public void TestSetBit()
{
Assert.AreEqual(one, zero.SetBit(0));
Assert.AreEqual(one, one.SetBit(0));
Assert.AreEqual(three, two.SetBit(0));
Assert.AreEqual(two, zero.SetBit(1));
Assert.AreEqual(three, one.SetBit(1));
Assert.AreEqual(two, two.SetBit(1));
// TODO Tests for setting bits in negative numbers
// TODO Tests for setting extended bits
for (int i = 0; i < 10; ++i)
{
BigInteger n = new BigInteger(128, random);
for (int j = 0; j < 10; ++j)
{
int pos = random.Next(128);
BigInteger m = n.SetBit(pos);
bool test = m.ShiftRight(pos).Remainder(two).Equals(one);
Assert.IsTrue(test);
}
}
for (int i = 0; i < 100; ++i)
{
BigInteger pow2 = one.ShiftLeft(i);
BigInteger minusPow2 = pow2.Negate();
Assert.AreEqual(pow2, pow2.SetBit(i));
Assert.AreEqual(minusPow2, minusPow2.SetBit(i));
BigInteger bigI = BigInteger.ValueOf(i);
BigInteger negI = bigI.Negate();
for (int j = 0; j < 10; ++j)
{
string data = "i=" + i + ", j=" + j;
Assert.AreEqual(bigI.Or(one.ShiftLeft(j)), bigI.SetBit(j), data);
Assert.AreEqual(negI.Or(one.ShiftLeft(j)), negI.SetBit(j), data);
}
}
}
/**
* generate suitable parameters for DSA, in line with
* <i>FIPS 186-3 A.1 Generation of the FFC Primes p and q</i>.
*/
protected virtual DsaParameters GenerateParameters_FIPS186_3()
{
// A.1.1.2 Generation of the Probable Primes p and q Using an Approved Hash Function
IDigest d = digest;
int outlen = d.GetDigestSize() * 8;
// 1. Check that the (L, N) pair is in the list of acceptable (L, N pairs) (see Section 4.2). If
// the pair is not in the list, then return INVALID.
// Note: checked at initialisation
// 2. If (seedlen < N), then return INVALID.
// FIXME This should be configurable (must be >= N)
int seedlen = N;
byte[] seed = new byte[seedlen / 8];
// 3. n = ceiling(L ⁄ outlen) – 1.
int n = (L - 1) / outlen;
// 4. b = L – 1 – (n ∗ outlen).
int b = (L - 1) % outlen;
byte[] output = new byte[d.GetDigestSize()];
for (;;)
{
// 5. Get an arbitrary sequence of seedlen bits as the domain_parameter_seed.
random.NextBytes(seed);
// 6. U = Hash (domain_parameter_seed) mod 2^(N–1).
Hash(d, seed, output);
BigInteger U = new BigInteger(1, output).Mod(BigInteger.One.ShiftLeft(N - 1));
// 7. q = 2^(N–1) + U + 1 – ( U mod 2).
BigInteger q = U.SetBit(0).SetBit(N - 1);
// 8. Test whether or not q is prime as specified in Appendix C.3.
// TODO Review C.3 for primality checking
if (!q.IsProbablePrime(certainty))
{
// 9. If q is not a prime, then go to step 5.
continue;
}
// 10. offset = 1.
// Note: 'offset' value managed incrementally
byte[] offset = Arrays.Clone(seed);
// 11. For counter = 0 to (4L – 1) do
int counterLimit = 4 * L;
for (int counter = 0; counter < counterLimit; ++counter)
{
// 11.1 For j = 0 to n do
// Vj = Hash ((domain_parameter_seed + offset + j) mod 2^seedlen).
// 11.2 W = V0 + (V1 ∗ 2^outlen) + ... + (V^(n–1) ∗ 2^((n–1) ∗ outlen)) + ((Vn mod 2^b) ∗ 2^(n ∗ outlen)).
// TODO Assemble w as a byte array
BigInteger W = BigInteger.Zero;
for (int j = 0, exp = 0; j <= n; ++j, exp += outlen)
{
Inc(offset);
Hash(d, offset, output);
BigInteger Vj = new BigInteger(1, output);
if (j == n)
{
Vj = Vj.Mod(BigInteger.One.ShiftLeft(b));
}
W = W.Add(Vj.ShiftLeft(exp));
}
// 11.3 X = W + 2^(L–1). Comment: 0 ≤ W < 2L–1; hence, 2L–1 ≤ X < 2L.
BigInteger X = W.Add(BigInteger.One.ShiftLeft(L - 1));
// 11.4 c = X mod 2q.
BigInteger c = X.Mod(q.ShiftLeft(1));
// 11.5 p = X - (c - 1). Comment: p ≡ 1 (mod 2q).
BigInteger p = X.Subtract(c.Subtract(BigInteger.One));
// 11.6 If (p < 2^(L - 1)), then go to step 11.9
if (p.BitLength != L)
continue;
// 11.7 Test whether or not p is prime as specified in Appendix C.3.
// TODO Review C.3 for primality checking
if (p.IsProbablePrime(certainty))
{
// 11.8 If p is determined to be prime, then return VALID and the values of p, q and
// (optionally) the values of domain_parameter_seed and counter.
// TODO Make configurable (8-bit unsigned)?
if (usageIndex >= 0)
{
BigInteger g = CalculateGenerator_FIPS186_3_Verifiable(d, p, q, seed, usageIndex);
if (g != null)
return new DsaParameters(p, q, g, new DsaValidationParameters(seed, counter, usageIndex));
}
{
BigInteger g = CalculateGenerator_FIPS186_3_Unverifiable(p, q, random);
return new DsaParameters(p, q, g, new DsaValidationParameters(seed, counter));
}
}
// 11.9 offset = offset + n + 1. Comment: Increment offset; then, as part of
// the loop in step 11, increment counter; if
// counter < 4L, repeat steps 11.1 through 11.8.
// Note: 'offset' value already incremented in inner loop
}
// 12. Go to step 5.
}
}
