)
          singleByteDivide(a, b, quotient, remainder);
        else
          multiByteDivide(a, b, quotient, remainder);

        /*
         * Console.Error.WriteLine(quotient.dataLength);
         * Console.Error.WriteLine("{0} = {1}({2}) + {3}  p = {4}", a.ToString(10),
         * b.ToString(10), quotient.ToString(10), remainder.ToString(10),
         * p[1].ToString(10));
         */

        q[0] = q[1];
        r[0] = r[1];
        q[1] = quotient;
        r[1] = remainder;

        a = b;
        b = remainder;

        step++;
      }

      if (r[0].dataLength > 1
          || (r[0].dataLength == 1 && r[0].data[0] != 1))
        throw(new ArithmeticException("No inverse!"));

      BigInteger result = ((p[0] - (p[1] * q[0])) % modulus);

      if ((result.data[maxLength - 1] & 0x80000000) != 0)
        result += modulus;      // get the least positive modulus

      return result;
    }
    //***********************************************************************
    // Generates a random number with the specified number of bits such
    // that gcd(number, this) = 1
    //***********************************************************************

    public BigInteger genCoPrime(int bits, Random rand)
    {
      bool done = false;
      BigInteger result = new BigInteger();

      while (!done) {
        result.genRandomBits(bits, rand);
        //Console.Error.WriteLine(result.ToString(16));

        // gcd test
        BigInteger g = result.gcd(this);
        if (g.dataLength == 1 && g.data[0] == 1)
          done = true;
      }

      return result;
    }
    //***********************************************************************
    // Generates a positive BigInteger that is probably prime.
    //***********************************************************************

    public static BigInteger genPseudoPrime(int bits, int confidence,
                                            Random rand)
    {
      BigInteger result = new BigInteger();
      bool done = false;

      while (!done) {
        result.genRandomBits(bits, rand);
        result.data[0] |= 0x01; // make it odd

        // prime test
        done = result.isProbablePrime(confidence);
      }
      return result;
    }
    //***********************************************************************
    // Overloading of the unary ++ operator
    //***********************************************************************

    public static BigInteger operator ++(BigInteger bi1)
    {
      BigInteger result = new BigInteger(bi1);

      long val, carry = 1;
      int index = 0;

      while (carry != 0 && index < maxLength) {
        val = (long) (result.data[index]);
        val++;

        result.data[index] = (uint) (val & 0xFFFFFFFF);
        carry = val >> 32;

        index++;
      }

      if (index > result.dataLength)
        result.dataLength = index;
      else {
        while (result.dataLength > 1
               && result.data[result.dataLength - 1] == 0)
          result.dataLength--;
      }

      // overflow check
      int lastPos = maxLength - 1;

      // overflow if initial value was +ve but ++ caused a sign
      // change to negative.

      if ((bi1.data[lastPos] & 0x80000000) == 0 &&
          (result.data[lastPos] & 0x80000000) !=
          (bi1.data[lastPos] & 0x80000000)) {
        throw(new ArithmeticException("Overflow in ++."));
      }
      return result;
    }
    //***********************************************************************
    // Overloading of subtraction operator
    //***********************************************************************

    public static BigInteger operator -(BigInteger bi1,
                                        BigInteger bi2)
    {
      BigInteger result = new BigInteger();

      result.dataLength =
        (bi1.dataLength >
         bi2.dataLength) ? bi1.dataLength : bi2.dataLength;

      long carryIn = 0;
      for (int i = 0; i < result.dataLength; i++) {
        long diff;

        diff = (long) bi1.data[i] - (long) bi2.data[i] - carryIn;
        result.data[i] = (uint) (diff & 0xFFFFFFFF);

        if (diff < 0)
          carryIn = 1;
        else
          carryIn = 0;
      }

      // roll over to negative
      if (carryIn != 0) {
        for (int i = result.dataLength; i < maxLength; i++)
          result.data[i] = 0xFFFFFFFF;
        result.dataLength = maxLength;
      }

      // fixed in v1.03 to give correct datalength for a - (-b)
      while (result.dataLength > 1
             && result.data[result.dataLength - 1] == 0)
        result.dataLength--;

      // overflow check

      int lastPos = maxLength - 1;
      if ((bi1.data[lastPos] & 0x80000000) !=
          (bi2.data[lastPos] & 0x80000000)
          && (result.data[lastPos] & 0x80000000) !=
          (bi1.data[lastPos] & 0x80000000)) {
        throw(new ArithmeticException());
      }

      return result;
    }
    //***********************************************************************
    // Constructor (Default value provided by BigInteger)
    //***********************************************************************

    public BigInteger(BigInteger bi)
    {
      data = new uint[maxLength];

      dataLength = bi.dataLength;

      for (int i = 0; i < dataLength; i++)
        data[i] = bi.data[i];
    }
    //***********************************************************************
    // Overloading of multiplication operator
    //***********************************************************************

    public static BigInteger operator *(BigInteger bi1,
                                        BigInteger bi2)
    {
      int lastPos = maxLength - 1;
      bool bi1Neg = false, bi2Neg = false;

      // take the absolute value of the inputs
      try {
        if ((bi1.data[lastPos] & 0x80000000) != 0)      // bi1 negative
        {
          bi1Neg = true;
          bi1 = -bi1;
        }
        if ((bi2.data[lastPos] & 0x80000000) != 0)      // bi2 negative
        {
          bi2Neg = true;
          bi2 = -bi2;
        }
      }
      catch(Exception) {
      }

      BigInteger result = new BigInteger();

      // multiply the absolute values
      try {
        for (int i = 0; i < bi1.dataLength; i++) {
          if (bi1.data[i] == 0)
            continue;

          ulong mcarry = 0;
          for (int j = 0, k = i; j < bi2.dataLength; j++, k++) {
            // k = i + j
            ulong val = ((ulong) bi1.data[i] * (ulong) bi2.data[j]) +
                        (ulong) result.data[k] + mcarry;

            result.data[k] = (uint) (val & 0xFFFFFFFF);
            mcarry = (val >> 32);
          }

          if (mcarry != 0)
            result.data[i + bi2.dataLength] = (uint) mcarry;
        }
      }
      catch(Exception) {
        throw(new ArithmeticException("Multiplication overflow."));
      }


      result.dataLength = bi1.dataLength + bi2.dataLength;
      if (result.dataLength > maxLength)
        result.dataLength = maxLength;

      while (result.dataLength > 1
             && result.data[result.dataLength - 1] == 0)
        result.dataLength--;

      // overflow check (result is -ve)
      if ((result.data[lastPos] & 0x80000000) != 0) {
        if (bi1Neg != bi2Neg && result.data[lastPos] == 0x80000000)     // different sign
        {
          // handle the special case where multiplication produces
          // a max negative number in 2's complement.

          if (result.dataLength == 1)
            return result;
          else {
            bool isMaxNeg = true;
            for (int i = 0; i < result.dataLength - 1 && isMaxNeg;
                 i++) {
              if (result.data[i] != 0)
                isMaxNeg = false;
            }

            if (isMaxNeg)
              return result;
          }
        }

        throw(new ArithmeticException("Multiplication overflow."));
      }

      // if input has different signs, then result is -ve
      if (bi1Neg != bi2Neg)
        return -result;

      return result;
    }
    //***********************************************************************
    // Tests the correct implementation of the modulo exponential function
    // using RSA encryption and decryption (using pre-computed encryption and
    // decryption keys).
    //***********************************************************************

    public static void RSATest(int rounds)
    {
      Random rand = new Random(1);
      byte[] val = new byte[64];

      // private and public key
      BigInteger bi_e =
        new
        BigInteger
        ("a932b948feed4fb2b692609bd22164fc9edb59fae7880cc1eaff7b3c9626b7e5b241c27a974833b2622ebe09beb451917663d47232488f23a117fc97720f1e7",
         16);
      BigInteger bi_d =
        new
        BigInteger
        ("4adf2f7a89da93248509347d2ae506d683dd3a16357e859a980c4f77a4e2f7a01fae289f13a851df6e9db5adaa60bfd2b162bbbe31f7c8f828261a6839311929d2cef4f864dde65e556ce43c89bbbf9f1ac5511315847ce9cc8dc92470a747b8792d6a83b0092d2e5ebaf852c85cacf34278efa99160f2f8aa7ee7214de07b7",
         16);
      BigInteger bi_n =
        new
        BigInteger
        ("e8e77781f36a7b3188d711c2190b560f205a52391b3479cdb99fa010745cbeba5f2adc08e1de6bf38398a0487c4a73610d94ec36f17f3f46ad75e17bc1adfec99839589f45f95ccc94cb2a5c500b477eb3323d8cfab0c8458c96f0147a45d27e45a4d11d54d77684f65d48f15fafcc1ba208e71e921b9bd9017c16a5231af7f",
         16);

      Console.Error.WriteLine("e =\n" + bi_e.ToString(10));
      Console.Error.WriteLine("\nd =\n" + bi_d.ToString(10));
      Console.Error.WriteLine("\nn =\n" + bi_n.ToString(10) + "\n");

      for (int count = 0; count < rounds; count++) {
        // generate data of random length
        int t1 = 0;
        while (t1 == 0)
          t1 = (int) (rand.NextDouble() * 65);

        bool done = false;
        while (!done) {
          for (int i = 0; i < 64; i++) {
            if (i < t1)
              val[i] = (byte) (rand.NextDouble() * 256);
            else
              val[i] = 0;

            if (val[i] != 0)
              done = true;
          }
        }

        while (val[0] == 0)
          val[0] = (byte) (rand.NextDouble() * 256);

        Console.Write("Round = " + count);

        // encrypt and decrypt data
        BigInteger bi_data = new BigInteger(val, t1);
        BigInteger bi_encrypted = bi_data.modPow(bi_e, bi_n);
        BigInteger bi_decrypted = bi_encrypted.modPow(bi_d, bi_n);

        // compare
        if (bi_decrypted != bi_data) {
          Console.Error.WriteLine("\nError at round " + count);
          Console.Error.WriteLine(bi_data + "\n");
          return;
        }
        Console.Error.WriteLine(" <PASSED>.");
      }

    }
    //***********************************************************************
    // Overloading of unary >> operators
    //***********************************************************************

    public static BigInteger operator >>(BigInteger bi1, int shiftVal)
    {
      BigInteger result = new BigInteger(bi1);
      result.dataLength = shiftRight(result.data, shiftVal);


      if ((bi1.data[maxLength - 1] & 0x80000000) != 0)  // negative
      {
        for (int i = maxLength - 1; i >= result.dataLength; i--)
          result.data[i] = 0xFFFFFFFF;

        uint mask = 0x80000000;
        for (int i = 0; i < 32; i++) {
          if ((result.data[result.dataLength - 1] & mask) != 0)
            break;

          result.data[result.dataLength - 1] |= mask;
          mask >>= 1;
        }
        result.dataLength = maxLength;
      }

      return result;
    }
    //***********************************************************************
    // Tests the correct implementation of the modulo exponential and
    // inverse modulo functions using RSA encryption and decryption.  The two
    // pseudoprimes p and q are fixed, but the two RSA keys are generated
    // for each round of testing.
    //***********************************************************************

    public static void RSATest2(int rounds)
    {
      Random rand = new Random();
      byte[] val = new byte[64];

      byte[] pseudoPrime1 = {
                              (byte) 0x85, (byte) 0x84, (byte) 0x64, (byte) 0xFD,
                              (byte) 0x70, (byte) 0x6A, (byte) 0x9F, (byte) 0xF0,
                              (byte) 0x94, (byte) 0x0C, (byte) 0x3E, (byte) 0x2C,
                              (byte) 0x74, (byte) 0x34, (byte) 0x05, (byte) 0xC9,
                              (byte) 0x55, (byte) 0xB3, (byte) 0x85, (byte) 0x32,
                              (byte) 0x98, (byte) 0x71, (byte) 0xF9, (byte) 0x41,
                              (byte) 0x21, (byte) 0x5F, (byte) 0x02, (byte) 0x9E,
                              (byte) 0xEA, (byte) 0x56, (byte) 0x8D, (byte) 0x8C,
                              (byte) 0x44, (byte) 0xCC, (byte) 0xEE, (byte) 0xEE,
                              (byte) 0x3D, (byte) 0x2C, (byte) 0x9D, (byte) 0x2C,
                              (byte) 0x12, (byte) 0x41, (byte) 0x1E, (byte) 0xF1,
                              (byte) 0xC5, (byte) 0x32, (byte) 0xC3, (byte) 0xAA,
                              (byte) 0x31, (byte) 0x4A, (byte) 0x52, (byte) 0xD8,
                              (byte) 0xE8, (byte) 0xAF, (byte) 0x42, (byte) 0xF4,
                              (byte) 0x72, (byte) 0xA1, (byte) 0x2A, (byte) 0x0D,
                              (byte) 0x97, (byte) 0xB1, (byte) 0x31, (byte) 0xB3,};

      byte[] pseudoPrime2 = {
                              (byte) 0x99, (byte) 0x98, (byte) 0xCA, (byte) 0xB8,
                              (byte) 0x5E, (byte) 0xD7, (byte) 0xE5, (byte) 0xDC,
                              (byte) 0x28, (byte) 0x5C, (byte) 0x6F, (byte) 0x0E,
                              (byte) 0x15, (byte) 0x09, (byte) 0x59, (byte) 0x6E,
                              (byte) 0x84, (byte) 0xF3, (byte) 0x81, (byte) 0xCD,
                              (byte) 0xDE, (byte) 0x42, (byte) 0xDC, (byte) 0x93,
                              (byte) 0xC2, (byte) 0x7A, (byte) 0x62, (byte) 0xAC,
                              (byte) 0x6C, (byte) 0xAF, (byte) 0xDE, (byte) 0x74,
                              (byte) 0xE3, (byte) 0xCB, (byte) 0x60, (byte) 0x20,
                              (byte) 0x38, (byte) 0x9C, (byte) 0x21, (byte) 0xC3,
                              (byte) 0xDC, (byte) 0xC8, (byte) 0xA2, (byte) 0x4D,
                              (byte) 0xC6, (byte) 0x2A, (byte) 0x35, (byte) 0x7F,
                              (byte) 0xF3, (byte) 0xA9, (byte) 0xE8, (byte) 0x1D,
                              (byte) 0x7B, (byte) 0x2C, (byte) 0x78, (byte) 0xFA,
                              (byte) 0xB8, (byte) 0x02, (byte) 0x55, (byte) 0x80,
                              (byte) 0x9B, (byte) 0xC2, (byte) 0xA5, (byte) 0xCB,};


      BigInteger bi_p = new BigInteger(pseudoPrime1);
      BigInteger bi_q = new BigInteger(pseudoPrime2);
      BigInteger bi_pq = (bi_p - 1) * (bi_q - 1);
      BigInteger bi_n = bi_p * bi_q;

      for (int count = 0; count < rounds; count++) {
        // generate private and public key
        BigInteger bi_e = bi_pq.genCoPrime(512, rand);
        BigInteger bi_d = bi_e.modInverse(bi_pq);

        Console.Error.WriteLine("\ne =\n" + bi_e.ToString(10));
        Console.Error.WriteLine("\nd =\n" + bi_d.ToString(10));
        Console.Error.WriteLine("\nn =\n" + bi_n.ToString(10) + "\n");

        // generate data of random length
        int t1 = 0;
        while (t1 == 0)
          t1 = (int) (rand.NextDouble() * 65);

        bool done = false;
        while (!done) {
          for (int i = 0; i < 64; i++) {
            if (i < t1)
              val[i] = (byte) (rand.NextDouble() * 256);
            else
              val[i] = 0;

            if (val[i] != 0)
              done = true;
          }
        }

        while (val[0] == 0)
          val[0] = (byte) (rand.NextDouble() * 256);

        Console.Write("Round = " + count);

        // encrypt and decrypt data
        BigInteger bi_data = new BigInteger(val, t1);
        BigInteger bi_encrypted = bi_data.modPow(bi_e, bi_n);
        BigInteger bi_decrypted = bi_encrypted.modPow(bi_d, bi_n);

        // compare
        if (bi_decrypted != bi_data) {
          Console.Error.WriteLine("\nError at round " + count);
          Console.Error.WriteLine(bi_data + "\n");
          return;
        }
        Console.Error.WriteLine(" <PASSED>.");
      }

    }
Beispiel #23
0
 public virtual BigInteger ToBigInteger()
 {
   if( null == _big_int ) {
     _big_int = new BigInteger(_buffer);
   }
   return _big_int;
 }
    //***********************************************************************
    // Tests the correct implementation of sqrt() method.
    //***********************************************************************

    public static void SqrtTest(int rounds)
    {
      Random rand = new Random();
      for (int count = 0; count < rounds; count++) {
        // generate data of random length
        int t1 = 0;
        while (t1 == 0)
          t1 = (int) (rand.NextDouble() * 1024);

        Console.Write("Round = " + count);

        BigInteger a = new BigInteger();
        a.genRandomBits(t1, rand);

        BigInteger b = a.sqrt();
        BigInteger c = (b + 1) * (b + 1);

        // check that b is the largest integer such that b*b <= a
        if (c <= a) {
          Console.Error.WriteLine("\nError at round " + count);
          Console.Error.WriteLine(a + "\n");
          return;
        }
        Console.Error.WriteLine(" <PASSED>.");
      }
    }
Beispiel #25
0
 public void Test() {
   System.Random r = new System.Random();
   for(int i = 0; i < 1024; i++) {
     //Test ClassOf and SetClass:
     int c = r.Next(160);
     byte[] buf0 = new byte[Address.MemSize];
     //Fill it with junk
     r.NextBytes(buf0);
     Address.SetClass(buf0, c);
     int c2 = Address.ClassOf(MemBlock.Reference(buf0, 0, Address.MemSize));
     Assert.AreEqual(c,c2, "Class Round Trip");
     //Test BigInteger stuff:
     int size = r.Next(1, MemSize + 1);
     byte[] buf1 = new byte[size];
     r.NextBytes(buf1);
     BigInteger b1 = new BigInteger(buf1);
     byte[] buf2 = Address.ConvertToAddressBuffer(b1);
     //Check to see if the bytes are equivalent:
     int min_len = System.Math.Min(buf1.Length, buf2.Length);
     bool all_eq = true;
     for(int j = 0; j < min_len; j++) {
       all_eq = all_eq
               && (buf2[buf2.Length - j - 1] == buf1[buf1.Length - j - 1]);
     }
     if( !all_eq ) {
       System.Console.Error.WriteLine("Buf1: ");
       foreach(byte b in buf1) {
         System.Console.Write("{0} ",b);
       }
       System.Console.Error.WriteLine();
       System.Console.Error.WriteLine("Buf2: ");
       foreach(byte b in buf2) {
         System.Console.Write("{0} ",b);
       }
       System.Console.Error.WriteLine();
     }
     Assert.IsTrue(all_eq, "bytes are equivalent");
     BigInteger b2 = new BigInteger(buf2);
     Assert.AreEqual(b1, b2, "BigInteger round trip");
   }
 }
    public static void Main(string[] args)
    {
      // Known problem -> these two pseudoprimes passes my implementation of
      // primality test but failed in JDK's isProbablePrime test.

      byte[] pseudoPrime1 = {
                              (byte) 0x00,
                              (byte) 0x85, (byte) 0x84, (byte) 0x64, (byte) 0xFD,
                              (byte) 0x70, (byte) 0x6A, (byte) 0x9F, (byte) 0xF0,
                              (byte) 0x94, (byte) 0x0C, (byte) 0x3E, (byte) 0x2C,
                              (byte) 0x74, (byte) 0x34, (byte) 0x05, (byte) 0xC9,
                              (byte) 0x55, (byte) 0xB3, (byte) 0x85, (byte) 0x32,
                              (byte) 0x98, (byte) 0x71, (byte) 0xF9, (byte) 0x41,
                              (byte) 0x21, (byte) 0x5F, (byte) 0x02, (byte) 0x9E,
                              (byte) 0xEA, (byte) 0x56, (byte) 0x8D, (byte) 0x8C,
                              (byte) 0x44, (byte) 0xCC, (byte) 0xEE, (byte) 0xEE,
                              (byte) 0x3D, (byte) 0x2C, (byte) 0x9D, (byte) 0x2C,
                              (byte) 0x12, (byte) 0x41, (byte) 0x1E, (byte) 0xF1,
                              (byte) 0xC5, (byte) 0x32, (byte) 0xC3, (byte) 0xAA,
                              (byte) 0x31, (byte) 0x4A, (byte) 0x52, (byte) 0xD8,
                              (byte) 0xE8, (byte) 0xAF, (byte) 0x42, (byte) 0xF4,
                              (byte) 0x72, (byte) 0xA1, (byte) 0x2A, (byte) 0x0D,
                              (byte) 0x97, (byte) 0xB1, (byte) 0x31, (byte) 0xB3,};

      byte[] pseudoPrime2 = {
                              (byte) 0x00,
                              (byte) 0x99, (byte) 0x98, (byte) 0xCA, (byte) 0xB8,
                              (byte) 0x5E, (byte) 0xD7, (byte) 0xE5, (byte) 0xDC,
                              (byte) 0x28, (byte) 0x5C, (byte) 0x6F, (byte) 0x0E,
                              (byte) 0x15, (byte) 0x09, (byte) 0x59, (byte) 0x6E,
                              (byte) 0x84, (byte) 0xF3, (byte) 0x81, (byte) 0xCD,
                              (byte) 0xDE, (byte) 0x42, (byte) 0xDC, (byte) 0x93,
                              (byte) 0xC2, (byte) 0x7A, (byte) 0x62, (byte) 0xAC,
                              (byte) 0x6C, (byte) 0xAF, (byte) 0xDE, (byte) 0x74,
                              (byte) 0xE3, (byte) 0xCB, (byte) 0x60, (byte) 0x20,
                              (byte) 0x38, (byte) 0x9C, (byte) 0x21, (byte) 0xC3,
                              (byte) 0xDC, (byte) 0xC8, (byte) 0xA2, (byte) 0x4D,
                              (byte) 0xC6, (byte) 0x2A, (byte) 0x35, (byte) 0x7F,
                              (byte) 0xF3, (byte) 0xA9, (byte) 0xE8, (byte) 0x1D,
                              (byte) 0x7B, (byte) 0x2C, (byte) 0x78, (byte) 0xFA,
                              (byte) 0xB8, (byte) 0x02, (byte) 0x55, (byte) 0x80,
                              (byte) 0x9B, (byte) 0xC2, (byte) 0xA5, (byte) 0xCB,};

      Console.
      WriteLine("List of primes < 2000\n---------------------");
      int limit = 100, count = 0;
      for (int i = 0; i < 2000; i++) {
        if (i >= limit) {
          Console.Error.WriteLine();
          limit += 100;
        }

        BigInteger p = new BigInteger(-i);

        if (p.isProbablePrime()) {
          Console.Write(i + ", ");
          count++;
        }
      }
      Console.Error.WriteLine("\nCount = " + count);


      BigInteger bi1 = new BigInteger(pseudoPrime1);
      Console.Error.WriteLine("\n\nPrimality testing for\n" +
                        bi1.ToString() + "\n");
      Console.Error.WriteLine("SolovayStrassenTest(5) = " +
                        bi1.SolovayStrassenTest(5));
      Console.Error.WriteLine("RabinMillerTest(5) = " +
                        bi1.RabinMillerTest(5));
      Console.Error.WriteLine("FermatLittleTest(5) = " +
                        bi1.FermatLittleTest(5));
      Console.Error.WriteLine("isProbablePrime() = " +
                        bi1.isProbablePrime());
      /* POB: added the above also for pseudoPrime2 to clear compiler warning */
      bi1 = new BigInteger(pseudoPrime2);
      Console.Error.WriteLine("\n\nPrimality testing for\n" +
                        bi1.ToString() + "\n");
      Console.Error.WriteLine("SolovayStrassenTest(5) = " +
                        bi1.SolovayStrassenTest(5));
      Console.Error.WriteLine("RabinMillerTest(5) = " +
                        bi1.RabinMillerTest(5));
      Console.Error.WriteLine("FermatLittleTest(5) = " +
                        bi1.FermatLittleTest(5));
      Console.Error.WriteLine("isProbablePrime() = " +
                        bi1.isProbablePrime());

      Console.Write("\nGenerating 512-bits random pseudoprime. . .");
      Random rand = new Random();
      BigInteger prime = BigInteger.genPseudoPrime(512, 5, rand);
      Console.Error.WriteLine("\n" + prime);

      //int dwStart = System.Environment.TickCount;
      //BigInteger.MulDivTest(100000);
      //BigInteger.RSATest(10);
      //BigInteger.RSATest2(10);
      //Console.Error.WriteLine(System.Environment.TickCount - dwStart);

    }
    //***********************************************************************
    // Constructor (Default value provided by a string of digits of the
    //              specified base)
    //
    // Example (base 10)
    // -----------------
    // To initialize "a" with the default value of 1234 in base 10
    //      BigInteger a = new BigInteger("1234", 10)
    //
    // To initialize "a" with the default value of -1234
    //      BigInteger a = new BigInteger("-1234", 10)
    //
    // Example (base 16)
    // -----------------
    // To initialize "a" with the default value of 0x1D4F in base 16
    //      BigInteger a = new BigInteger("1D4F", 16)
    //
    // To initialize "a" with the default value of -0x1D4F
    //      BigInteger a = new BigInteger("-1D4F", 16)
    //
    // Note that string values are specified in the <sign><magnitude>
    // format.
    //
    //***********************************************************************

    public BigInteger(string value, int radix)
    {
      BigInteger multiplier = new BigInteger(1);
      BigInteger result = new BigInteger();
      value = (value.ToUpper()).Trim();
      int limit = 0;

      if (value[0] == '-')
        limit = 1;

      for (int i = value.Length - 1; i >= limit; i--) {
        int posVal = (int) value[i];

        if (posVal >= '0' && posVal <= '9')
          posVal -= '0';
        else if (posVal >= 'A' && posVal <= 'Z')
          posVal = (posVal - 'A') + 10;
        else
          posVal = 9999999;     // arbitrary large


        if (posVal >= radix)
          throw(new
                ArithmeticException
                ("Invalid string in constructor."));
        else {
          if (value[0] == '-')
            posVal = -posVal;

          result = result + (multiplier * posVal);

          if ((i - 1) >= limit)
            multiplier = multiplier * radix;
        }
      }

      if (value[0] == '-')      // negative values
      {
        if ((result.data[maxLength - 1] & 0x80000000) == 0)
          throw(new
                ArithmeticException
                ("Negative underflow in constructor."));
      }
      else         // positive values
      {
        if ((result.data[maxLength - 1] & 0x80000000) != 0)
          throw(new
                ArithmeticException
                ("Positive overflow in constructor."));
      }

      data = new uint[maxLength];
      for (int i = 0; i < result.dataLength; i++)
        data[i] = result.data[i];

      dataLength = result.dataLength;
    }
    //***********************************************************************
    // Overloading of addition operator
    //***********************************************************************

    public static BigInteger operator +(BigInteger bi1,
                                        BigInteger bi2)
    {
      BigInteger result = new BigInteger();

      result.dataLength =
        (bi1.dataLength >
         bi2.dataLength) ? bi1.dataLength : bi2.dataLength;

      long carry = 0;
      for (int i = 0; i < result.dataLength; i++) {
        long sum = (long) bi1.data[i] + (long) bi2.data[i] + carry;
        carry = sum >> 32;
        result.data[i] = (uint) (sum & 0xFFFFFFFF);
      }

      if (carry != 0 && result.dataLength < maxLength) {
        result.data[result.dataLength] = (uint) (carry);
        result.dataLength++;
      }

      while (result.dataLength > 1
             && result.data[result.dataLength - 1] == 0)
        result.dataLength--;


      // overflow check
      int lastPos = maxLength - 1;
      if ((bi1.data[lastPos] & 0x80000000) ==
          (bi2.data[lastPos] & 0x80000000)
          && (result.data[lastPos] & 0x80000000) !=
          (bi1.data[lastPos] & 0x80000000)) {
        throw(new ArithmeticException());
      }

      return result;
    }
Beispiel #29
0
 public AHAddress(BigInteger big_int):base(big_int)
 {
   if (ClassOf(_buffer) != this.Class) {
     throw new System.
     ArgumentException("Class of address is not my class:  ",
                       this.ToString());
   }
 }
    private bool LucasStrongTestHelper(BigInteger thisVal)
    {
      // Do the test (selects D based on Selfridge)
      // Let D be the first element of the sequence
      // 5, -7, 9, -11, 13, ... for which J(D,n) = -1
      // Let P = 1, Q = (1-D) / 4

      long D = 5, sign = -1, dCount = 0;
      bool done = false;

      while (!done) {
        int Jresult = BigInteger.Jacobi(D, thisVal);

        if (Jresult == -1)
          done = true;  // J(D, this) = 1
        else {
          if (Jresult == 0 && Math.Abs(D) < thisVal)    // divisor found
            return false;

          if (dCount == 20) {
            // check for square
            BigInteger root = thisVal.sqrt();
            if (root * root == thisVal)
              return false;
          }

          //Console.Error.WriteLine(D);
          D = (Math.Abs(D) + 2) * sign;
          sign = -sign;
        }
        dCount++;
      }

      long Q = (1 - D) >> 2;

      /*
       * Console.Error.WriteLine("D = " + D);
       * Console.Error.WriteLine("Q = " + Q);
       * Console.Error.WriteLine("(n,D) = " + thisVal.gcd(D));
       * Console.Error.WriteLine("(n,Q) = " + thisVal.gcd(Q));
       * Console.Error.WriteLine("J(D|n) = " + BigInteger.Jacobi(D, thisVal));
       */

      BigInteger p_add1 = thisVal + 1;
      int s = 0;

      for (int index = 0; index < p_add1.dataLength; index++) {
        uint mask = 0x01;

        for (int i = 0; i < 32; i++) {
          if ((p_add1.data[index] & mask) != 0) {
            index = p_add1.dataLength;  // to break the outer loop
            break;
          }
          mask <<= 1;
          s++;
        }
      }

      BigInteger t = p_add1 >> s;

      // calculate constant = b^(2k) / m
      // for Barrett Reduction
      BigInteger constant = new BigInteger();

      int nLen = thisVal.dataLength << 1;
      constant.data[nLen] = 0x00000001;
      constant.dataLength = nLen + 1;

      constant = constant / thisVal;

      BigInteger[] lucas =
        LucasSequenceHelper(1, Q, t, thisVal, constant, 0);
      bool isPrime = false;

      if ((lucas[0].dataLength == 1 && lucas[0].data[0] == 0) ||
          (lucas[1].dataLength == 1 && lucas[1].data[0] == 0)) {
        // u(t) = 0 or V(t) = 0
        isPrime = true;
      }

      for (int i = 1; i < s; i++) {
        if (!isPrime) {
          // doubling of index
          lucas[1] =
            thisVal.BarrettReduction(lucas[1] * lucas[1], thisVal,
                                     constant);
          lucas[1] = (lucas[1] - (lucas[2] << 1)) % thisVal;

          //lucas[1] = ((lucas[1] * lucas[1]) - (lucas[2] << 1)) % thisVal;

          if ((lucas[1].dataLength == 1 && lucas[1].data[0] == 0))
            isPrime = true;
        }

        lucas[2] = thisVal.BarrettReduction(lucas[2] * lucas[2], thisVal, constant);    //Q^k
      }


      if (isPrime) // additional checks for composite numbers
      {
        // If n is prime and gcd(n, Q) == 1, then
        // Q^((n+1)/2) = Q * Q^((n-1)/2) is congruent to (Q * J(Q, n)) mod n

        BigInteger g = thisVal.gcd(Q);
        if (g.dataLength == 1 && g.data[0] == 1)        // gcd(this, Q) == 1
        {
          if ((lucas[2].data[maxLength - 1] & 0x80000000) != 0)
            lucas[2] += thisVal;

          BigInteger temp =
            (Q * BigInteger.Jacobi(Q, thisVal)) % thisVal;
          if ((temp.data[maxLength - 1] & 0x80000000) != 0)
            temp += thisVal;

          if (lucas[2] != temp)
            isPrime = false;
        }
      }

      return isPrime;
    }