public virtual Number Pow (Number x, Number y)
{
if (y.IsZero ())
return ToElement (Number.One);
if (y.IsOne ())
return x;
Number a = x;
Number b = ToElement (Number.One);
if (y.GetBit (0) == 1)
b = a;
for (int i = 1; i < y.BitCount (); i ++) {
a = Multiply (a, a);
if (y.GetBit (i) == 1)
b = Multiply (a, b);
}
return b;
}
public unsafe ECPoint Multiply (Number scaler)
{
ECPoint[] P = SetupMultiplyHelperPoints ();
#if true
scaler = new Number (scaler, 1);
int l = scaler.BitCount () - 1;
int *b = stackalloc int [l >> 2];
int* e = stackalloc int[l >> 2];
int d = ComputeSignedWindowDecomposition (scaler, b, e);
ECPoint Q = P[b[d - 1]];
for (int i = d - 2; i >= 0; i --) {
for (int k = 0; k < e[i + 1] - e[i]; k ++)
Q = Q.Double ();
if (b[i] > 0)
Q = Q.Add (P[b[i]]);
else
Q = Q.Add (P[-b[i]].Invert ());
}
for (int k = 0; k < e[0]; k++)
Q = Q.Double ();
#else
#if true
if (P == null) {
P = _multiplyHelperPoints = new ECPoint[16];
P[1] = this;
P[2] = this.Double ();
P[3] = P[1].Add (P[2]);
P[5] = P[3].Add (P[2]);
P[7] = P[5].Add (P[2]);
P[9] = P[7].Add (P[2]);
P[11] = P[9].Add (P[2]);
P[13] = P[11].Add (P[2]);
P[15] = P[13].Add (P[2]);
}
int j = scaler.BitCount () - 1;
ECPoint Q = _field.GetInfinityPoint (_group);
while (j >= 0) {
if (scaler.GetBit (j) == 0) {
Q = Q.Double ();
j--;
} else {
int n = j - 1;
uint h = (1 << 3) | (scaler.GetBit (n--) << 2) | (scaler.GetBit (n--) << 1) | scaler.GetBit (n);
int t = j - 3;
while ((h & 1) == 0) {
h >>= 1;
t++;
}
for (int i = 1; i <= j - t + 1; i++)
Q = Q.Double ();
Q = Q.Add (P[(int)h]);
j = t - 1;
}
}
#else
ECPoint inv = Invert ();
if (P == null) {
P = _multiplyHelperPoints = new ECPoint[16];
P[1] = this;
P[2] = this.Double ();
P[3] = P[1].Add (P[2]);
P[5] = P[3].Add (P[2]);
P[7] = P[5].Add (P[2]);
P[9] = P[7].Add (P[2]);
P[11] = P[9].Add (P[2]);
P[13] = P[11].Add (P[2]);
P[15] = P[13].Add (P[2]);
}
int j = scaler.BitCount () - 1;
ECPoint Q = _field.GetInfinityPoint (_group);
while (j >= 0) {
uint continuous = scaler.GetContinuousBitCount (j);
if (continuous == 0) {
Q = Q.Double ();
j--;
} else if (continuous <= 4) {
int n = j - 1;
uint h = (1 << 3) | (scaler.GetBit (n--) << 2) | (scaler.GetBit (n--) << 1) | scaler.GetBit (n);
int t = j - 3;
while ((h & 1) == 0) {
h >>= 1;
t++;
}
for (int i = 1; i <= j - t + 1; i++)
Q = Q.Double ();
Q = Q.Add (P[(int)h]);
j = t - 1;
} else {
Q = Q.Add (this);
for (uint i = 0; i < continuous; i ++)
Q = Q.Double ();
Q = Q.Add (inv);
j -= (int)continuous;
}
}
#endif
#endif
return Q;
}
public static unsafe ECPoint MultiplyAndAdd (ECPoint p1, Number scaler1, ECPoint p2, Number scaler2)
{
#if true
int l = scaler1.BitCount ();
if (l < scaler2.BitCount ())
l = scaler2.BitCount ();
int* b1 = stackalloc int[l >> 2];
int* b2 = stackalloc int[l >> 2];
int* e1 = stackalloc int[l >> 2];
int* e2 = stackalloc int[l >> 2];
int d1 = ComputeSignedWindowDecomposition (scaler1, b1, e1) - 1;
int d2 = ComputeSignedWindowDecomposition (scaler2, b2, e2) - 1;
ECPoint[] p1ary = p1.SetupMultiplyHelperPoints ();
ECPoint[] p2ary = p2.SetupMultiplyHelperPoints ();
int lastE;
ECPoint Q;
if (e1[d1] == e2[d2]) {
Q = p1ary[b1[d1]].Add (p2ary[b2[d2--]]);
lastE = e1[d1--];
} else if (e1[d1] > e2[d2]) {
Q = p1ary[b1[d1]];
lastE = e1[d1--];
} else {
Q = p2ary[b2[d2]];
lastE = e2[d2--];
}
while (d1 >= 0 || d2 >= 0) {
int nextE;
int nextType = 0;
if (d1 >= 0 && d2 >= 0 && e1[d1] == e2[d2]) {
nextE = e1[d1];
nextType = 0;
} else if ((d1 >= 0 && d2 < 0) || (d1 >= 0 && e1[d1] > e2[d2])) {
nextE = e1[d1];
nextType = 1;
} else {
nextE = e2[d2];
nextType = 2;
}
for (int k = 0; k < lastE - nextE; k ++)
Q = Q.Double ();
if (nextType == 0 || nextType == 1) {
if (b1[d1] > 0)
Q = Q.Add (p1ary[b1[d1--]]);
else
Q = Q.Add (p1ary[-b1[d1--]].Invert ());
}
if (nextType == 0 || nextType == 2) {
if (b2[d2] > 0)
Q = Q.Add (p2ary[b2[d2--]]);
else
Q = Q.Add (p2ary[-b2[d2--]].Invert ());
}
lastE = nextE;
}
for (int k = 0; k < lastE; k++)
Q = Q.Double ();
return Q;
#else
int l = scaler1.BitCount ();
if (l < scaler2.BitCount ())
l = scaler2.BitCount ();
ECPoint Z = p1.Add (p2);
ECPoint R = p1._field.GetInfinityPoint (p1._group);
for (int i = l - 1; i >= 0; i --) {
R = R.Double ();
uint ki = scaler1.GetBit (i);
uint li = scaler2.GetBit (i);
if (ki == 0) {
if (li == 1)
R = R.Add (p2);
} else {
if (li == 0)
R = R.Add (p1);
else
R = R.Add (Z);
}
}
return R;
#endif
}
static unsafe int ComputeSignedWindowDecomposition (Number scaler, int *b, int *e)
{
int l = scaler.BitCount () - 1;
int pow2w = 1 << MultiplyWindowSize;
int pow2whalf = 1 << (MultiplyWindowSize - 1);
int d = 0, j = 0;
while (j <= l) {
if (scaler.GetBit (j) == 0) {
j++;
} else {
int t = j + MultiplyWindowSize - 1;
if (t > l) t = l;
uint h = 0;
for (int q = t; q >= j; q--)
h = (h << 1) + scaler.GetBit (q);
if (h > pow2whalf) {
b[d] = (int)h - pow2w;
scaler.PlusBit (t + 1);
l = scaler.BitCount () - 1;
} else {
b[d] = (int)h;
}
e[d] = j;
d++;
j = t + 1;
}
}
return d;
}