public void testInvertFq()
{
SecureRandom random = new SecureRandom();
// Verify an example from the NTRU tutorial
IntegerPolynomial a = new IntegerPolynomial(new int[] { -1, 1, 1, 0, -1, 0, 1, 0, 0, 1, -1 });
IntegerPolynomial b = a.InvertFq(32);
assertEqualsMod(new int[] { 5, 9, 6, 16, 4, 15, 16, 22, 20, 18, 30 }, b.coeffs, 32);
verifyInverse(a, b, 32);
// test 3 random polynomials
int numInvertible = 0;
while (numInvertible < 3)
{
a = DenseTernaryPolynomial.GenerateRandom(853, random);
b = a.InvertFq(2048);
if (b != null)
{
numInvertible++;
verifyInverse(a, b, 2048);
}
}
// test a non-invertible polynomial
a = new IntegerPolynomial(new int[] { -1, 0, 1, 1, 0, 0, -1, 0, -1, 0, 1 });
b = a.InvertFq(32);
Assert.IsNull(b);
}
public void testMult()
{
BigDecimalPolynomial a = new BigDecimalPolynomial(new BigIntPolynomial(new IntegerPolynomial(new int[] { 4, -1, 9, 2, 1, -5, 12, -7, 0, -9, 5 })));
BigDecimalPolynomial b = new BigDecimalPolynomial(new BigIntPolynomial(new IntegerPolynomial(new int[] { -6, 0, 0, 13, 3, -2, -4, 10, 11, 2, -1 })));
BigDecimalPolynomial c = a.Multiply(b);
decimal[] expectedCoeffs = new BigDecimalPolynomial(new BigIntPolynomial(new IntegerPolynomial(new int[] { 2, -189, 77, 124, -29, 0, -75, 124, -49, 267, 34 }))).getCoeffs();
decimal[] cCoeffs = c.getCoeffs();
Assert.AreEqual(expectedCoeffs.Length, cCoeffs.Length);
for (int i = 0; i != cCoeffs.Length; i++)
{
Assert.AreEqual(expectedCoeffs[i], cCoeffs[i]);
}
// multiply a polynomial by its inverse modulo 2048 and check that the result is 1
SecureRandom random = new SecureRandom();
IntegerPolynomial d, dInv;
do
{
d = DenseTernaryPolynomial.GenerateRandom(1001, 333, 334, random);
dInv = d.InvertFq(2048);
}while (dInv == null);
d.Mod(2048);
BigDecimalPolynomial e = new BigDecimalPolynomial(new BigIntPolynomial(d));
BigIntPolynomial f = new BigIntPolynomial(dInv);
IntegerPolynomial g = new IntegerPolynomial(e.Multiply(f).round());
g.ModPositive(2048);
Assert.True(g.EqualsOne());
}
public void testResultant()
{
SecureRandom random = new SecureRandom();
NTRUSigningKeyGenerationParameters parameters = NTRUSigningKeyGenerationParameters.APR2011_439;
IntegerPolynomial a = DenseTernaryPolynomial.GenerateRandom(parameters.N, parameters.d, parameters.d, random);
Resultant r = a.Resultant();
if (r.Rho.GetCoeffs().Length > parameters.N)
{
BigInteger[] trimmedArray = new BigInteger[parameters.N];
Array.Copy(r.Rho.GetCoeffs(), trimmedArray, parameters.N);
r.Rho.coeffs = trimmedArray;
}
verifyResultant(a, r);
a = new IntegerPolynomial(new int[] { 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 1, -1, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, -1, -1, 0, -1, 1, -1, 0, -1, 0, -1, -1, -1, 0, 0, 0, 1, 1, -1, -1, -1, 0, -1, -1, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 1, 0, 0, 1, 1, -1, 0, 1, -1, 0, 1, 0, 1, 0, -1, -1, 0, 1, 0, -1, 1, 1, 1, 1, 0, 0, -1, -1, 1, 0, 0, -1, -1, 0, -1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, -1, 0, 0, 0, 0, -1, 0, 0, 0, 1, 0, 1, 0, 1, -1, 0, 0, 1, 1, 1, 0, 0, 0, -1, 0, 0, 0, 0, 1, 0, 1, 0, -1, -1, 0, -1, -1, -1, 0, -1, -1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, -1, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, -1, -1, 0, -1, -1, 1, 1, 0, 0, -1, 1, 0, 0, 0, -1, 1, -1, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 1, 1, 0, 0, -1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, -1, 0, 1, 0, -1, -1, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 1, -1, 1, -1, -1, 1, -1, 0, 1, 0, 0, 0, 1, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, -1, 0, 1, -1, 0, 0, 1, 1, 0, 0, 1, 1, 0, -1, 0, -1, 1, -1, -1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, -1, 0, 0, 1, -1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, -1, -1, 0, 0, -1, 0, 1, 1, -1, 1, -1, 0, 0, 0, 1 });
r = a.Resultant();
if (r.Rho.GetCoeffs().Length > a.coeffs.Length)
{
BigInteger[] trimmedArray = new BigInteger[a.coeffs.Length];
Array.Copy(r.Rho.GetCoeffs(), trimmedArray, a.coeffs.Length);
r.Rho.coeffs = trimmedArray;
}
verifyResultant(a, r);
}
public void testFromToBinary3Tight()
{
int[] c = new int[] { 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 1, 0, 1, 0, -1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -1, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0 };
IntegerPolynomial poly1 = new IntegerPolynomial(c);
IntegerPolynomial poly2 = IntegerPolynomial.FromBinary3Tight(poly1.ToBinary3Tight(), c.Length);
Assert.True(poly1.coeffs.SequenceEqual(poly2.coeffs));
IntegerPolynomial poly3 = new IntegerPolynomial(new int[] { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, -1, -1, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 });
byte[] arr = poly3.ToBinary3Tight();
IntegerPolynomial poly4 = IntegerPolynomial.FromBinary3Tight(arr, 1499);
Assert.True(poly3.coeffs.SequenceEqual(poly4.coeffs));
IntegerPolynomial poly5 = new IntegerPolynomial(new int[] { 0, 0, 0, 1, -1, -1, -1 });
arr = poly5.ToBinary3Tight();
IntegerPolynomial poly6 = IntegerPolynomial.FromBinary3Tight(arr, 7);
Assert.True(poly5.coeffs.SequenceEqual(poly6.coeffs));
SecureRandom random = new SecureRandom();
for (int i = 0; i < 100; i++)
{
IntegerPolynomial poly7 = DenseTernaryPolynomial.GenerateRandom(157, random);
arr = poly7.ToBinary3Tight();
IntegerPolynomial poly8 = IntegerPolynomial.FromBinary3Tight(arr, 157);
Assert.True(poly7.coeffs.SequenceEqual(poly8.coeffs));
}
}
public void testEncodeDecodeMod3Tight()
{
SecureRandom random = new SecureRandom();
int[] coeffs = DenseTernaryPolynomial.GenerateRandom(1000, random).coeffs;
byte[] data = ArrayEncoder.EncodeMod3Tight(coeffs);
int[] coeffs2 = ArrayEncoder.DecodeMod3Tight(data, 1000);
Assert.True(coeffs.SequenceEqual(coeffs2));
}
/**
* Generates a "sparse" or "dense" polynomial containing numOnes ints equal to 1,
* numNegOnes int equal to -1, and the rest equal to 0.
*
* @param N
* @param numOnes
* @param numNegOnes
* @param sparse whether to create a {@link SparseTernaryPolynomial} or {@link DenseTernaryPolynomial}
* @return a ternary polynomial
*/
public static ITernaryPolynomial GenerateRandomTernary(int N, int numOnes, int numNegOnes, bool sparse, SecureRandom random)
{
if (sparse)
{
return(SparseTernaryPolynomial.GenerateRandom(N, numOnes, numNegOnes, random));
}
else
{
return(DenseTernaryPolynomial.GenerateRandom(N, numOnes, numNegOnes, random));
}
}
/// <remarks>
/// Generates the ephemeral secret polynomial 'g'.
/// </remarks>
private IntegerPolynomial GenerateG(IRandom Rng)
{
int N = _encParams.N;
int dg = _encParams.Dg;
while (true)
{
DenseTernaryPolynomial g = DenseTernaryPolynomial.GenerateRandom(N, dg, dg - 1, Rng);
if (g.IsInvertiblePow2())
{
return(g);
}
}
}
/// <remarks>
/// Generates the ephemeral secret polynomial 'g'.
/// </remarks>
private IntegerPolynomial GenerateG(IRandom RngEngine)
{
var N = this.m_ntruParams.N;
var dg = this.m_ntruParams.Dg;
while (true)
{
var g = DenseTernaryPolynomial.GenerateRandom(N, dg, dg - 1, RngEngine);
if (g.IsInvertiblePow2())
{
return(g);
}
}
}
/**
* tests mult(IntegerPolynomial) and mult(BigIntPolynomial)
*/
public void testMult()
{
SecureRandom random = new SecureRandom();
SparseTernaryPolynomial p1 = SparseTernaryPolynomial.GenerateRandom(1000, 500, 500, random);
IntegerPolynomial p2 = DenseTernaryPolynomial.GenerateRandom(1000, random);
IntegerPolynomial prod1 = p1.Multiply(p2);
IntegerPolynomial prod2 = p1.Multiply(p2);
Assert.AreEqual(prod1.coeffs, prod2.coeffs);
BigIntPolynomial p3 = new BigIntPolynomial(p2);
BigIntPolynomial prod3 = p1.Multiply(p3);
Assert.AreEqual((new BigIntPolynomial(prod1)).coeffs, prod3.coeffs);
}
public void testResultantMod()
{
int p = 46337; // prime; must be less than sqrt(2^31) or integer overflows will occur
IntegerPolynomial a = new IntegerPolynomial(new int[] { 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 1, -1, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, -1, -1, 0, -1, 1, -1, 0, -1, 0, -1, -1, -1, 0, 0, 0, 1, 1, -1, -1, -1, 0, -1, -1, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 1, 0, 0, 1, 1, -1, 0, 1, -1, 0, 1, 0, 1, 0, -1, -1, 0, 1, 0, -1, 1, 1, 1, 1, 0, 0, -1, -1, 1, 0, 0, -1, -1, 0, -1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, -1, 0, 0, 0, 0, -1, 0, 0, 0, 1, 0, 1, 0, 1, -1, 0, 0, 1, 1, 1, 0, 0, 0, -1, 0, 0, 0, 0, 1, 0, 1, 0, -1, -1, 0, -1, -1, -1, 0, -1, -1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, -1, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, -1, -1, 0, -1, -1, 1, 1, 0, 0, -1, 1, 0, 0, 0, -1, 1, -1, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 1, 1, 0, 0, -1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, -1, 0, 1, 0, -1, -1, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 1, -1, 1, -1, -1, 1, -1, 0, 1, 0, 0, 0, 1, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, -1, 0, 1, -1, 0, 0, 1, 1, 0, 0, 1, 1, 0, -1, 0, -1, 1, -1, -1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, -1, 0, 0, 1, -1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, -1, -1, 0, 0, -1, 0, 1, 1, -1, 1, -1, 0, 0, 0, 1 });
verifyResultant(a, a.Resultant(p), p);
SecureRandom random = new SecureRandom();
for (int i = 0; i < 10; i++)
{
a = DenseTernaryPolynomial.GenerateRandom(853, random);
verifyResultant(a, a.Resultant(p), p);
}
}
/// <summary>
/// Test the validity of the BigDecimalPolynomial implementation
/// </summary>
///
/// <returns>State</returns>
public string Test()
{
try
{
BigDecimalPolynomial a = CreateBigDecimalPolynomial(new int[] { 4, -1, 9, 2, 1, -5, 12, -7, 0, -9, 5 });
BigIntPolynomial b = new BigIntPolynomial(new IntegerPolynomial(new int[] { -6, 0, 0, 13, 3, -2, -4, 10, 11, 2, -1 }));
BigDecimalPolynomial c = a.Multiply(b);
if (!Compare.AreEqual(c.Coeffs, CreateBigDecimalPolynomial(new int[] { 2, -189, 77, 124, -29, 0, -75, 124, -49, 267, 34 }).Coeffs))
{
throw new Exception("The BigDecimalPolynomial test failed!");
}
// multiply a polynomial by its inverse modulo 2048 and check that the result is 1
IntegerPolynomial d, dInv;
CSPRng rng = new CSPRng();
do
{
d = DenseTernaryPolynomial.GenerateRandom(1001, 333, 334, rng);
dInv = d.InvertFq(2048);
} while (dInv == null);
d.Mod(2048);
BigDecimalPolynomial e = CreateBigDecimalPolynomial(d.Coeffs);
BigIntPolynomial f = new BigIntPolynomial(dInv);
IntegerPolynomial g = new IntegerPolynomial(e.Multiply(f).Round());
g.ModPositive(2048);
if (!g.EqualsOne())
{
throw new Exception("The BigDecimalPolynomial test failed!");
}
OnProgress(new TestEventArgs("Passed BigDecimalPolynomial tests"));
return(SUCCESS);
}
catch (Exception Ex)
{
string message = Ex.Message == null ? "" : Ex.Message;
throw new Exception(FAILURE + message);
}
}
public void testMult()
{
testMult(new int[] { 2 }, new int[] { -1 });
testMult(new int[] { 2, 0 }, new int[] { -1, 0 });
testMult(new int[] { 2, 0, 3 }, new int[] { -1, 0, 1 });
testMult(new int[] { 2, 0, 3, 1 }, new int[] { -1, 0, 1, 1 });
testMult(new int[] { 2, 0, 3, 1, 2 }, new int[] { -1, 0, 1, 1, 0 });
testMult(new int[] { 2, 0, 3, 1, 1, 5 }, new int[] { 1, -1, 1, 1, 0, 1 });
testMult(new int[] { 2, 0, 3, 1, 1, 5, 1, 4 }, new int[] { 1, 0, 1, 1, -1, 1, 0, -1 });
testMult(new int[] { 1368, 2047, 672, 871, 1662, 1352, 1099, 1608 }, new int[] { 1, 0, 1, 1, -1, 1, 0, -1 });
// test random polynomials
SecureRandom rng = new SecureRandom();
for (int i = 0; i < 10; i++)
{
int[] coeffs1 = new int[rng.NextInt(2000) + 1];
int[] coeffs2 = DenseTernaryPolynomial.GenerateRandom(coeffs1.Length, rng).coeffs;
testMult(coeffs1, coeffs2);
}
}
/// <summary>
/// Test the validity of the DenseTernaryPolynomial implementation
/// </summary>
///
/// <returns>State</returns>
public string Test()
{
try
{
CheckTernarity(PolynomialGeneratorForTesting.generateRandom(1499));
CSPRng rng = new CSPRng();
for (int i = 0; i < 10; i++)
{
int N = rng.Next(2000) + 10;
int numOnes = rng.Next(N);
int numNegOnes = rng.Next(N - numOnes);
CheckTernarity(DenseTernaryPolynomial.GenerateRandom(N, numOnes, numNegOnes, rng));
}
OnProgress(new TestEventArgs("Passed DenseTernaryPolynomial Ternarity"));
return(SUCCESS);
}
catch (Exception Ex)
{
string message = Ex.Message == null ? "" : Ex.Message;
throw new Exception(FAILURE + message);
}
}
public AsymmetricCipherKeyPair GenerateKeyPair()
{
int N = Parameters.N;
int q = Parameters.q;
int df = Parameters.df;
int df1 = Parameters.df1;
int df2 = Parameters.df2;
int df3 = Parameters.df3;
int dg = Parameters.dg;
bool fastFp = Parameters.fastFp;
bool sparse = Parameters.sparse;
IPolynomial t;
IntegerPolynomial fq;
IntegerPolynomial fp = null;
// choose a random f that is invertible mod 3 and q
while (true)
{
IntegerPolynomial f;
// choose random t, calculate f and fp
if (fastFp)
{
// if fastFp=true, f is always invertible mod 3
t = Parameters.polyType == (int)NTRUParameters.TERNARY_POLYNOMIAL_TYPE_SIMPLE ? Util.GenerateRandomTernary(N, df, df, sparse, Parameters.Random) : (IPolynomial)ProductFormPolynomial.GenerateRandom(N, df1, df2, df3, df3, Parameters.Random);
f = t.ToIntegerPolynomial();
f.Multiply(3);
f.coeffs[0] += 1;
}
else
{
t = Parameters.polyType == (int)NTRUParameters.TERNARY_POLYNOMIAL_TYPE_SIMPLE ? Util.GenerateRandomTernary(N, df, df - 1, sparse, Parameters.Random) : (IPolynomial)ProductFormPolynomial.GenerateRandom(N, df1, df2, df3, df3 - 1, Parameters.Random);
f = t.ToIntegerPolynomial();
fp = f.InvertF3();
if (fp == null)
{
continue;
}
}
fq = f.InvertFq(q);
if (fq == null)
{
continue;
}
break;
}
// if fastFp=true, fp=1
if (fastFp)
{
fp = new IntegerPolynomial(N);
fp.coeffs[0] = 1;
}
// choose a random g that is invertible mod q
DenseTernaryPolynomial g;
while (true)
{
g = DenseTernaryPolynomial.GenerateRandom(N, dg, dg - 1, Parameters.Random);
if (g.InvertFq(q) != null)
{
break;
}
}
IntegerPolynomial h = g.Multiply(fq, q);
h.Multiply3(q);
h.EnsurePositive(q);
g.Clear();
fq.Clear();
NTRUEncryptionPrivateKeyParameters priv = new NTRUEncryptionPrivateKeyParameters(h, t, fp, Parameters.GetEncryptionParameters());
NTRUEncryptionPublicKeyParameters pub = new NTRUEncryptionPublicKeyParameters(h, Parameters.GetEncryptionParameters());
return(new AsymmetricCipherKeyPair(pub, priv));
}
/**
* Creates a NtruSign basis consisting of polynomials <code>f, g, F, G, h</code>.<br/>
* If <code>KeyGenAlg=FLOAT</code>, the basis may not be valid and this method must be rerun if that is the case.<br/>
* @see #generateBoundedBasis()
*/
private FGBasis generateBasis()
{
int N = param.N;
int q = param.q;
int d = param.d;
int d1 = param.d1;
int d2 = param.d2;
int d3 = param.d3;
BasisType basisType = param.basisType;
IPolynomial f;
IntegerPolynomial fInt;
IPolynomial g;
IntegerPolynomial gInt;
IntegerPolynomial fq;
Resultant rf;
Resultant rg;
BigIntEuclidean r;
int _2n1 = 2 * N + 1;
bool primeCheck = param.primeCheck;
Random rng = new Random();
do
{
do
{
if (param.polyType == TernaryPolynomialType.SIMPLE)
{
f = DenseTernaryPolynomial.GenerateRandom(N, d + 1, d);
}
else
{
f = ProductFormPolynomial.GenerateRandom(N, d1, d2, d3 + 1, d3);
}
fInt = f.ToIntegerPolynomial();
} while (primeCheck && fInt.Resultant(_2n1).Res.Equals(BigInteger.Zero));
fq = fInt.InvertFq(q);
} while (fq == null);
rf = fInt.Resultant();
do
{
do
{
do
{
if (param.polyType == TernaryPolynomialType.SIMPLE)
{
g = DenseTernaryPolynomial.GenerateRandom(N, d + 1, d);
}
else
{
g = ProductFormPolynomial.GenerateRandom(N, d1, d2, d3 + 1, d3);
}
gInt = g.ToIntegerPolynomial();
} while (primeCheck && gInt.Resultant(_2n1).Res.Equals(BigInteger.Zero));
} while (!gInt.IsInvertiblePow2());
rg = gInt.Resultant();
r = BigIntEuclidean.Calculate(rf.Res, rg.Res);
} while (!r.GCD.Equals(BigInteger.One));
BigIntPolynomial A = rf.Rho.Clone();
A.Multiply(r.X.Multiply(BigInteger.ValueOf(q)));
BigIntPolynomial B = rg.Rho.Clone();
B.Multiply(r.Y.Multiply(BigInteger.ValueOf(-q)));
BigIntPolynomial C;
if (param.keyGenAlg == KeyGenAlg.RESULTANT)
{
int[] fRevCoeffs = new int[N];
int[] gRevCoeffs = new int[N];
fRevCoeffs[0] = fInt.Coeffs[0];
gRevCoeffs[0] = gInt.Coeffs[0];
for (int i = 1; i < N; i++)
{
fRevCoeffs[i] = fInt.Coeffs[N - i];
gRevCoeffs[i] = gInt.Coeffs[N - i];
}
IntegerPolynomial fRev = new IntegerPolynomial(fRevCoeffs);
IntegerPolynomial gRev = new IntegerPolynomial(gRevCoeffs);
IntegerPolynomial t = f.Multiply(fRev);
t.Add(g.Multiply(gRev));
Resultant rt = t.Resultant();
C = fRev.Multiply(B); // fRev.mult(B) is actually faster than new SparseTernaryPolynomial(fRev).mult(B), possibly due to cache locality?
C.Add(gRev.Multiply(A));
C = C.MultBig(rt.Rho);
C.Divide(rt.Res);
}
else // KeyGenAlg.FLOAT
// calculate ceil(log10(N))
{
int log10N = 0;
for (int i = 1; i < N; i *= 10)
{
log10N++;
}
// * Cdec needs to be accurate to 1 decimal place so it can be correctly rounded;
// * fInv loses up to (#digits of longest coeff of B) places in fInv.mult(B);
// * multiplying fInv by B also multiplies the rounding error by a factor of N;
// so make #decimal places of fInv the sum of the above.
BigDecimalPolynomial fInv = rf.Rho.Divide(new BigDecimal(rf.Res), B.GetMaxCoeffLength() + 1 + log10N);
BigDecimalPolynomial gInv = rg.Rho.Divide(new BigDecimal(rg.Res), A.GetMaxCoeffLength() + 1 + log10N);
BigDecimalPolynomial Cdec = fInv.Multiply(B);
Cdec.Add(gInv.Multiply(A));
Cdec.Halve();
C = Cdec.Round();
}
BigIntPolynomial F = B.Clone();
F.Subtract(f.Multiply(C));
BigIntPolynomial G = A.Clone();
G.Subtract(g.Multiply(C));
IntegerPolynomial FInt = new IntegerPolynomial(F);
IntegerPolynomial GInt = new IntegerPolynomial(G);
minimizeFG(fInt, gInt, FInt, GInt, N);
IPolynomial fPrime;
IntegerPolynomial h;
if (basisType == BasisType.STANDARD)
{
fPrime = FInt;
h = g.Multiply(fq, q);
}
else
{
fPrime = g;
h = FInt.Multiply(fq, q);
}
h.ModPositive(q);
return(new FGBasis(f, fPrime, h, FInt, GInt, param.q, param.polyType, param.basisType, param.keyNormBoundSq));
}
