public override Number Subtract (Number x, Number y)
{
if (x.data.Length < 6 || y.data.Length < 6)
return ToElement (base.Subtract (x, y));
int cmp = x.CompareTo (y);
if (cmp == 0)
return PADDED_ZERO;
uint[] pz = new uint[6], px = x.data, py = y.data;
if (cmp > 0) {
uint tmp, carry;
tmp = py[0]; carry = ((pz[0] = px[0] - tmp) > ~tmp ? 1U : 0U);
tmp = py[1] + carry; carry = (tmp < carry | (pz[1] = px[1] - tmp) > ~tmp ? 1U : 0U);
tmp = py[2] + carry; carry = (tmp < carry | (pz[2] = px[2] - tmp) > ~tmp ? 1U : 0U);
tmp = py[3] + carry; carry = (tmp < carry | (pz[3] = px[3] - tmp) > ~tmp ? 1U : 0U);
tmp = py[4] + carry; carry = (tmp < carry | (pz[4] = px[4] - tmp) > ~tmp ? 1U : 0U);
pz[5] = px[5] - py[5] - carry;
} else {
long tmp;
int carry = 0;
pz[0] = (uint)(tmp = ((long)px[0]) + ((long)P1) - ((long)py[0]) - carry); carry = (tmp < 0 ? 1 : tmp > 0xFFFFFFFF ? -1 : 0);
pz[1] = (uint)(tmp = ((long)px[1]) + ((long)P2) - ((long)py[1]) - carry); carry = (tmp < 0 ? 1 : tmp > 0xFFFFFFFF ? -1 : 0);
pz[2] = (uint)(tmp = ((long)px[2]) + ((long)P3) - ((long)py[2]) - carry); carry = (tmp < 0 ? 1 : tmp > 0xFFFFFFFF ? -1 : 0);
pz[3] = (uint)(tmp = ((long)px[3]) + ((long)P4) - ((long)py[3]) - carry); carry = (tmp < 0 ? 1 : tmp > 0xFFFFFFFF ? -1 : 0);
pz[4] = (uint)(tmp = ((long)px[4]) + ((long)P5) - ((long)py[4]) - carry); carry = (tmp < 0 ? 1 : tmp > 0xFFFFFFFF ? -1 : 0);
pz[5] = (uint)(tmp = ((long)px[5]) + ((long)P6) - ((long)py[5]) - carry);
}
return new Number (pz);
}
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 override Number Multiply (Number x, Number y)
{
if (x.data.Length < 8 || y.data.Length < 8) throw new ArgumentException ();
uint[] px = x.data, py = y.data;
ulong r0, r1, r2, r3, r4, r5, r6, r7;
uint tmp32;
ulong tmp, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7;
ulong d1, d2, d3, d4, d5;
ulong triple1, triple2;
const ulong mask = 0xFFFFFFFF;
const ulong carry = 0x100000000UL;
const ulong negative = ulong.MaxValue - (((ulong)uint.MaxValue) * 16) * 8;
tmp = ((ulong)px[0]) * ((ulong)py[0]); r0 = tmp & mask; r1 = tmp >> 32;
tmp = ((ulong)px[1]) * ((ulong)py[0]); r1 += tmp & mask; r2 = tmp >> 32;
tmp = ((ulong)px[2]) * ((ulong)py[0]); r2 += tmp & mask; r3 = tmp >> 32;
tmp = ((ulong)px[3]) * ((ulong)py[0]); r3 += tmp & mask; r4 = tmp >> 32;
tmp = ((ulong)px[4]) * ((ulong)py[0]); r4 += tmp & mask; r5 = tmp >> 32;
tmp = ((ulong)px[5]) * ((ulong)py[0]); r5 += tmp & mask; r6 = tmp >> 32;
tmp = ((ulong)px[6]) * ((ulong)py[0]); r6 += tmp & mask; r7 = tmp >> 32;
tmp = ((ulong)px[7]) * ((ulong)py[0]); r7 += tmp & mask; tmp32 = (uint)(tmp >> 32);
r7 += tmp32;
r6 -= tmp32;
r3 -= tmp32;
r0 += tmp32;
tmp = ((ulong)px[0]) * ((ulong)py[1]); r1 += tmp & mask; r2 += tmp >> 32;
tmp = ((ulong)px[1]) * ((ulong)py[1]); r2 += tmp & mask; r3 += tmp >> 32;
tmp = ((ulong)px[2]) * ((ulong)py[1]); r3 += tmp & mask; r4 += tmp >> 32;
tmp = ((ulong)px[3]) * ((ulong)py[1]); r4 += tmp & mask; r5 += tmp >> 32;
tmp = ((ulong)px[4]) * ((ulong)py[1]); r5 += tmp & mask; r6 += tmp >> 32;
tmp = ((ulong)px[5]) * ((ulong)py[1]); r6 += tmp & mask; r7 += tmp >> 32;
tmp = ((ulong)px[6]) * ((ulong)py[1]); r7 += tmp & mask; tmp1 = (uint)(tmp >> 32);
tmp = ((ulong)px[7]) * ((ulong)py[1]); tmp1 += (uint)tmp; tmp32 = (uint)(tmp >> 32);
r7 += tmp1;
r6 -= tmp1 + tmp32;
r4 -= tmp32;
r3 -= tmp1 + tmp32;
r1 += tmp32;
r0 += tmp1 + tmp32;
tmp = ((ulong)px[0]) * ((ulong)py[2]); r2 += tmp & mask; r3 += tmp >> 32;
tmp = ((ulong)px[1]) * ((ulong)py[2]); r3 += tmp & mask; r4 += tmp >> 32;
tmp = ((ulong)px[2]) * ((ulong)py[2]); r4 += tmp & mask; r5 += tmp >> 32;
tmp = ((ulong)px[3]) * ((ulong)py[2]); r5 += tmp & mask; r6 += tmp >> 32;
tmp = ((ulong)px[4]) * ((ulong)py[2]); r6 += tmp & mask; r7 += tmp >> 32;
tmp = ((ulong)px[5]) * ((ulong)py[2]); r7 += tmp & mask; tmp1 = (uint)(tmp >> 32);
tmp = ((ulong)px[6]) * ((ulong)py[2]); tmp1 += (uint)tmp; tmp2 = (uint)(tmp >> 32);
tmp = ((ulong)px[7]) * ((ulong)py[2]); tmp2 += (uint)tmp; tmp32 = (uint)(tmp >> 32);
r7 += tmp1 - tmp32;
r6 -= tmp1 + tmp2;
r5 -= tmp32;
r4 -= tmp2 + tmp32;
r3 -= tmp1 + tmp2;
r2 += tmp32;
r1 += tmp2 + tmp32;
r0 += tmp1 + tmp2;
tmp = ((ulong)px[0]) * ((ulong)py[3]); r3 += tmp & mask; r4 += tmp >> 32;
tmp = ((ulong)px[1]) * ((ulong)py[3]); r4 += tmp & mask; r5 += tmp >> 32;
tmp = ((ulong)px[2]) * ((ulong)py[3]); r5 += tmp & mask; r6 += tmp >> 32;
tmp = ((ulong)px[3]) * ((ulong)py[3]); r6 += tmp & mask; r7 += tmp >> 32;
tmp = ((ulong)px[4]) * ((ulong)py[3]); r7 += tmp & mask; tmp1 = (uint)(tmp >> 32);
tmp = ((ulong)px[5]) * ((ulong)py[3]); tmp1 += (uint)tmp; tmp2 = (uint)(tmp >> 32);
tmp = ((ulong)px[6]) * ((ulong)py[3]); tmp2 += (uint)tmp; tmp3 = (uint)(tmp >> 32);
tmp = ((ulong)px[7]) * ((ulong)py[3]); tmp3 += (uint)tmp; tmp32 = (uint)(tmp >> 32);
d1 = ((ulong)tmp32) << 1;
r7 += tmp1 - tmp3 - tmp32;
r6 -= tmp1 + tmp2;
r5 -= tmp3 + tmp32;
r4 -= tmp2 + tmp3;
r3 -= tmp1 + tmp2 - d1;
r2 += tmp3 + tmp32;
r1 += tmp2 + tmp3;
r0 += tmp1 + tmp2 - tmp32;
tmp = ((ulong)px[0]) * ((ulong)py[4]); r4 += tmp & mask; r5 += tmp >> 32;
tmp = ((ulong)px[1]) * ((ulong)py[4]); r5 += tmp & mask; r6 += tmp >> 32;
tmp = ((ulong)px[2]) * ((ulong)py[4]); r6 += tmp & mask; r7 += tmp >> 32;
tmp = ((ulong)px[3]) * ((ulong)py[4]); r7 += tmp & mask; tmp1 = (uint)(tmp >> 32);
tmp = ((ulong)px[4]) * ((ulong)py[4]); tmp1 += (uint)tmp; tmp2 = (uint)(tmp >> 32);
tmp = ((ulong)px[5]) * ((ulong)py[4]); tmp2 += (uint)tmp; tmp3 = (uint)(tmp >> 32);
tmp = ((ulong)px[6]) * ((ulong)py[4]); tmp3 += (uint)tmp; tmp4 = (uint)(tmp >> 32);
tmp = ((ulong)px[7]) * ((ulong)py[4]); tmp4 += (uint)tmp; tmp32 = (uint)(tmp >> 32);
d1 = tmp4 << 1;
d2 = ((ulong)tmp32) << 1;
r7 += tmp1 - tmp3 - tmp4 - tmp32;
r6 -= tmp1 + tmp2;
r5 -= tmp3 + tmp4;
r4 -= tmp2 + tmp3 - d2;
r3 -= tmp1 + tmp2 - d1 - d2;
r2 += tmp3 + tmp4;
r1 += tmp2 + tmp3 - tmp32;
r0 += tmp1 + tmp2 - tmp4 - tmp32;
tmp = ((ulong)px[0]) * ((ulong)py[5]); r5 += tmp & mask; r6 += tmp >> 32;
tmp = ((ulong)px[1]) * ((ulong)py[5]); r6 += tmp & mask; r7 += tmp >> 32;
tmp = ((ulong)px[2]) * ((ulong)py[5]); r7 += tmp & mask; tmp1 = (uint)(tmp >> 32);
tmp = ((ulong)px[3]) * ((ulong)py[5]); tmp1 += (uint)tmp; tmp2 = (uint)(tmp >> 32);
tmp = ((ulong)px[4]) * ((ulong)py[5]); tmp2 += (uint)tmp; tmp3 = (uint)(tmp >> 32);
tmp = ((ulong)px[5]) * ((ulong)py[5]); tmp3 += (uint)tmp; tmp4 = (uint)(tmp >> 32);
tmp = ((ulong)px[6]) * ((ulong)py[5]); tmp4 += (uint)tmp; tmp5 = (uint)(tmp >> 32);
tmp = ((ulong)px[7]) * ((ulong)py[5]); tmp5 += (uint)tmp; tmp32 = (uint)(tmp >> 32);
d1 = tmp4 << 1;
d2 = tmp5 << 1;
d3 = ((ulong)tmp32) << 1;
r7 += tmp1 - tmp3 - tmp4 - tmp5 - tmp32;
r6 -= tmp1 + tmp2 - tmp32;
r5 -= tmp3 + tmp4 - d3;
r4 -= tmp2 + tmp3 - d2 - d3;
r3 -= tmp1 + tmp2 - d1 - d2 - tmp32;
r2 += tmp3 + tmp4 - tmp32;
r1 += tmp2 + tmp3 - tmp5 - tmp32;
r0 += tmp1 + tmp2 - tmp4 - tmp5 - tmp32;
tmp = ((ulong)px[0]) * ((ulong)py[6]); r6 += tmp & mask; r7 += tmp >> 32;
tmp = ((ulong)px[1]) * ((ulong)py[6]); r7 += tmp & mask; tmp1 = (uint)(tmp >> 32);
tmp = ((ulong)px[2]) * ((ulong)py[6]); tmp1 += (uint)tmp; tmp2 = (uint)(tmp >> 32);
tmp = ((ulong)px[3]) * ((ulong)py[6]); tmp2 += (uint)tmp; tmp3 = (uint)(tmp >> 32);
tmp = ((ulong)px[4]) * ((ulong)py[6]); tmp3 += (uint)tmp; tmp4 = (uint)(tmp >> 32);
tmp = ((ulong)px[5]) * ((ulong)py[6]); tmp4 += (uint)tmp; tmp5 = (uint)(tmp >> 32);
tmp = ((ulong)px[6]) * ((ulong)py[6]); tmp5 += (uint)tmp; tmp6 = (uint)(tmp >> 32);
tmp = ((ulong)px[7]) * ((ulong)py[6]); tmp6 += (uint)tmp; tmp32 = (uint)(tmp >> 32);
d1 = tmp4 << 1;
d2 = tmp5 << 1;
d3 = tmp6 << 1;
d4 = ((ulong)tmp32) << 1;
triple1 = d4 + tmp32;
r7 += tmp1 - tmp3 - tmp4 - tmp5 - tmp6;
r6 -= tmp1 + tmp2 - tmp6 - triple1;
r5 -= tmp3 + tmp4 - d3 - d4;
r4 -= tmp2 + tmp3 - d2 - d3 - tmp32;
r3 -= tmp1 + tmp2 - d1 - d2 - tmp6;
r2 += tmp3 + tmp4 - tmp6 - tmp32;
r1 += tmp2 + tmp3 - tmp5 - tmp6 - tmp32;
r0 += tmp1 + tmp2 - tmp4 - tmp5 - tmp6 - tmp32;
tmp = ((ulong)px[0]) * ((ulong)py[7]); r7 += tmp & mask; tmp1 = (uint)(tmp >> 32);
tmp = ((ulong)px[1]) * ((ulong)py[7]); tmp1 += (uint)tmp; tmp2 = (uint)(tmp >> 32);
tmp = ((ulong)px[2]) * ((ulong)py[7]); tmp2 += (uint)tmp; tmp3 = (uint)(tmp >> 32);
tmp = ((ulong)px[3]) * ((ulong)py[7]); tmp3 += (uint)tmp; tmp4 = (uint)(tmp >> 32);
tmp = ((ulong)px[4]) * ((ulong)py[7]); tmp4 += (uint)tmp; tmp5 = (uint)(tmp >> 32);
tmp = ((ulong)px[5]) * ((ulong)py[7]); tmp5 += (uint)tmp; tmp6 = (uint)(tmp >> 32);
tmp = ((ulong)px[6]) * ((ulong)py[7]); tmp6 += (uint)tmp; tmp7 = (uint)(tmp >> 32);
tmp = ((ulong)px[7]) * ((ulong)py[7]); tmp7 += (uint)tmp; tmp32 = (uint)(tmp >> 32);
d1 = tmp4 << 1;
d2 = tmp5 << 1;
d3 = tmp6 << 1;
d4 = tmp7 << 1;
d5 = ((ulong)tmp32) << 1;
triple1 = d4 + tmp7;
triple2 = d5 + tmp32;
r7 += tmp1 - tmp3 - tmp4 - tmp5 - tmp6 + triple2;
r6 -= tmp1 + tmp2 - tmp6 - triple1 - d5;
r5 -= tmp3 + tmp4 - d3 - d4 - tmp32;
r4 -= tmp2 + tmp3 - d2 - d3 - tmp7;
r3 -= tmp1 + tmp2 - d1 - d2 - tmp6 + tmp32;
r2 += tmp3 + tmp4 - tmp6 - tmp7 - tmp32;
r1 += tmp2 + tmp3 - tmp5 - tmp6 - tmp7 - tmp32;
r0 += tmp1 + tmp2 - tmp4 - tmp5 - tmp6 - tmp7;
// check negative-value
while (r0 >= negative) { r1--; r0 += carry; }
while (r1 >= negative) { r2--; r1 += carry; }
while (r2 >= negative) { r3--; r2 += carry; }
while (r3 >= negative) { r4--; r3 += carry; }
while (r4 >= negative) { r5--; r4 += carry; }
while (r5 >= negative) { r6--; r5 += carry; }
while (r6 >= negative) { r7--; r6 += carry; }
while (r7 >= negative) {
r0 += P1;
r1 += P2;
r2 += P3;
r3 += P4;
r4 += P5;
r5 += P6;
r6 += P7;
r7 += P8;
}
// check carry
while (r0 > mask || r1 > mask || r2 > mask || r3 > mask || r4 > mask || r5 > mask || r6 > mask || r7 > mask) {
if (r7 > mask) {
tmp32 = (uint)(r7 >> 32);
r0 += tmp32;
r3 -= tmp32;
r6 -= tmp32;
r7 = tmp32 + (ulong)((uint)r7);
// check negative-value
while (r3 >= negative) { r4--; r3 += carry; }
while (r4 >= negative) { r5--; r4 += carry; }
while (r5 >= negative) { r6--; r5 += carry; }
while (r6 >= negative) { r7--; r6 += carry; }
}
tmp32 = (uint)(r0 >> 32); r0 = (uint)r0; r1 += tmp32;
tmp32 = (uint)(r1 >> 32); r1 = (uint)r1; r2 += tmp32;
tmp32 = (uint)(r2 >> 32); r2 = (uint)r2; r3 += tmp32;
tmp32 = (uint)(r3 >> 32); r3 = (uint)r3; r4 += tmp32;
tmp32 = (uint)(r4 >> 32); r4 = (uint)r4; r5 += tmp32;
tmp32 = (uint)(r5 >> 32); r5 = (uint)r5; r6 += tmp32;
tmp32 = (uint)(r6 >> 32); r6 = (uint)r6; r7 += tmp32;
}
Number ret = new Number (new uint[] {
(uint)r0, (uint)r1, (uint)r2,
(uint)r3, (uint)r4, (uint)r5,
(uint)r6, (uint)r7
});
while (ret.CompareTo (PRIME) >= 0)
ret.SubtractInPlace (PRIME);
return ret;
}
public unsafe void Reduce (Number x)
{
int k = mod.length, kp1 = k + 1, km1 = k - 1;
if (x.length < k)
return;
Number q = new Number (x.length - km1 + constant.length);
Number r = new Number (kp1);
fixed (uint* pq = q.data, pr = r.data, pm = mod.data, px = x.data, pc = constant.data) {
Number.Multiply (px + km1, x.length - km1, pc, constant.length, pq);
x.length = (x.length > kp1 ? kp1 : x.length);
x.Normalize ();
uint* xs = pq + kp1, xe = xs + q.length - kp1;
uint* ys = pm, ye = ys + mod.length;
uint* zs = pr, ze = zs + kp1;
for (; xs < xe; xs++, zs++) {
if (*xs == 0) continue;
ulong carry = 0;
uint* zp = zs;
for (uint* yp = ys; yp < ye && zp < ze; yp++, zp++) {
carry += ((ulong)*xs) * ((ulong)*yp) + ((ulong)*zp);
*zp = (uint)carry;
carry >>= 32;
}
if (carry != 0 && zp < ze)
*zp = (uint)carry;
}
r.Normalize ();
if (r.CompareTo (x) <= 0) {
x.length = Number.Subtract (px, x.length, pr, r.length, px);
} else {
Number val = new Number (kp1 + 1);
val.data[kp1] = 1;
fixed (uint* pv = val.data) {
val.length = Number.Subtract (pv, val.length, pr, r.length, pv);
x.length = Number.Add (px, x.length, pv, val.length, px);
}
}
x.Normalize ();
while (x.CompareTo (mod) >= 0) {
x.length = Number.Subtract (px, x.length, pm, mod.length, px);
}
}
}
public static bool LeftSmallerThanRight(Number num1, Number num2)
{
return num1.CompareTo(num2) < 0;
}
public virtual Number Sqrt (Number x)
{
if ((mod % (uint)4) == 3) {
Number tmp = Pow (x, (mod >> 2) + 1);
if (x.CompareTo (Multiply (tmp, tmp)) == 0)
return tmp;
throw new ArithmeticException ();
}
throw new NotImplementedException ();
}
public override ECPoint ExportECPoint (Number x, Number y, Number z, ECGroup group)
{
if (montOne == null) montOne = ToElement (Number.One);
if (z.CompareTo (montOne) == 0)
return new ECPoint (group, Multiply (x, Number.One), Multiply (y, Number.One), Number.One);
Number izm = Invert (z);
Number iz = Multiply (izm, Number.One);
Number z2 = Multiply (iz, izm);
return new ECPoint (group, Multiply (x, z2), Multiply (y, (Multiply (z2, izm))), Number.One);
}
