public static void DoPrivate(RSAPrivateKey sk,
byte[] x, int off, int len)
{
/*
* Check that the source array has the proper length
* (identical to the length of the modulus).
*/
if (len != sk.N.Length)
{
throw new CryptoException(
"Invalid source length for RSA private");
}
/*
* Reduce the source value to the proper range.
*/
ModInt mx = new ModInt(sk.N);
mx.DecodeReduce(x, off, len);
/*
* Compute m1 = x^dp mod p.
*/
ModInt m1 = new ModInt(sk.P);
m1.Set(mx);
m1.Pow(sk.DP);
/*
* Compute m2 = x^dq mod q.
*/
ModInt m2 = new ModInt(sk.Q);
m2.Set(mx);
m2.Pow(sk.DQ);
/*
* Compute h = (m1 - m2) / q mod p.
* (Result goes in m1.)
*/
ModInt m3 = m1.Dup();
m3.Set(m2);
m1.Sub(m3);
m3.Decode(sk.IQ);
m1.ToMonty();
m1.MontyMul(m3);
/*
* Compute m_2 + q*h. This works on plain integers, but
* we have efficient and constant-time code for modular
* integers, so we will do it modulo n.
*/
m3 = mx;
m3.Set(m1);
m1 = m3.Dup();
m1.Decode(sk.Q);
m1.ToMonty();
m3.MontyMul(m1);
m1.Set(m2);
m3.Add(m1);
/*
* Write result back in x[].
*/
m3.Encode(x, off, len);
}
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);
}
}