internal override uint EqCT(MutableECPoint Q)
{
MutableECPointPrime R = SameCurve(Q);
if (affine != 0)
{
if (R.affine != 0)
{
return(mx.EqCT(R.mx)
& my.EqCT(R.my)
& mz.EqCT(R.mz));
}
else
{
return(EqCTMixed(R, this));
}
}
else if (R.affine != 0)
{
return(EqCTMixed(this, R));
}
/*
* Both points are in Jacobian coordinates.
* If Z1 and Z2 are non-zero, then equality is
* achieved if and only if both following equations
* are true:
* X1*(Z2^2) = X2*(Z1^2)
* Y1*(Z2^3) = Y2*(Z1^3)
* If Z1 or Z2 is zero, then equality is achieved
* if and only if both are zero.
*/
mt1.Set(mz);
mt1.MontySquare();
mt2.Set(R.mz);
mt2.MontySquare();
mt3.Set(mx);
mt3.MontyMul(mt2);
mt4.Set(R.mx);
mt4.MontyMul(mt1);
uint r = mt3.EqCT(mt4);
mt1.MontyMul(mz);
mt2.MontyMul(R.mz);
mt3.Set(my);
mt3.MontyMul(mt2);
mt4.Set(R.my);
mt4.MontyMul(mt1);
r &= mt3.EqCT(mt4);
uint z1z = mz.IsZeroCT;
uint z2z = R.mz.IsZeroCT;
return((r & ~(z1z | z2z)) ^ (z1z & z2z));
}
internal override uint EqCT(MutableECPoint Q)
{
MutableECPointCurve25519 R = SameCurve(Q);
return(x.EqCT(R.x));
}
internal override uint DecodeCT(byte[] enc)
{
/*
* Format (specified in IEEE P1363, annex E):
*
* 0x00 point at infinity
* 0x02+b <X> compressed, b = lsb of Y
* 0x04 <X> <Y> uncompressed
* 0x06+b <X> <Y> uncompressed, b = lsb of Y
*
* Coordinates X and Y are in unsigned big-endian
* notation with exactly the length of the modulus.
*
* We want constant-time decoding, up to the encoded
* length. This means that the four following situations
* can be differentiated:
* -- Point is zero (length = 1)
* -- Point is compressed (length = 1 + flen)
* -- Point is uncompressed or hybrid (length = 1 + 2*flen)
* -- Length is neither 1, 1+flen or 1+2*flen.
*/
int flen = curve.flen;
uint good = 0xFFFFFFFF;
if (enc.Length == 1)
{
/*
* 1-byte encoding is point at infinity; the
* byte shall have value 0.
*/
int z = enc[0];
good &= ~(uint)((z | -z) >> 31);
SetZero();
}
else if (enc.Length == 1 + flen)
{
/*
* Compressed encoding. Leading byte is 0x02 or
* 0x03.
*/
int z = (enc[0] & 0xFE) - 0x02;
good &= ~(uint)((z | -z) >> 31);
uint lsbValue = (uint)(enc[0] & 1);
good &= mx.Decode(enc, 1, flen);
RebuildY2();
if (curve.pMod4 == 3)
{
good &= my.SqrtBlum();
}
else
{
/*
* Square roots modulo a non-Blum prime
* are a bit more complex. We do not
* support them yet (TODO).
*/
good = 0x00000000;
}
/*
* Adjust Y depending on LSB.
*/
mt1.Set(my);
mt1.Negate();
uint dn = (uint)-(int)(my.GetLSB() ^ lsbValue);
my.CondCopy(mt1, dn);
/*
* A corner case: LSB adjustment works only if
* Y != 0. If Y is 0 and requested LSB is 1,
* then the decoding fails. Note that this case
* cannot happen with usual prime curves, because
* they have a prime order, implying that there is
* no valid point such that Y = 0 (that would be
* a point of order 2).
*/
good &= ~(uint)-(int)(my.GetLSB() ^ lsbValue);
mz.Set(1);
}
else if (enc.Length == 1 + (flen << 1))
{
/*
* Uncompressed or hybrid. Leading byte is either
* 0x04, 0x06 or 0x07. We verify that the X and
* Y coordinates fulfill the curve equation.
*/
int fb = enc[0];
int z = (fb & 0xFC) - 0x04;
good &= ~(uint)((z | -z) >> 31);
z = fb - 0x05;
good &= (uint)((z | -z) >> 31);
good &= mx.Decode(enc, 1, flen);
RebuildY2();
mt1.Set(my);
mt1.FromMonty();
good &= my.Decode(enc, 1 + flen, flen);
mt2.Set(my);
mt2.MontySquare();
good &= mt1.EqCT(mt2);
/*
* We must check the LSB for hybrid encoding.
* The check fails if the encoding is marked as
* hybrid AND the LSB does not match.
*/
int lm = (fb >> 1) & ((int)my.GetLSB() ^ fb) & 1;
good &= ~(uint)-lm;
mz.Set(1);
}
else
{
good = 0x00000000;
}
/*
* If decoding failed, then we force the value to 0.
* Otherwise, we got a value. Either way, this uses
* affine coordinates.
*/
mx.CondCopy(curve.mp, ~good);
my.CondCopy(curve.mp, ~good);
mz.CondCopy(curve.mp, ~good);
affine = 0xFFFFFFFF;
return(good);
}
public static bool VerifyRaw(ECPublicKey pk,
byte[] hash, int hashOff, int hashLen,
byte[] sig, int sigOff, int sigLen)
{
try {
/*
* Get the curve.
*/
ECCurve curve = pk.Curve;
/*
* Get r and s from signature. This also verifies
* that they do not exceed the subgroup order.
*/
if (sigLen == 0 || (sigLen & 1) != 0)
{
return(false);
}
int tlen = sigLen >> 1;
ModInt oneQ = new ModInt(curve.SubgroupOrder);
oneQ.Set(1);
ModInt r = oneQ.Dup();
ModInt s = oneQ.Dup();
r.Decode(sig, sigOff, tlen);
s.Decode(sig, sigOff + tlen, tlen);
/*
* If either r or s was too large, it got set to
* zero. We also don't want real zeros.
*/
if (r.IsZero || s.IsZero)
{
return(false);
}
/*
* Convert the hash value to an integer modulo q.
* As per FIPS 186-4, if the hash value is larger
* than q, then we keep the qlen leftmost bits of
* the hash value.
*/
int qBitLength = oneQ.ModBitLength;
int hBitLength = hashLen << 3;
byte[] hv;
if (hBitLength <= qBitLength)
{
hv = new byte[hashLen];
Array.Copy(hash, hashOff, hv, 0, hashLen);
}
else
{
int qlen = (qBitLength + 7) >> 3;
hv = new byte[qlen];
Array.Copy(hash, hashOff, hv, 0, qlen);
int rs = (8 - (qBitLength & 7)) & 7;
BigInt.RShift(hv, rs);
}
ModInt z = oneQ.Dup();
z.DecodeReduce(hv);
/*
* Apply the verification algorithm:
* w = 1/s mod q
* u = z*w mod q
* v = r*w mod q
* T = u*G + v*Pub
* test whether T.x mod q == r.
*/
/*
* w = 1/s mod q
*/
ModInt w = s.Dup();
w.Invert();
/*
* u = z*w mod q
*/
w.ToMonty();
ModInt u = w.Dup();
u.MontyMul(z);
/*
* v = r*w mod q
*/
ModInt v = w.Dup();
v.MontyMul(r);
/*
* Compute u*G
*/
MutableECPoint T = curve.MakeGenerator();
uint good = T.MulSpecCT(u.Encode());
/*
* Compute v*iPub
*/
MutableECPoint M = pk.iPub.Dup();
good &= M.MulSpecCT(v.Encode());
/*
* Compute T = u*G+v*iPub
*/
uint nd = T.AddCT(M);
M.DoubleCT();
T.Set(M, ~nd);
good &= ~T.IsInfinityCT;
/*
* Get T.x, reduced modulo q.
* Signature is valid if and only if we get
* the same value as r (and we did not encounter
* an error previously).
*/
s.DecodeReduce(T.X);
return((good & r.EqCT(s)) != 0);
} catch (CryptoException) {
/*
* Exceptions may occur if the key or signature
* have invalid values (non invertible, out of
* range...). Any such occurrence means that the
* signature is not valid.
*/
return(false);
}
}