Ejemplo n.º 1
0
        public static BigInt ModPower(BigInt a, BigInt b, BigInt c)
        {       // returns (a ^ b) mod c
            // eg 28 ^ 23 mod 55 = 7

            // There's a trick to this.  a ^ b is usually way too big to handle, so we break it
            // into pieces, using the fact that xy mod c = ( x mod c )( y mod c ) mod c.
            // Please see www.carljohansen.co.uk/rsa for a full explanation.

            a.EnsureInitialized();
            b.EnsureInitialized();
            c.EnsureInitialized();

            int    numBdigits = b.NumDigits;
            BigInt prevResult, finalProduct = 1;
            int    i;

            BigInt[] arrResidues = new BigInt[numBdigits + 1];
            BigInt   accumulation2, accumulation4, accumulation8;

            arrResidues[0] = a;
            prevResult     = arrResidues[0];

            for (i = 1; i < numBdigits; i++)
            {
                //have to calculate (prevResult^10) mod c.  This is (prevResult^2^2^2) mod c * (prevResult^2) mod c
                accumulation2 = (prevResult * prevResult) % c;
                accumulation4 = (accumulation2 * accumulation2) % c;
                accumulation8 = (accumulation4 * accumulation4) % c;

                arrResidues[i] = (accumulation2 * accumulation8) % c;
                prevResult     = arrResidues[i];
            }

            for (i = numBdigits - 1; i >= 0; i--)
            {
                int currChunk = b.GetChunkAbsolute(i / 3);
                int currDigit;
                if (i % 3 == 0)
                {
                    currDigit = currChunk % 10;
                }
                else if (i % 3 == 1)
                {
                    currDigit = (currChunk % 100) / 10;
                }
                else
                {
                    currDigit = currChunk / 100;
                }
                for (int j = 0; j < currDigit; j++)
                {
                    finalProduct *= arrResidues[i];
                    finalProduct %= c;
                }
            }

            return(finalProduct);
        }
Ejemplo n.º 2
0
        /// <summary>
        /// Compares two BigInts
        /// </summary>
        /// <returns>1 if a > b, 0 if a == b, -1 if a is less than b</returns>
        public static short Compare(BigInt a, BigInt b)
        {
            a.EnsureInitialized();
            b.EnsureInitialized();

            if (a.IsZero() && b.IsZero())
            {
                return(0);
            }

            if (a.Sign != b.Sign)
            {   //a and b have different signs
                if (a.Sign == 1)
                {
                    return(1);  //every positive number is bigger than every negative number
                }
                else
                {
                    return(-1); //and vice versa
                }
            }
            else if (a.NumDigits > b.NumDigits)
            {                   //a has more digits than b (a and b have same sign)
                return(a.Sign); // If both are positive then a > b.  If both are negative then a < b
            }
            else if (a.NumDigits < b.NumDigits)
            {                           //a has fewer digits than b (a and b have same sign)
                return((short)-a.Sign); // If both are positive then a < b.  If both are negative then a > b
            }
            else
            {
                short aChunk, bChunk;
                for (int i = a.NumChunks - 1; i >= 0; i--)
                {
                    aChunk = a.GetChunk(i);
                    bChunk = b.GetChunk(i);
                    if (aChunk < bChunk)
                    {
                        return(-1);
                    }
                    else if (aChunk > bChunk)
                    {
                        return(1);
                    }
                }
                //they must be equal
                return(0);
            }
        }
Ejemplo n.º 3
0
 public static void DivAndMod(BigInt a, BigInt b, out BigInt remainder, out BigInt result)
 {
     a.EnsureInitialized();
     b.EnsureInitialized();
     DivAndMod(DivModOperationType.DivAndMod, a, b, out remainder, out result);
 }