public ECPoint Add(ECPoint other)
{
if (this.IsInifinity())
{
return(other);
}
if (other.IsInifinity())
{
return(this);
}
Number z1p2 = this._z2, z2p2 = other._z2, z1p3 = this._z3, z2p3 = other._z3;
if (z1p2 == null)
{
this._z2 = z1p2 = _field.Multiply(_z, _z);
}
if (z2p2 == null)
{
other._z2 = z2p2 = _field.Multiply(other._z, other._z);
}
if (z1p3 == null)
{
this._z3 = z1p3 = _field.Multiply(z1p2, this._z);
}
if (z2p3 == null)
{
other._z3 = z2p3 = _field.Multiply(z2p2, other._z);
}
Number u1 = _field.Multiply(_x, z2p2);
Number u2 = _field.Multiply(other._x, z1p2);
Number H = _field.Subtract(u2, u1);
Number s1 = _field.Multiply(_y, z2p3);
Number s2 = _field.Multiply(other._y, z1p3);
Number r = _field.Subtract(s2, s1);
if (H.IsZero())
{
if (r.IsZero())
{
return(Double());
}
return(_field.GetInfinityPoint(_group));
}
Number H2 = _field.Multiply(H, H);
Number H3 = _field.Multiply(H2, H);
Number X = _field.Subtract(_field.Subtract(_field.Multiply(r, r), H3), _field.Multiply(_field.Add(u1, u1), H2));
Number Y = _field.Subtract(_field.Multiply(r, _field.Subtract(_field.Multiply(u1, H2), X)), _field.Multiply(s1, H3));
Number Z = _field.Multiply(_field.Multiply(_z, other._z), H);
return(new ECPoint(_group, X, Y, Z));
}
/// <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();
}
}
/// <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 ();
}
}
