Exemple #1
0
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());
   }
Exemple #2
0
// 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");
   }
Exemple #3
0
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);
   }
Exemple #4
0
// 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);
   }
Exemple #5
0
// 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);
   }
Exemple #6
0
// 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);
   }