public ECPoint (ECGroup group, Number x, Number y, Number z)
{
_group = group;
_field = group.FiniteField;
_x = x;
_y = y;
_z = z;
}
public ECGroup (Number a, Number b, Number mod, IFiniteField field)
{
_a = a;
_b = b;
_mod = mod;
_field = field;
_a_is_minus3 = (mod.CompareTo (a + Number.Three) == 0);
}
public ECDomainParameters (ECGroup group, ECPoint G, Number order, uint h, uint bits, IFiniteField fieldN, Uri uri)
{
_group = group;
_G = G;
_order = order;
_h = h;
_bits = bits;
_fieldN = fieldN;
_uri = uri;
}
public void SqrtTest ()
{
IFiniteField[] ffList = new IFiniteField[2];
ffList[0] = new SECP192r1 ();
ffList[1] = new Montgomery (ffList[0].Modulus);
int repeats = 10;
foreach (IFiniteField ff in ffList) {
for (int i = 0; i < repeats; i++) {
Number x = ff.ToElement (Number.CreateRandomElement (ff.Modulus));
Number xx = ff.Multiply (x, x);
Number sqrt = ff.Sqrt (xx);
Assert.IsTrue (ff.Multiply (sqrt, sqrt).CompareTo (xx) == 0);
}
}
}
public void PowTest ()
{
IFiniteField[] ffList = new IFiniteField[2];
ffList[0] = new SECP192r1 ();
ffList[1] = new Montgomery (ffList[0].Modulus);
foreach (IFiniteField ff in ffList) {
Number x = ff.ToElement (Number.CreateRandomElement (ff.Modulus));
Number pow2 = ff.Multiply (x, x);
Number pow3 = ff.Multiply (pow2, x);
Number pow4 = ff.Multiply (pow3, x);
Assert.IsTrue (ff.Pow (x, Number.Zero).CompareTo (ff.ToElement (Number.One)) == 0);
Assert.IsTrue (ff.Pow (x, Number.One).CompareTo (x) == 0);
Assert.IsTrue (ff.Pow (x, Number.Two).CompareTo (pow2) == 0);
Assert.IsTrue (ff.Pow (x, Number.Three).CompareTo (pow3) == 0);
Assert.IsTrue (ff.Pow (x, Number.Four).CompareTo (pow4) == 0);
}
}
/// <summary>バイト配列より点を作成する (SEC1, 2.3.4)</summary>
public ECPoint (ECGroup group, byte[] data)
{
_group = group;
_field = group.FiniteField;
switch (data[0]) {
case 0: { // 無限遠点
ECPoint tmp = _field.GetInfinityPoint (_group);
_x = tmp._x;
_y = tmp._y;
_z = tmp._z;
return;
}
case 2:
case 3: { // 点圧縮済みデータ
int keyBits = group.P.BitCount ();
int keyBytes = (keyBits >> 3) + ((keyBits & 7) == 0 ? 0 : 1);
if (data.Length != keyBytes + 1)
throw new ArgumentException ();
Number x = _field.ToElement (new Number (data, 1, keyBytes, false));
Number y2 = _field.Add (_field.Multiply (_field.Add (_field.Multiply (x, x), _group.A), x), _group.B); // (x^2 + a)*x + b
Number y = _field.Sqrt (y2);
if (_field.ToNormal (y).GetBit (0) != data[0] - 2)
y = _field.Modulus - y;
_x = x;
_y = y;
_z = _field.ToElement (Number.One);
return;
}
case 4: { // 非圧縮データ
int keyBits = group.P.BitCount ();
int keyBytes = (keyBits >> 3) + ((keyBits & 7) == 0 ? 0 : 1);
_x = _field.ToElement (new Number (data, 1, keyBytes, false));
_y = _field.ToElement (new Number (data, 1 + keyBytes, keyBytes, false));
_z = _field.ToElement (Number.One);
return;
}
default:
throw new ArgumentException ();
}
}
protected ECCurve(IFiniteField field)
{
this.m_field = field;
}
internal GenericPolynomialExtensionField(IFiniteField subfield, IPolynomial polynomial)
{
this.subfield = subfield;
this.minimalPolynomial = polynomial;
}
public ECDomainParameters (ECGroup group, ECPoint G, Number order, uint h, uint bits, IFiniteField fieldN)
: this (group, G, order, h, bits, fieldN, null)
{
}
public static bool IsFpField(IFiniteField field)
{
return field.Dimension == 1;
}
public static bool IsF2mField(IFiniteField field)
{
return field.Dimension > 1 && field.Characteristic.Equals(BigInteger.Two)
&& field is IPolynomialExtensionField;
}
internal GenericPolynomialExtensionField(IFiniteField subfield, IPolynomial polynomial)
{
this.subfield = subfield;
minimalPolynomial = polynomial;
}
protected ECCurve(IFiniteField field)
{
this.m_field = field;
}
