/*
* Compute a modular exponentiation (x^e mod n). Conditions:
* -- x[], e[] and n[] use big-endian encoding.
* -- x[] must be numerically smaller than n[].
* -- n[] must be odd.
* Result is returned as a newly allocated array of bytes of
* the same length as n[].
*/
public static byte[] ModPow(byte[] x, byte[] e, byte[] n)
{
ModInt mx = new ModInt(n);
mx.Decode(x);
mx.Pow(e);
return(mx.Encode());
}
public static byte[] SignRaw(ECPrivateKey sk, IDigest rfc6979Hash,
byte[] hash, int hashOff, int hashLen)
{
ECCurve curve = sk.Curve;
byte[] q = curve.SubgroupOrder;
RFC6979 rf = new RFC6979(rfc6979Hash, q, sk.X,
hash, hashOff, hashLen, rfc6979Hash != null);
ModInt mh = rf.GetHashMod();
ModInt mx = mh.Dup();
mx.Decode(sk.X);
/*
* Compute DSA signature. We use a loop to enumerate
* candidates for k until a proper one is found (it
* is VERY improbable that we may have to loop).
*/
ModInt mr = mh.Dup();
ModInt ms = mh.Dup();
ModInt mk = mh.Dup();
byte[] k = new byte[q.Length];
for (;;)
{
rf.NextK(k);
MutableECPoint G = curve.MakeGenerator();
if (G.MulSpecCT(k) == 0)
{
/*
* We may get an error here only if the
* curve is invalid (generator does not
* produce the expected subgroup).
*/
throw new CryptoException(
"Invalid EC private key / curve");
}
mr.DecodeReduce(G.X);
if (mr.IsZero)
{
continue;
}
ms.Set(mx);
ms.ToMonty();
ms.MontyMul(mr);
ms.Add(mh);
mk.Decode(k);
mk.Invert();
ms.ToMonty();
ms.MontyMul(mk);
byte[] sig = new byte[q.Length << 1];
mr.Encode(sig, 0, q.Length);
ms.Encode(sig, q.Length, q.Length);
return(sig);
}
}
/*
* Create a new instance with the provided elements. The
* constructor verifies that the provided private integer
* is non-zero and is less than the subgroup order.
*/
public ECPrivateKey(ECCurve curve, byte[] X)
{
this.curve = curve;
ModInt ms = new ModInt(curve.SubgroupOrder);
uint good = ms.Decode(X);
good &= ~ms.IsZeroCT;
if (good == 0)
{
throw new CryptoException("Invalid private key");
}
priv = ms.Encode();
dpk = null;
}
internal RFC6979(IDigest h, byte[] q, byte[] x,
byte[] hv, int hvOff, int hvLen, bool deterministic)
{
if (h == null)
{
h = new SHA256();
}
else
{
h = h.Dup();
h.Reset();
}
drbg = new HMAC_DRBG(h);
mh = new ModInt(q);
qlen = mh.ModBitLength;
int qolen = (qlen + 7) >> 3;
this.q = new byte[qolen];
Array.Copy(q, q.Length - qolen, this.q, 0, qolen);
int hlen = hvLen << 3;
if (hlen > qlen)
{
byte[] htmp = new byte[hvLen];
Array.Copy(hv, hvOff, htmp, 0, hv.Length);
BigInt.RShift(htmp, hlen - qlen);
hv = htmp;
hvOff = 0;
}
mh.DecodeReduce(hv, hvOff, hvLen);
ModInt mx = mh.Dup();
mx.Decode(x);
byte[] seed = new byte[(qolen << 1) + (deterministic ? 0 : 32)];
mx.Encode(seed, 0, qolen);
mh.Encode(seed, qolen, qolen);
if (!deterministic)
{
RNG.GetBytes(seed, qolen << 1,
seed.Length - (qolen << 1));
}
drbg.SetSeed(seed);
}
/*
* CheckValid() will verify that the prime factors are indeed
* prime, and that all other values are correct.
*/
public void CheckValid()
{
/*
* Factors ought to be prime.
*/
if (!BigInt.IsPrime(p) || !BigInt.IsPrime(q))
{
throw new CryptoException("Invalid RSA private key"
+ " (non-prime factor)");
}
/*
* FIXME: Verify that:
* dp = d mod p-1
* e*dp = 1 mod p-1
* dq = d mod q-1
* e*dq = 1 mod q-1
* (This is not easy with existing code because p-1 and q-1
* are even, but ModInt tolerates only odd moduli.)
*
* CheckExp(p, d, dp, e);
* CheckExp(q, d, dq, e);
*/
/*
* Verify that:
* q*iq = 1 mod p
*/
ModInt x = new ModInt(p);
ModInt y = x.Dup();
x.DecodeReduce(q);
x.ToMonty();
y.Decode(iq);
x.MontyMul(y);
if (!x.IsOne)
{
throw new CryptoException("Invalid RSA private key"
+ " (wrong CRT coefficient)");
}
}
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 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);
}
/*
* Checks enforced by the constructor:
* -- modulus is odd and at least 80-bit long
* -- subgroup order is odd and at least 30-bit long
* -- parameters a[] and b[] are lower than modulus
* -- coordinates gx and gy are lower than modulus
* -- coordinates gx and gy match curve equation
*/
internal ECCurvePrime(string name, byte[] mod, byte[] a, byte[] b,
byte[] gx, byte[] gy, byte[] subgroupOrder, byte[] cofactor)
: base(subgroupOrder, cofactor)
{
this.mod = mod = BigInt.NormalizeBE(mod);
int modLen = BigInt.BitLength(mod);
if (modLen < 80)
{
throw new CryptoException(
"Invalid curve: modulus is too small");
}
if ((mod[mod.Length - 1] & 0x01) == 0)
{
throw new CryptoException(
"Invalid curve: modulus is even");
}
int sgLen = BigInt.BitLength(subgroupOrder);
if (sgLen < 30)
{
throw new CryptoException(
"Invalid curve: subgroup is too small");
}
if ((subgroupOrder[subgroupOrder.Length - 1] & 0x01) == 0)
{
throw new CryptoException(
"Invalid curve: subgroup order is even");
}
mp = new ModInt(mod);
flen = (modLen + 7) >> 3;
pMod4 = mod[mod.Length - 1] & 3;
this.a = a = BigInt.NormalizeBE(a);
this.b = b = BigInt.NormalizeBE(b);
if (BigInt.CompareCT(a, mod) >= 0 ||
BigInt.CompareCT(b, mod) >= 0)
{
throw new CryptoException(
"Invalid curve: out-of-range parameter");
}
ma = mp.Dup();
ma.Decode(a);
ma.Add(3);
aIsM3 = ma.IsZero;
ma.Sub(3);
mb = mp.Dup();
mb.Decode(b);
this.gx = gx = BigInt.NormalizeBE(gx);
this.gy = gy = BigInt.NormalizeBE(gy);
if (BigInt.CompareCT(gx, mod) >= 0 ||
BigInt.CompareCT(gy, mod) >= 0)
{
throw new CryptoException(
"Invalid curve: out-of-range coordinates");
}
MutableECPointPrime G = new MutableECPointPrime(this);
G.Set(gx, gy, true);
hashCode = (int)(BigInt.HashInt(mod)
^ BigInt.HashInt(a) ^ BigInt.HashInt(b)
^ BigInt.HashInt(gx) ^ BigInt.HashInt(gy));
if (name == null)
{
name = string.Format("generic prime {0}/{1}",
modLen, sgLen);
}
this.name = name;
}
/*
* Test an integer for primality. This function runs up to 50
* Miller-Rabin rounds, which is a lot of overkill but ensures
* that non-primes will be reliably detected (with overwhelming
* probability) even with maliciously crafted inputs. "Normal"
* non-primes will be detected most of the time at the first
* iteration.
*
* This function is not constant-time.
*/
public static bool IsPrime(byte[] x)
{
x = NormalizeBE(x);
/*
* Handle easy cases:
* 0 is not prime
* small primes (one byte) are known in a constant bit-field
* even numbers (larger than one byte) are non-primes
*/
if (x.Length == 0)
{
return(false);
}
if (x.Length == 1)
{
return(IsSmallPrime(x[0]));
}
if ((x[x.Length - 1] & 0x01) == 0)
{
return(false);
}
/*
* Perform some trial divisions by small primes.
*/
for (int sp = 3; sp < 256; sp += 2)
{
if (!IsSmallPrime(sp))
{
continue;
}
int z = 0;
foreach (byte b in x)
{
z = ((z << 8) + b) % sp;
}
if (z == 0)
{
return(false);
}
}
/*
* Run some Miller-Rabin rounds. We use as basis random
* integers that are one byte smaller than the modulus.
*/
ModInt xm1 = new ModInt(x);
ModInt y = xm1.Dup();
y.Set(1);
xm1.Sub(y);
byte[] e = xm1.Encode();
ModInt a = new ModInt(x);
byte[] buf = new byte[x.Length - 1];
for (int i = 0; i < 50; i++)
{
RNG.GetBytes(buf);
a.Decode(buf);
a.Pow(e);
if (!a.IsOne)
{
return(false);
}
}
return(true);
}
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);
}
}