bool PointGFp::operator==(const PointGFp& other) const
{
if(m_curve != other.m_curve)
return false;
// If this is zero, only equal if other is also zero
if(is_zero())
return other.is_zero();
return (get_affine_x() == other.get_affine_x() &&
get_affine_y() == other.get_affine_y());
}
// encoding and decoding
secure_vector<uint8_t> EC2OSP(const PointGFp& point, uint8_t format)
{
if(point.is_zero())
return secure_vector<uint8_t>(1); // single 0 byte
const size_t p_bytes = point.get_curve().get_p().bytes();
BigInt x = point.get_affine_x();
BigInt y = point.get_affine_y();
secure_vector<uint8_t> bX = BigInt::encode_1363(x, p_bytes);
secure_vector<uint8_t> bY = BigInt::encode_1363(y, p_bytes);
if(format == PointGFp::UNCOMPRESSED)
{
secure_vector<uint8_t> result;
result.push_back(0x04);
result += bX;
result += bY;
return result;
}
else if(format == PointGFp::COMPRESSED)
{
secure_vector<uint8_t> result;
result.push_back(0x02 | static_cast<uint8_t>(y.get_bit(0)));
result += bX;
return result;
}
else if(format == PointGFp::HYBRID)
{
secure_vector<uint8_t> result;
result.push_back(0x06 | static_cast<uint8_t>(y.get_bit(0)));
result += bX;
result += bY;
return result;
}
else
throw Invalid_Argument("EC2OSP illegal point encoding");
}
bool ECDSA_Verification_Operation::verify(const byte msg[], size_t msg_len,
const byte sig[], size_t sig_len)
{
if(sig_len != order.bytes()*2)
return false;
BigInt e(msg, msg_len);
BigInt r(sig, sig_len / 2);
BigInt s(sig + sig_len / 2, sig_len / 2);
if(r <= 0 || r >= order || s <= 0 || s >= order)
return false;
BigInt w = inverse_mod(s, order);
PointGFp R = w * multi_exponentiate(base_point, e,
public_point, r);
if(R.is_zero())
return false;
return (R.get_affine_x() % order == r);
}
// Point addition
void PointGFp::add(const PointGFp& rhs, std::vector<BigInt>& ws_bn)
{
if(is_zero())
{
m_coord_x = rhs.m_coord_x;
m_coord_y = rhs.m_coord_y;
m_coord_z = rhs.m_coord_z;
return;
}
else if(rhs.is_zero())
return;
const BigInt& p = m_curve.get_p();
const size_t cap_size = 2*m_curve.get_p_words() + 2;
for(size_t i = 0; i != ws_bn.size(); ++i)
ws_bn[i].ensure_capacity(cap_size);
BigInt& rhs_z2 = ws_bn[0];
BigInt& U1 = ws_bn[1];
BigInt& S1 = ws_bn[2];
BigInt& lhs_z2 = ws_bn[3];
BigInt& U2 = ws_bn[4];
BigInt& S2 = ws_bn[5];
BigInt& H = ws_bn[6];
BigInt& r = ws_bn[7];
BigInt& tmp = ws_bn[9];
secure_vector<word>& monty_ws = ws_bn[8].get_word_vector();
/*
https://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html#addition-add-1998-cmo-2
*/
m_curve.sqr(rhs_z2, rhs.m_coord_z, monty_ws);
m_curve.mul(U1, m_coord_x, rhs_z2, monty_ws);
m_curve.mul(tmp, rhs.m_coord_z, rhs_z2, monty_ws); // z^3
m_curve.mul(S1, m_coord_y, tmp, monty_ws);
m_curve.sqr(lhs_z2, m_coord_z, monty_ws);
m_curve.mul(U2, rhs.m_coord_x, lhs_z2, monty_ws);
m_curve.mul(tmp, m_coord_z, lhs_z2, monty_ws);
m_curve.mul(S2, rhs.m_coord_y, tmp, monty_ws);
H = U2;
H -= U1;
if(H.is_negative())
H += p;
r = S2;
r -= S1;
if(r.is_negative())
r += p;
if(H.is_zero())
{
if(r.is_zero())
{
mult2(ws_bn);
return;
}
// setting to zero:
m_coord_x = 0;
m_coord_y = 1;
m_coord_z = 0;
return;
}
m_curve.sqr(U2, H, monty_ws);
m_curve.mul(S2, U2, H, monty_ws);
m_curve.mul(tmp, U1, U2, monty_ws);
U2 = tmp;
m_curve.sqr(m_coord_x, r, monty_ws);
m_coord_x -= S2;
m_coord_x -= (U2 << 1);
while(m_coord_x.is_negative())
m_coord_x += p;
U2 -= m_coord_x;
if(U2.is_negative())
U2 += p;
m_curve.mul(m_coord_y, r, U2, monty_ws);
m_curve.mul(tmp, S1, S2, monty_ws);
m_coord_y -= tmp;
if(m_coord_y.is_negative())
m_coord_y += p;
m_curve.mul(tmp, m_coord_z, rhs.m_coord_z, monty_ws);
m_curve.mul(m_coord_z, tmp, H, monty_ws);
}
// Point addition
void PointGFp::add(const PointGFp& rhs, std::vector<BigInt>& ws_bn)
{
if(is_zero())
{
coord_x = rhs.coord_x;
coord_y = rhs.coord_y;
coord_z = rhs.coord_z;
return;
}
else if(rhs.is_zero())
return;
const BigInt& p = curve.get_p();
BigInt& rhs_z2 = ws_bn[0];
BigInt& U1 = ws_bn[1];
BigInt& S1 = ws_bn[2];
BigInt& lhs_z2 = ws_bn[3];
BigInt& U2 = ws_bn[4];
BigInt& S2 = ws_bn[5];
BigInt& H = ws_bn[6];
BigInt& r = ws_bn[7];
monty_sqr(rhs_z2, rhs.coord_z);
monty_mult(U1, coord_x, rhs_z2);
monty_mult(S1, coord_y, monty_mult(rhs.coord_z, rhs_z2));
monty_sqr(lhs_z2, coord_z);
monty_mult(U2, rhs.coord_x, lhs_z2);
monty_mult(S2, rhs.coord_y, monty_mult(coord_z, lhs_z2));
H = U2;
H -= U1;
if(H.is_negative())
H += p;
r = S2;
r -= S1;
if(r.is_negative())
r += p;
if(H.is_zero())
{
if(r.is_zero())
{
mult2(ws_bn);
return;
}
*this = PointGFp(curve); // setting myself to zero
return;
}
monty_sqr(U2, H);
monty_mult(S2, U2, H);
U2 = monty_mult(U1, U2);
monty_sqr(coord_x, r);
coord_x -= S2;
coord_x -= (U2 << 1);
while(coord_x.is_negative())
coord_x += p;
U2 -= coord_x;
if(U2.is_negative())
U2 += p;
monty_mult(coord_y, r, U2);
coord_y -= monty_mult(S1, S2);
if(coord_y.is_negative())
coord_y += p;
monty_mult(coord_z, monty_mult(coord_z, rhs.coord_z), H);
}
// Point addition
void PointGFp::add(const PointGFp& rhs, std::vector<BigInt>& ws_bn)
{
if(is_zero())
{
m_coord_x = rhs.m_coord_x;
m_coord_y = rhs.m_coord_y;
m_coord_z = rhs.m_coord_z;
return;
}
else if(rhs.is_zero())
return;
const BigInt& p = m_curve.get_p();
BigInt& rhs_z2 = ws_bn[0];
BigInt& U1 = ws_bn[1];
BigInt& S1 = ws_bn[2];
BigInt& lhs_z2 = ws_bn[3];
BigInt& U2 = ws_bn[4];
BigInt& S2 = ws_bn[5];
BigInt& H = ws_bn[6];
BigInt& r = ws_bn[7];
/*
http://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html#addition-add-1998-cmo-2
*/
curve_sqr(rhs_z2, rhs.m_coord_z);
curve_mult(U1, m_coord_x, rhs_z2);
curve_mult(S1, m_coord_y, curve_mult(rhs.m_coord_z, rhs_z2));
curve_sqr(lhs_z2, m_coord_z);
curve_mult(U2, rhs.m_coord_x, lhs_z2);
curve_mult(S2, rhs.m_coord_y, curve_mult(m_coord_z, lhs_z2));
H = U2;
H -= U1;
if(H.is_negative())
H += p;
r = S2;
r -= S1;
if(r.is_negative())
r += p;
if(H.is_zero())
{
if(r.is_zero())
{
mult2(ws_bn);
return;
}
// setting to zero:
m_coord_x = 0;
m_coord_y = 1;
m_coord_z = 0;
return;
}
curve_sqr(U2, H);
curve_mult(S2, U2, H);
U2 = curve_mult(U1, U2);
curve_sqr(m_coord_x, r);
m_coord_x -= S2;
m_coord_x -= (U2 << 1);
while(m_coord_x.is_negative())
m_coord_x += p;
U2 -= m_coord_x;
if(U2.is_negative())
U2 += p;
curve_mult(m_coord_y, r, U2);
m_coord_y -= curve_mult(S1, S2);
if(m_coord_y.is_negative())
m_coord_y += p;
curve_mult(m_coord_z, curve_mult(m_coord_z, rhs.m_coord_z), H);
}