C++ PointGFp类代码示例

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());
   }

PointGFp multi_exponentiate(const PointGFp& p1, const BigInt& z1,
                            const PointGFp& p2, const BigInt& z2)
   {
   const PointGFp p3 = p1 + p2;

   PointGFp H(p1.get_curve()); // create as zero
   size_t bits_left = std::max(z1.bits(), z2.bits());

   std::vector<BigInt> ws(9);

   while(bits_left)
      {
      H.mult2(ws);

      const bool z1_b = z1.get_bit(bits_left - 1);
      const bool z2_b = z2.get_bit(bits_left - 1);

      if(z1_b == true && z2_b == true)
         H.add(p3, ws);
      else if(z1_b)
         H.add(p1, ws);
      else if(z2_b)
         H.add(p2, ws);

      --bits_left;
      }

   if(z1.is_negative() != z2.is_negative())
      H.negate();

   return H;
   }

// 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");
   }

PointGFp operator*(const BigInt& scalar, const PointGFp& point)
   {
   //BOTAN_ASSERT(point.on_the_curve(), "Input is on the curve");

   const CurveGFp& curve = point.get_curve();

   const size_t scalar_bits = scalar.bits();

   std::vector<BigInt> ws(9);

   if(scalar_bits <= 2)
      {
      const byte abs_val = scalar.byte_at(0);

      if(abs_val == 0)
         return PointGFp::zero_of(curve);

      PointGFp result = point;

      if(abs_val == 2)
         result.mult2(ws);

      if(scalar.is_negative())
         result.negate();

      return result;
      }

   PointGFp R[2] = { PointGFp(curve), point };

   for(size_t i = scalar_bits; i > 0; i--)
      {
      const size_t b = scalar.get_bit(i - 1);
      R[b ^ 1].add(R[b], ws);
      R[b].mult2(ws);
      }

   if(scalar.is_negative())
      R[0].negate();

   //BOTAN_ASSERT(R[0].on_the_curve(), "Output is on the curve");

   return R[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);
   }

Blinded_Point_Multiply::Blinded_Point_Multiply(const PointGFp& base, const BigInt& order, size_t h) :
   m_h(h > 0 ? h : 4), m_order(order), m_ws(9)
   {
   // Upper bound is a sanity check rather than hard limit
   if(m_h < 1 || m_h > 8)
      throw std::invalid_argument("Blinded_Point_Multiply invalid h param");

   const CurveGFp& curve = base.get_curve();

#if BOTAN_POINTGFP_BLINDED_MULTIPLY_USE_MONTGOMERY_LADDER

   const PointGFp inv = -base;

   m_U.resize(6*m_h + 3);

   m_U[3*m_h+0] = inv;
   m_U[3*m_h+1] = PointGFp::zero_of(curve);
   m_U[3*m_h+2] = base;

   for(size_t i = 1; i <= 3 * m_h + 1; ++i)
      {
      m_U[3*m_h+1+i] = m_U[3*m_h+i];
      m_U[3*m_h+1+i].add(base, m_ws);

      m_U[3*m_h+1-i] = m_U[3*m_h+2-i];
      m_U[3*m_h+1-i].add(inv, m_ws);
      }
#else
   m_U.resize(1 << m_h);
   m_U[0] = PointGFp::zero_of(curve);
   m_U[1] = base;

   for(size_t i = 2; i < m_U.size(); ++i)
      {
      m_U[i] = m_U[i-1];
      m_U[i].add(base, m_ws);
      }
#endif
   }

// 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);
//.........这里部分代码省略.........

PointGFp multi_exponentiate(const PointGFp& x, const BigInt& z1,
                            const PointGFp& y, const BigInt& z2)
   {
   const size_t z_bits = round_up(std::max(z1.bits(), z2.bits()), 2);

   std::vector<BigInt> ws(PointGFp::WORKSPACE_SIZE);

   PointGFp x2 = x;
   x2.mult2(ws);

   const PointGFp x3(x2.plus(x, ws));

   PointGFp y2 = y;
   y2.mult2(ws);

   const PointGFp y3(y2.plus(y, ws));

   const PointGFp M[16] = {
      x.zero(),        // 0000
      x,               // 0001
      x2,              // 0010
      x3,              // 0011
      y,               // 0100
      y.plus(x, ws),   // 0101
      y.plus(x2, ws),  // 0110
      y.plus(x3, ws),  // 0111
      y2,              // 1000
      y2.plus(x, ws),  // 1001
      y2.plus(x2, ws), // 1010
      y2.plus(x3, ws), // 1011
      y3,              // 1100
      y3.plus(x, ws),  // 1101
      y3.plus(x2, ws), // 1110
      y3.plus(x3, ws), // 1111
   };

   PointGFp H = x.zero();

   for(size_t i = 0; i != z_bits; i += 2)
      {
      if(i > 0)
         {
         H.mult2(ws);
         H.mult2(ws);
         }

      const uint8_t z1_b = z1.get_substring(z_bits - i - 2, 2);
      const uint8_t z2_b = z2.get_substring(z_bits - i - 2, 2);

      const uint8_t z12 = (4*z2_b) + z1_b;

      H.add(M[z12], ws);
      }

   if(z1.is_negative() != z2.is_negative())
      H.negate();

   return H;
   }

// 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);
   }

PointGFp operator*(const BigInt& scalar, const PointGFp& point)
   {
   const CurveGFp& curve = point.get_curve();

   if(scalar.is_zero())
      return PointGFp(curve); // zero point

   std::vector<BigInt> ws(9);

   if(scalar.abs() <= 2) // special cases for small values
      {
      byte value = scalar.abs().byte_at(0);

      PointGFp result = point;

      if(value == 2)
         result.mult2(ws);

      if(scalar.is_negative())
         result.negate();

      return result;
      }

   const size_t scalar_bits = scalar.bits();

#if 0

   PointGFp x1 = PointGFp(curve);
   PointGFp x2 = point;

   size_t bits_left = scalar_bits;

   // Montgomery Ladder
   while(bits_left)
      {
      const bool bit_set = scalar.get_bit(bits_left - 1);

      if(bit_set)
         {
         x1.add(x2, ws);
         x2.mult2(ws);
         }
      else
         {
         x2.add(x1, ws);
         x1.mult2(ws);
         }

      --bits_left;
      }

   if(scalar.is_negative())
      x1.negate();

   return x1;

#else
   const size_t window_size = 4;

   std::vector<PointGFp> Ps(1 << window_size);
   Ps[0] = PointGFp(curve);
   Ps[1] = point;

   for(size_t i = 2; i != Ps.size(); ++i)
      {
      Ps[i] = Ps[i-1];
      Ps[i].add(point, ws);
      }

   PointGFp H(curve); // create as zero
   size_t bits_left = scalar_bits;

   while(bits_left >= window_size)
      {
      for(size_t i = 0; i != window_size; ++i)
         H.mult2(ws);

      const u32bit nibble = scalar.get_substring(bits_left - window_size,
                                                 window_size);

      H.add(Ps[nibble], ws);

      bits_left -= window_size;
      }

   while(bits_left)
      {
      H.mult2(ws);
      if(scalar.get_bit(bits_left-1))
         H.add(point, ws);

      --bits_left;
      }

   if(scalar.is_negative())
      H.negate();

   return H;
#endif
//.........这里部分代码省略.........

// 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);
   }

PointGFp Blinded_Point_Multiply::blinded_multiply(const BigInt& scalar_in,
                                                  RandomNumberGenerator& rng)
   {
   if(scalar_in.is_negative())
      throw std::invalid_argument("Blinded_Point_Multiply scalar must be positive");

#if BOTAN_POINTGFP_SCALAR_BLINDING_BITS > 0
   // Choose a small mask m and use k' = k + m*order (Coron's 1st countermeasure)
   const BigInt mask(rng, BOTAN_POINTGFP_SCALAR_BLINDING_BITS, false);
   const BigInt scalar = scalar_in + m_order * mask;
#else
   const BigInt& scalar = scalar_in;
#endif

   const size_t scalar_bits = scalar.bits();

   // Randomize each point representation (Coron's 3rd countermeasure)
   for(size_t i = 0; i != m_U.size(); ++i)
      m_U[i].randomize_repr(rng);

#if BOTAN_POINTGFP_BLINDED_MULTIPLY_USE_MONTGOMERY_LADDER
   PointGFp R = m_U.at(3*m_h + 2); // base point
   int32_t alpha = 0;

   R.randomize_repr(rng);

   /*
   Algorithm 7 from "Randomizing the Montgomery Powering Ladder"
   Duc-Phong Le, Chik How Tan and Michael Tunstall
   http://eprint.iacr.org/2015/657

   It takes a random walk through (a subset of) the set of addition
   chains that end in k.
   */
   for(size_t i = scalar_bits; i > 0; i--)
      {
      const int32_t ki = scalar.get_bit(i);

      // choose gamma from -h,...,h
      const int32_t gamma = static_cast<int32_t>((rng.next_byte() % (2*m_h))) - m_h;
      const int32_t l = gamma - 2*alpha + ki - (ki ^ 1);

      R.mult2(m_ws);
      R.add(m_U.at(3*m_h + 1 + l), m_ws);
      alpha = gamma;
      }

   const int32_t k0 = scalar.get_bit(0);
   R.add(m_U[3*m_h + 1 - alpha - (k0 ^ 1)], m_ws);

#else

   // N-bit windowing exponentiation:

   size_t windows = round_up(scalar_bits, m_h) / m_h;

   PointGFp R = m_U[0];

   if(windows > 0)
      {
      windows--;
      const u32bit nibble = scalar.get_substring(windows*m_h, m_h);
      R.add(m_U[nibble], m_ws);

      /*
      Randomize after adding the first nibble as before the addition R
      is zero, and we cannot effectively randomize the point
      representation of the zero point.
      */
      R.randomize_repr(rng);

      while(windows)
         {
         for(size_t i = 0; i != m_h; ++i)
            R.mult2(m_ws);

         const u32bit nibble = scalar.get_substring((windows-1)*m_h, m_h);
         R.add(m_U[nibble], m_ws);
         windows--;
         }
      }
#endif

   //BOTAN_ASSERT(R.on_the_curve(), "Output is on the curve");

   return R;
   }