/**
* Tests if the basis is valid.
* @param h the polynomial h (either from the public key or from this basis)
* @return <code>true</code> if the basis is valid, <code>false</code> otherwise
*/
public bool isValid(IntegerPolynomial h)
{
if (f.ToIntegerPolynomial().Coeffs.Length != N)
return false;
if (fPrime.ToIntegerPolynomial().Coeffs.Length != N)
return false;
if (h.Coeffs.Length != N || !h.IsReduced(q))
return false;
// determine F, G, g from f, fPrime, h using the eqn. fG-Fg=q
IPolynomial FPoly = basisType == BasisType.STANDARD ? fPrime : f.Multiply(h, q);
IntegerPolynomial F = FPoly.ToIntegerPolynomial();
IntegerPolynomial fq = f.ToIntegerPolynomial().InvertFq(q);
IPolynomial g;
if (basisType == BasisType.STANDARD)
g = f.Multiply(h, q);
else
g = fPrime;
IntegerPolynomial G = g.Multiply(F);
G.Coeffs[0] -= q;
G = G.Multiply(fq, q);
G.ModCenter(q);
// check norms of F and G
if (!new FGBasis(f, fPrime, h, F, G, q, polyType, basisType, keyNormBoundSq).isNormOk())
return false;
// check norms of f and g
int factor = N / 24;
if (f.ToIntegerPolynomial().CenteredNormSq(q) * factor >= F.CenteredNormSq(q))
return false;
if (g.ToIntegerPolynomial().CenteredNormSq(q) * factor >= G.CenteredNormSq(q))
return false;
// check ternarity
if (polyType == TernaryPolynomialType.SIMPLE)
{
if (!f.ToIntegerPolynomial().IsTernary())
return false;
if (!g.ToIntegerPolynomial().IsTernary())
return false;
}
else
{
if (!(f.GetType().IsAssignableFrom(typeof(ProductFormPolynomial))))
return false;
if (!(g.GetType().IsAssignableFrom(typeof(ProductFormPolynomial))))
return false;
}
return true;
}
/// <summary>
/// Tests if the key pair is valid.
/// <para>See IEEE 1363.1 section 9.2.4.1.</para>
/// </summary>
///
/// <returns>if the key pair is valid, <c>true</c> otherwise false</returns>
public bool IsValid()
{
int N = ((NTRUPrivateKey)PrivateKey).N;
int q = ((NTRUPrivateKey)PrivateKey).Q;
TernaryPolynomialType polyType = ((NTRUPrivateKey)PrivateKey).PolyType;
if (((NTRUPublicKey)PublicKey).N != N)
{
return(false);
}
if (((NTRUPublicKey)PublicKey).Q != q)
{
return(false);
}
if (((NTRUPrivateKey)PrivateKey).T.ToIntegerPolynomial().Coeffs.Length != N)
{
return(false);
}
IntegerPolynomial h = ((NTRUPublicKey)PublicKey).H.ToIntegerPolynomial();
if (h.Coeffs.Length != N)
{
return(false);
}
if (!h.IsReduced(q))
{
return(false);
}
IntegerPolynomial f = ((NTRUPrivateKey)PrivateKey).T.ToIntegerPolynomial();
if (polyType == TernaryPolynomialType.SIMPLE && !f.IsTernary())
{
return(false);
}
// if t is a ProductFormPolynomial, ternarity of f1,f2,f3 doesn't need to be verified
if (polyType == TernaryPolynomialType.PRODUCT && !(((NTRUPrivateKey)PrivateKey).T.GetType().Equals(typeof(ProductFormPolynomial))))
{
return(false);
}
if (polyType == TernaryPolynomialType.PRODUCT)
{
f.Multiply(3);
f.Coeffs[0] += 1;
f.ModPositive(q);
}
// the key generator pre-multiplies h by 3, so divide by 9 instead of 3
int inv9 = IntEuclidean.Calculate(9, q).X; // 9^-1 mod q
IntegerPolynomial g = f.Multiply(h, q);
g.Multiply(inv9);
g.ModCenter(q);
if (!g.IsTernary())
{
return(false);
}
int dg = N / 3; // see EncryptionParameters.Initialize()
if (g.Count(1) != dg)
{
return(false);
}
if (g.Count(-1) != dg - 1)
{
return(false);
}
return(true);
}
/**
* Tests if the basis is valid.
* @param h the polynomial h (either from the public key or from this basis)
* @return <code>true</code> if the basis is valid, <code>false</code> otherwise
*/
public bool isValid(IntegerPolynomial h)
{
if (f.ToIntegerPolynomial().Coeffs.Length != N)
{
return(false);
}
if (fPrime.ToIntegerPolynomial().Coeffs.Length != N)
{
return(false);
}
if (h.Coeffs.Length != N || !h.IsReduced(q))
{
return(false);
}
// determine F, G, g from f, fPrime, h using the eqn. fG-Fg=q
IPolynomial FPoly = basisType == BasisType.STANDARD ? fPrime : f.Multiply(h, q);
IntegerPolynomial F = FPoly.ToIntegerPolynomial();
IntegerPolynomial fq = f.ToIntegerPolynomial().InvertFq(q);
IPolynomial g;
if (basisType == BasisType.STANDARD)
{
g = f.Multiply(h, q);
}
else
{
g = fPrime;
}
IntegerPolynomial G = g.Multiply(F);
G.Coeffs[0] -= q;
G = G.Multiply(fq, q);
G.ModCenter(q);
// check norms of F and G
if (!new FGBasis(f, fPrime, h, F, G, q, polyType, basisType, keyNormBoundSq).isNormOk())
{
return(false);
}
// check norms of f and g
int factor = N / 24;
if (f.ToIntegerPolynomial().CenteredNormSq(q) * factor >= F.CenteredNormSq(q))
{
return(false);
}
if (g.ToIntegerPolynomial().CenteredNormSq(q) * factor >= G.CenteredNormSq(q))
{
return(false);
}
// check ternarity
if (polyType == TernaryPolynomialType.SIMPLE)
{
if (!f.ToIntegerPolynomial().IsTernary())
{
return(false);
}
if (!g.ToIntegerPolynomial().IsTernary())
{
return(false);
}
}
else
{
if (!(f.GetType().IsAssignableFrom(typeof(ProductFormPolynomial))))
{
return(false);
}
if (!(g.GetType().IsAssignableFrom(typeof(ProductFormPolynomial))))
{
return(false);
}
}
return(true);
}
