private static void PointAdd(PointExt p, PointAccum r)
{
int[] a = F.Create();
int[] b = F.Create();
int[] c = F.Create();
int[] d = F.Create();
int[] e = r.u;
int[] f = F.Create();
int[] g = F.Create();
int[] h = r.v;
F.Apm(r.y, r.x, b, a);
F.Apm(p.y, p.x, d, c);
F.Mul(a, c, a);
F.Mul(b, d, b);
F.Mul(r.u, r.v, c);
F.Mul(c, p.t, c);
F.Mul(c, C_d2, c);
F.Mul(r.z, p.z, d);
F.Add(d, d, d);
F.Apm(b, a, h, e);
F.Apm(d, c, g, f);
F.Carry(g);
F.Mul(e, f, r.x);
F.Mul(g, h, r.y);
F.Mul(f, g, r.z);
}
public static bool ValidatePublicKeyFull(byte[] pk, int pkOff)
{
PointAffine p = new PointAffine();
if (!DecodePointVar(pk, pkOff, false, p))
{
return(false);
}
F.Normalize(p.x);
F.Normalize(p.y);
if (IsNeutralElementVar(p.x, p.y))
{
return(false);
}
PointAccum r = new PointAccum();
ScalarMultOrderVar(p, r);
F.Normalize(r.x);
F.Normalize(r.y);
F.Normalize(r.z);
return(IsNeutralElementVar(r.x, r.y, r.z));
}
private static void ScalarMultBaseEncoded(byte[] k, byte[] r, int rOff)
{
PointAccum p = new PointAccum();
ScalarMultBase(k, p);
EncodePoint(p, r, rOff);
}
private static void ScalarMultOrderVar(PointAffine p, PointAccum r)
{
int width = 5;
sbyte[] ws_p = GetWnafVar(L, width);
PointExt[] tp = PointPrecomputeVar(PointCopy(p), 1 << (width - 2));
PointSetNeutral(r);
for (int bit = 252; ;)
{
int wp = ws_p[bit];
if (wp != 0)
{
int sign = wp >> 31;
int index = (wp ^ sign) >> 1;
PointAddVar((sign != 0), tp[index], r);
}
if (--bit < 0)
{
break;
}
PointDouble(r);
}
}
private static void PointSetNeutral(PointAccum p)
{
X25519Field.Zero(p.x);
X25519Field.One(p.y);
X25519Field.One(p.z);
X25519Field.Zero(p.u);
X25519Field.One(p.v);
}
private static void PointSetNeutral(PointAccum p)
{
F.Zero(p.x);
F.One(p.y);
F.One(p.z);
F.Zero(p.u);
F.One(p.v);
}
private static PointExt PointCopy(PointAccum p)
{
PointExt r = new PointExt();
X25519Field.Copy(p.x, 0, r.x, 0);
X25519Field.Copy(p.y, 0, r.y, 0);
X25519Field.Copy(p.z, 0, r.z, 0);
X25519Field.Mul(p.u, p.v, r.t);
return(r);
}
private static void ScalarMultBaseEncoded(byte[] k, byte[] r, int rOff)
{
PointAccum p = new PointAccum();
ScalarMultBase(k, p);
if (0 == EncodePoint(p, r, rOff))
{
throw new InvalidOperationException();
}
}
private static bool ImplVerify(byte[] sig, int sigOff, byte[] pk, int pkOff, byte[] ctx, byte phflag,
byte[] m, int mOff, int mLen)
{
if (!CheckContextVar(ctx, phflag))
{
throw new ArgumentException("ctx");
}
byte[] R = Arrays.CopyOfRange(sig, sigOff, sigOff + PointBytes);
byte[] S = Arrays.CopyOfRange(sig, sigOff + PointBytes, sigOff + SignatureSize);
if (!CheckPointVar(R))
{
return(false);
}
if (!CheckScalarVar(S))
{
return(false);
}
PointExt pA = new PointExt();
if (!DecodePointVar(pk, pkOff, true, pA))
{
return(false);
}
IDigest d = CreateDigest();
byte[] h = new byte[d.GetDigestSize()];
Dom2(d, phflag, ctx);
d.BlockUpdate(R, 0, PointBytes);
d.BlockUpdate(pk, pkOff, PointBytes);
d.BlockUpdate(m, mOff, mLen);
d.DoFinal(h, 0);
byte[] k = ReduceScalar(h);
uint[] nS = new uint[ScalarUints];
DecodeScalar(S, 0, nS);
uint[] nA = new uint[ScalarUints];
DecodeScalar(k, 0, nA);
PointAccum pR = new PointAccum();
ScalarMultStraussVar(nS, nA, pA, pR);
byte[] check = new byte[PointBytes];
EncodePoint(pR, check, 0);
return(Arrays.AreEqual(check, R));
}
internal static void ScalarMultBaseYZ(byte[] k, int kOff, int[] y, int[] z)
{
byte[] n = new byte[ScalarBytes];
PruneScalar(k, kOff, n);
PointAccum p = new PointAccum();
ScalarMultBase(n, p);
X25519Field.Copy(p.y, 0, y, 0);
X25519Field.Copy(p.z, 0, z, 0);
}
private static void ScalarMultBase(byte[] k, PointAccum r)
{
Precompute();
PointSetNeutral(r);
uint[] n = new uint[ScalarUints];
DecodeScalar(k, 0, n);
// Recode the scalar into signed-digit form, then group comb bits in each block
{
uint c1 = Nat.CAdd(ScalarUints, ~(int)n[0] & 1, n, L, n); Debug.Assert(c1 == 0);
uint c2 = Nat.ShiftDownBit(ScalarUints, n, 1U); Debug.Assert(c2 == (1U << 31));
for (int i = 0; i < ScalarUints; ++i)
{
n[i] = Interleave.Shuffle2(n[i]);
}
}
PointPrecomp p = new PointPrecomp();
int cOff = (PrecompSpacing - 1) * PrecompTeeth;
for (; ;)
{
for (int b = 0; b < PrecompBlocks; ++b)
{
uint w = n[b] >> cOff;
int sign = (int)(w >> (PrecompTeeth - 1)) & 1;
int abs = ((int)w ^ -sign) & PrecompMask;
Debug.Assert(sign == 0 || sign == 1);
Debug.Assert(0 <= abs && abs < PrecompPoints);
PointLookup(b, abs, p);
X25519Field.CSwap(sign, p.ypx_h, p.ymx_h);
X25519Field.CNegate(sign, p.xyd);
PointAddPrecomp(p, r);
}
if ((cOff -= PrecompTeeth) < 0)
{
break;
}
PointDouble(r);
}
}
private static void EncodePoint(PointAccum p, byte[] r, int rOff)
{
int[] x = X25519Field.Create();
int[] y = X25519Field.Create();
X25519Field.Inv(p.z, y);
X25519Field.Mul(p.x, y, x);
X25519Field.Mul(p.y, y, y);
X25519Field.Normalize(x);
X25519Field.Normalize(y);
X25519Field.Encode(y, r, rOff);
r[rOff + PointBytes - 1] |= (byte)((x[0] & 1) << 7);
}
private static void ScalarMultStraussVar(uint[] nb, uint[] np, PointExt p, PointAccum r)
{
Precompute();
int width = 5;
sbyte[] ws_b = GetWnaf(nb, WnafWidthBase);
sbyte[] ws_p = GetWnaf(np, width);
PointExt[] tp = PointPrecompVar(p, 1 << (width - 2));
PointSetNeutral(r);
int bit = 255;
while (bit > 0 && ((byte)ws_b[bit] | (byte)ws_p[bit]) == 0)
{
--bit;
}
for (; ;)
{
int wb = ws_b[bit];
if (wb != 0)
{
int sign = wb >> 31;
int index = (wb ^ sign) >> 1;
PointAddVar((sign != 0), precompBaseTable[index], r);
}
int wp = ws_p[bit];
if (wp != 0)
{
int sign = wp >> 31;
int index = (wp ^ sign) >> 1;
PointAddVar((sign != 0), tp[index], r);
}
if (--bit < 0)
{
break;
}
PointDouble(r);
}
}
public static bool Verify(byte[] sig, int sigOff, byte[] pk, int pkOff, byte[] m, int mOff, int mLen)
{
byte[] R = Arrays.CopyOfRange(sig, sigOff, sigOff + PointBytes);
byte[] S = Arrays.CopyOfRange(sig, sigOff + PointBytes, sigOff + SignatureSize);
if (!CheckPointVar(R))
{
return(false);
}
if (!CheckScalarVar(S))
{
return(false);
}
PointExt pA = new PointExt();
if (!DecodePointVar(pk, pkOff, true, pA))
{
return(false);
}
Sha512Digest d = new Sha512Digest();
byte[] h = new byte[d.GetDigestSize()];
d.BlockUpdate(R, 0, PointBytes);
d.BlockUpdate(pk, pkOff, PointBytes);
d.BlockUpdate(m, mOff, mLen);
d.DoFinal(h, 0);
byte[] k = ReduceScalar(h);
uint[] nS = new uint[ScalarUints];
DecodeScalar(S, 0, nS);
uint[] nA = new uint[ScalarUints];
DecodeScalar(k, 0, nA);
PointAccum pR = new PointAccum();
ScalarMultStraussVar(nS, nA, pA, pR);
byte[] check = new byte[PointBytes];
EncodePoint(pR, check, 0);
return(Arrays.AreEqual(check, R));
}
internal static void ScalarMultBaseYZ(byte[] k, int kOff, int[] y, int[] z)
{
byte[] n = new byte[ScalarBytes];
PruneScalar(k, kOff, n);
PointAccum p = new PointAccum();
ScalarMultBase(n, p);
if (0 == CheckPoint(p.x, p.y, p.z))
{
throw new InvalidOperationException();
}
X25519Field.Copy(p.y, 0, y, 0);
X25519Field.Copy(p.z, 0, z, 0);
}
private static void ScalarMult(byte[] k, PointAffine p, PointAccum r)
{
uint[] n = new uint[ScalarUints];
DecodeScalar(k, 0, n);
Debug.Assert(0U == (n[0] & 7));
Debug.Assert(1U == n[ScalarUints - 1] >> 30);
Nat.ShiftDownBits(ScalarUints, n, 3, 1U);
// Recode the scalar into signed-digit form
{
uint c1 = Nat.CAdd(ScalarUints, ~(int)n[0] & 1, n, L, n); Debug.Assert(c1 == 0U);
uint c2 = Nat.ShiftDownBit(ScalarUints, n, 0U); Debug.Assert(c2 == (1U << 31));
}
Debug.Assert(1U == n[ScalarUints - 1] >> 28);
int[] table = PointPrecompute(p, 8);
PointExt q = new PointExt();
// Replace first 4 doublings (2^4 * P) with 1 addition (P + 15 * P)
PointCopy(p, r);
PointLookup(table, 7, q);
PointAdd(q, r);
int w = 62;
for (;;)
{
PointLookup(n, w, table, q);
PointAdd(q, r);
PointDouble(r);
PointDouble(r);
PointDouble(r);
if (--w < 0)
{
break;
}
PointDouble(r);
}
}
private static int EncodePoint(PointAccum p, byte[] r, int rOff)
{
int[] x = F.Create();
int[] y = F.Create();
F.Inv(p.z, y);
F.Mul(p.x, y, x);
F.Mul(p.y, y, y);
F.Normalize(x);
F.Normalize(y);
int result = CheckPoint(x, y);
F.Encode(y, r, rOff);
r[rOff + PointBytes - 1] |= (byte)((x[0] & 1) << 7);
return(result);
}
private static void ScalarMultStrausVar(uint[] nb, uint[] np, PointAffine p, PointAccum r)
{
Precompute();
int width = 5;
sbyte[] ws_b = GetWnafVar(nb, WnafWidthBase);
sbyte[] ws_p = GetWnafVar(np, width);
PointExt[] tp = PointPrecomputeVar(PointCopy(p), 1 << (width - 2));
PointSetNeutral(r);
for (int bit = 252;;)
{
int wb = ws_b[bit];
if (wb != 0)
{
int sign = wb >> 31;
int index = (wb ^ sign) >> 1;
PointAddVar((sign != 0), precompBaseTable[index], r);
}
int wp = ws_p[bit];
if (wp != 0)
{
int sign = wp >> 31;
int index = (wp ^ sign) >> 1;
PointAddVar((sign != 0), tp[index], r);
}
if (--bit < 0)
{
break;
}
PointDouble(r);
}
}
private static void PointAddPrecomp(PointPrecomp p, PointAccum r)
{
int[] a = F.Create();
int[] b = F.Create();
int[] c = F.Create();
int[] e = r.u;
int[] f = F.Create();
int[] g = F.Create();
int[] h = r.v;
F.Apm(r.y, r.x, b, a);
F.Mul(a, p.ymx_h, a);
F.Mul(b, p.ypx_h, b);
F.Mul(r.u, r.v, c);
F.Mul(c, p.xyd, c);
F.Apm(b, a, h, e);
F.Apm(r.z, c, g, f);
F.Carry(g);
F.Mul(e, f, r.x);
F.Mul(g, h, r.y);
F.Mul(f, g, r.z);
}
private static void PointAddPrecomp(PointPrecomp p, PointAccum r)
{
int[] A = X25519Field.Create();
int[] B = X25519Field.Create();
int[] C = X25519Field.Create();
int[] E = r.u;
int[] F = X25519Field.Create();
int[] G = X25519Field.Create();
int[] H = r.v;
X25519Field.Apm(r.y, r.x, B, A);
X25519Field.Mul(A, p.ymx_h, A);
X25519Field.Mul(B, p.ypx_h, B);
X25519Field.Mul(r.u, r.v, C);
X25519Field.Mul(C, p.xyd, C);
X25519Field.Apm(B, A, H, E);
X25519Field.Apm(r.z, C, G, F);
X25519Field.Carry(G);
X25519Field.Mul(E, F, r.x);
X25519Field.Mul(G, H, r.y);
X25519Field.Mul(F, G, r.z);
}
private static void PointAddVar(bool negate, PointExt p, PointAccum r)
{
int[] a = F.Create();
int[] b = F.Create();
int[] c = F.Create();
int[] d = F.Create();
int[] e = r.u;
int[] f = F.Create();
int[] g = F.Create();
int[] h = r.v;
int[] nc, nd, nf, ng;
if (negate)
{
nc = d; nd = c; nf = g; ng = f;
}
else
{
nc = c; nd = d; nf = f; ng = g;
}
F.Apm(r.y, r.x, b, a);
F.Apm(p.y, p.x, nd, nc);
F.Mul(a, c, a);
F.Mul(b, d, b);
F.Mul(r.u, r.v, c);
F.Mul(c, p.t, c);
F.Mul(c, C_d2, c);
F.Mul(r.z, p.z, d);
F.Add(d, d, d);
F.Apm(b, a, h, e);
F.Apm(d, c, ng, nf);
F.Carry(ng);
F.Mul(e, f, r.x);
F.Mul(g, h, r.y);
F.Mul(f, g, r.z);
}
private static void PointAddVar(bool negate, PointExt p, PointAccum r)
{
int[] A = X25519Field.Create();
int[] B = X25519Field.Create();
int[] C = X25519Field.Create();
int[] D = X25519Field.Create();
int[] E = r.u;
int[] F = X25519Field.Create();
int[] G = X25519Field.Create();
int[] H = r.v;
int[] c, d, f, g;
if (negate)
{
c = D; d = C; f = G; g = F;
}
else
{
c = C; d = D; f = F; g = G;
}
X25519Field.Apm(r.y, r.x, B, A);
X25519Field.Apm(p.y, p.x, d, c);
X25519Field.Mul(A, C, A);
X25519Field.Mul(B, D, B);
X25519Field.Mul(r.u, r.v, C);
X25519Field.Mul(C, p.t, C);
X25519Field.Mul(C, C_d2, C);
X25519Field.Mul(r.z, p.z, D);
X25519Field.Add(D, D, D);
X25519Field.Apm(B, A, H, E);
X25519Field.Apm(D, C, g, f);
X25519Field.Carry(g);
X25519Field.Mul(E, F, r.x);
X25519Field.Mul(G, H, r.y);
X25519Field.Mul(F, G, r.z);
}
private static void PointDouble(PointAccum r)
{
int[] a = F.Create();
int[] b = F.Create();
int[] c = F.Create();
int[] e = r.u;
int[] f = F.Create();
int[] g = F.Create();
int[] h = r.v;
F.Sqr(r.x, a);
F.Sqr(r.y, b);
F.Sqr(r.z, c);
F.Add(c, c, c);
F.Apm(a, b, h, g);
F.Add(r.x, r.y, e);
F.Sqr(e, e);
F.Sub(h, e, e);
F.Add(c, g, f);
F.Carry(f);
F.Mul(e, f, r.x);
F.Mul(g, h, r.y);
F.Mul(f, g, r.z);
}
private static void PointDouble(PointAccum r)
{
int[] A = X25519Field.Create();
int[] B = X25519Field.Create();
int[] C = X25519Field.Create();
int[] E = r.u;
int[] F = X25519Field.Create();
int[] G = X25519Field.Create();
int[] H = r.v;
X25519Field.Sqr(r.x, A);
X25519Field.Sqr(r.y, B);
X25519Field.Sqr(r.z, C);
X25519Field.Add(C, C, C);
X25519Field.Apm(A, B, H, G);
X25519Field.Add(r.x, r.y, E);
X25519Field.Sqr(E, E);
X25519Field.Sub(H, E, E);
X25519Field.Add(C, G, F);
X25519Field.Carry(F);
X25519Field.Mul(E, F, r.x);
X25519Field.Mul(G, H, r.y);
X25519Field.Mul(F, G, r.z);
}
private static void PointExtendXY(PointAccum p)
{
F.One(p.z);
F.Copy(p.x, 0, p.u, 0);
F.Copy(p.y, 0, p.v, 0);
}
private static void Precompute()
{
PointAccum p = new PointAccum();
X25519Field.Copy(B_x, 0, p.x, 0);
X25519Field.Copy(B_y, 0, p.y, 0);
PointExtendXY(p);
precompBase = new int[PrecompBlocks * PrecompPoints * 3 * X25519Field.Size];
int off = 0;
for (int b = 0; b < PrecompBlocks; ++b)
{
PointExt[] ds = new PointExt[PrecompTeeth];
PointExt sum = new PointExt();
PointSetNeutral(sum);
for (int t = 0; t < PrecompTeeth; ++t)
{
PointExt q = PointCopy(p);
PointAddVar(true, sum, q, sum);
PointDouble(p);
ds[t] = PointCopy(p);
if (b + t != PrecompBlocks + PrecompTeeth - 2)
{
for (int s = 1; s < PrecompSpacing; ++s)
{
PointDouble(p);
}
}
}
PointExt[] points = new PointExt[PrecompPoints];
int k = 0;
points[k++] = sum;
for (int t = 0; t < (PrecompTeeth - 1); ++t)
{
int size = 1 << t;
for (int j = 0; j < size; ++j, ++k)
{
PointAddVar(false, points[k - size], ds[t], points[k] = new PointExt());
}
}
for (int i = 0; i < PrecompPoints; ++i)
{
PointExt q = points[i];
int[] x = new int[X25519Field.Size];
int[] y = new int[X25519Field.Size];
X25519Field.Add(q.z, q.z, x);
X25519Field.Inv(x, y);
X25519Field.Mul(q.x, y, x);
X25519Field.Mul(q.y, y, y);
PointPrecomp r = new PointPrecomp();
X25519Field.Apm(y, x, r.ypx_h, r.ymx_h);
X25519Field.Mul(x, y, r.xyd);
X25519Field.Mul(r.xyd, C_d4, r.xyd);
X25519Field.Normalize(r.ypx_h);
X25519Field.Normalize(r.ymx_h);
X25519Field.Copy(r.ypx_h, 0, precompBase, off); off += X25519Field.Size;
X25519Field.Copy(r.ymx_h, 0, precompBase, off); off += X25519Field.Size;
X25519Field.Copy(r.xyd, 0, precompBase, off); off += X25519Field.Size;
}
}
}
private static void PointCopy(PointAffine p, PointAccum r)
{
F.Copy(p.x, 0, r.x, 0);
F.Copy(p.y, 0, r.y, 0);
PointExtendXY(r);
}
public static void Precompute()
{
lock (precompLock)
{
if (precompBase != null)
{
return;
}
// Precomputed table for the base point in verification ladder
{
PointExt b = new PointExt();
X25519Field.Copy(B_x, 0, b.x, 0);
X25519Field.Copy(B_y, 0, b.y, 0);
PointExtendXY(b);
precompBaseTable = PointPrecompVar(b, 1 << (WnafWidthBase - 2));
}
PointAccum p = new PointAccum();
X25519Field.Copy(B_x, 0, p.x, 0);
X25519Field.Copy(B_y, 0, p.y, 0);
PointExtendXY(p);
precompBase = new int[PrecompBlocks * PrecompPoints * 3 * X25519Field.Size];
int off = 0;
for (int b = 0; b < PrecompBlocks; ++b)
{
PointExt[] ds = new PointExt[PrecompTeeth];
PointExt sum = new PointExt();
PointSetNeutral(sum);
for (int t = 0; t < PrecompTeeth; ++t)
{
PointExt q = PointCopy(p);
PointAddVar(true, sum, q, sum);
PointDouble(p);
ds[t] = PointCopy(p);
if (b + t != PrecompBlocks + PrecompTeeth - 2)
{
for (int s = 1; s < PrecompSpacing; ++s)
{
PointDouble(p);
}
}
}
PointExt[] points = new PointExt[PrecompPoints];
int k = 0;
points[k++] = sum;
for (int t = 0; t < (PrecompTeeth - 1); ++t)
{
int size = 1 << t;
for (int j = 0; j < size; ++j, ++k)
{
PointAddVar(false, points[k - size], ds[t], points[k] = new PointExt());
}
}
Debug.Assert(k == PrecompPoints);
for (int i = 0; i < PrecompPoints; ++i)
{
PointExt q = points[i];
int[] x = X25519Field.Create();
int[] y = X25519Field.Create();
X25519Field.Add(q.z, q.z, x);
// TODO[ed25519] Batch inversion
X25519Field.Inv(x, y);
X25519Field.Mul(q.x, y, x);
X25519Field.Mul(q.y, y, y);
PointPrecomp r = new PointPrecomp();
X25519Field.Apm(y, x, r.ypx_h, r.ymx_h);
X25519Field.Mul(x, y, r.xyd);
X25519Field.Mul(r.xyd, C_d4, r.xyd);
X25519Field.Normalize(r.ypx_h);
X25519Field.Normalize(r.ymx_h);
//X25519Field.Normalize(r.xyd);
X25519Field.Copy(r.ypx_h, 0, precompBase, off); off += X25519Field.Size;
X25519Field.Copy(r.ymx_h, 0, precompBase, off); off += X25519Field.Size;
X25519Field.Copy(r.xyd, 0, precompBase, off); off += X25519Field.Size;
}
}
Debug.Assert(off == precompBase.Length);
}
}
private static void PointExtendXY(PointAccum p)
{
X25519Field.One(p.z);
X25519Field.Copy(p.x, 0, p.u, 0);
X25519Field.Copy(p.y, 0, p.v, 0);
}
public static void Precompute()
{
lock (precompLock)
{
if (precompBase != null)
{
return;
}
// Precomputed table for the base point in verification ladder
{
PointExt b = new PointExt();
F.Copy(B_x, 0, b.x, 0);
F.Copy(B_y, 0, b.y, 0);
PointExtendXY(b);
precompBaseTable = PointPrecomputeVar(b, 1 << (WnafWidthBase - 2));
}
PointAccum p = new PointAccum();
F.Copy(B_x, 0, p.x, 0);
F.Copy(B_y, 0, p.y, 0);
PointExtendXY(p);
precompBase = F.CreateTable(PrecompBlocks * PrecompPoints * 3);
int off = 0;
for (int b = 0; b < PrecompBlocks; ++b)
{
PointExt[] ds = new PointExt[PrecompTeeth];
PointExt sum = new PointExt();
PointSetNeutral(sum);
for (int t = 0; t < PrecompTeeth; ++t)
{
PointExt q = PointCopy(p);
PointAddVar(true, sum, q, sum);
PointDouble(p);
ds[t] = PointCopy(p);
if (b + t != PrecompBlocks + PrecompTeeth - 2)
{
for (int s = 1; s < PrecompSpacing; ++s)
{
PointDouble(p);
}
}
}
PointExt[] points = new PointExt[PrecompPoints];
int k = 0;
points[k++] = sum;
for (int t = 0; t < (PrecompTeeth - 1); ++t)
{
int size = 1 << t;
for (int j = 0; j < size; ++j, ++k)
{
PointAddVar(false, points[k - size], ds[t], points[k] = new PointExt());
}
}
Debug.Assert(k == PrecompPoints);
int[] cs = F.CreateTable(PrecompPoints);
// TODO[ed25519] A single batch inversion across all blocks?
{
int[] u = F.Create();
F.Copy(points[0].z, 0, u, 0);
F.Copy(u, 0, cs, 0);
int i = 0;
while (++i < PrecompPoints)
{
F.Mul(u, points[i].z, u);
F.Copy(u, 0, cs, i * F.Size);
}
F.Add(u, u, u);
F.InvVar(u, u);
--i;
int[] t = F.Create();
while (i > 0)
{
int j = i--;
F.Copy(cs, i * F.Size, t, 0);
F.Mul(t, u, t);
F.Copy(t, 0, cs, j * F.Size);
F.Mul(u, points[j].z, u);
}
F.Copy(u, 0, cs, 0);
}
for (int i = 0; i < PrecompPoints; ++i)
{
PointExt q = points[i];
int[] x = F.Create();
int[] y = F.Create();
//F.Add(q.z, q.z, x);
//F.InvVar(x, y);
F.Copy(cs, i * F.Size, y, 0);
F.Mul(q.x, y, x);
F.Mul(q.y, y, y);
PointPrecomp r = new PointPrecomp();
F.Apm(y, x, r.ypx_h, r.ymx_h);
F.Mul(x, y, r.xyd);
F.Mul(r.xyd, C_d4, r.xyd);
F.Normalize(r.ypx_h);
F.Normalize(r.ymx_h);
//F.Normalize(r.xyd);
F.Copy(r.ypx_h, 0, precompBase, off); off += F.Size;
F.Copy(r.ymx_h, 0, precompBase, off); off += F.Size;
F.Copy(r.xyd, 0, precompBase, off); off += F.Size;
}
}
Debug.Assert(off == precompBase.Length);
}
}
