Example #1
0
        public bool RabinMillerTest(int certainty, Random random)
        {
            Debug.Assert(certainty > 0);
            Debug.Assert(BitLength > 2);
            Debug.Assert(TestBit(0));

            // let n = 1 + d . 2^s
            BigInteger n = this;
            int s = n.GetLowestSetBitMaskFirst(-1 << 1);
            Debug.Assert(s >= 1);
            BigInteger r = n.ShiftRight(s);

            // NOTE: Avoid conversion to/from Montgomery form and check for R/-R as result instead

            BigInteger montRadix = One.ShiftLeft(32 * n.magnitude.Length).Remainder(n);
            BigInteger minusMontRadix = n.Subtract(montRadix);

            do
            {
                BigInteger a;
                do
                {
                    a = new BigInteger(n.BitLength, random);
                }
                while (a.sign == 0 || a.CompareTo(n) >= 0
                    || a.IsEqualMagnitude(montRadix) || a.IsEqualMagnitude(minusMontRadix));

                BigInteger y = ModPowMonty(a, r, n, false);

                if (!y.Equals(montRadix))
                {
                    int j = 0;
                    while (!y.Equals(minusMontRadix))
                    {
                        if (++j == s)
                            return false;

                        y = ModPowMonty(y, Two, n, false);

                        if (y.Equals(montRadix))
                            return false;
                    }
                }

                certainty -= 2; // composites pass for only 1/4 possible 'a'
            }
            while (certainty > 0);

            return true;
        }