/*

* Point arithmetic on elliptic curves over GF(p)

*

* (C) 2007 Martin Doering, Christoph Ludwig, Falko Strenzke

*     2008-2011,2012,2014,2015,2018 Jack Lloyd

*

* Botan is released under the Simplified BSD License (see license.txt)

*/

#include <botan/point_gfp.h>

#include <botan/numthry.h>

#include <botan/rng.h>

#include <botan/internal/rounding.h>

#include <botan/internal/ct_utils.h>

namespace Botan {

PointGFp::PointGFp(const CurveGFp& curve) :

   m_curve(curve),

   m_coord_x(0),

   m_coord_y(curve.get_1_rep()),

   m_coord_z(0)

   {

   // Assumes Montgomery rep of zero is zero

   }

PointGFp::PointGFp(const CurveGFp& curve, const BigInt& x, const BigInt& y) :

   m_curve(curve),

   m_coord_x(x),

   m_coord_y(y),

   m_coord_z(m_curve.get_1_rep())

   {

   if(x < 0 || x >= curve.get_p())

      throw Invalid_Argument("Invalid PointGFp affine x");

   if(y < 0 || y >= curve.get_p())

      throw Invalid_Argument("Invalid PointGFp affine y");

   secure_vector<word> monty_ws(m_curve.get_ws_size());

   m_curve.to_rep(m_coord_x, monty_ws);

   m_curve.to_rep(m_coord_y, monty_ws);

   }

void PointGFp::randomize_repr(RandomNumberGenerator& rng)

   {

   secure_vector<word> ws(m_curve.get_ws_size());

   randomize_repr(rng, ws);

   }

void PointGFp::randomize_repr(RandomNumberGenerator& rng, secure_vector<word>& ws)

   {

   const BigInt mask = BigInt::random_integer(rng, 2, m_curve.get_p());

   /*

   * No reason to convert this to Montgomery representation first,

   * just pretend the random mask was chosen as Redc(mask) and the

   * random mask we generated above is in the Montgomery

   * representation.

   * //m_curve.to_rep(mask, ws);

   */

   const BigInt mask2 = m_curve.sqr_to_tmp(mask, ws);

   const BigInt mask3 = m_curve.mul_to_tmp(mask2, mask, ws);

   m_coord_x = m_curve.mul_to_tmp(m_coord_x, mask2, ws);

   m_coord_y = m_curve.mul_to_tmp(m_coord_y, mask3, ws);

   m_coord_z = m_curve.mul_to_tmp(m_coord_z, mask, ws);

   }

namespace {

inline void resize_ws(std::vector<BigInt>& ws_bn, size_t cap_size)

   {

   BOTAN_ASSERT(ws_bn.size() >= PointGFp::WORKSPACE_SIZE,

                "Expected size for PointGFp workspace");

   for(size_t i = 0; i != ws_bn.size(); ++i)

      if(ws_bn[i].size() < cap_size)

         ws_bn[i].get_word_vector().resize(cap_size);

   }

inline word all_zeros(const word x[], size_t len)

   {

   word z = 0;

   for(size_t i = 0; i != len; ++i)

      z |= x[i];

   return CT::Mask<word>::is_zero(z).value();

   }

}

void PointGFp::add_affine(const word x_words[], size_t x_size,

                          const word y_words[], size_t y_size,

                          std::vector<BigInt>& ws_bn)

   {

   if(all_zeros(x_words, x_size) & all_zeros(y_words, y_size))

      {

      return;

      }

   if(is_zero())

      {

      m_coord_x.set_words(x_words, x_size);

      m_coord_y.set_words(y_words, y_size);

      m_coord_z = m_curve.get_1_rep();

      return;

      }

   resize_ws(ws_bn, m_curve.get_ws_size());

   secure_vector<word>& ws = ws_bn[0].get_word_vector();

   secure_vector<word>& sub_ws = ws_bn[1].get_word_vector();

   BigInt& T0 = ws_bn[2];

   BigInt& T1 = ws_bn[3];

   BigInt& T2 = ws_bn[4];

   BigInt& T3 = ws_bn[5];

   BigInt& T4 = ws_bn[6];

   /*

   https://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html#addition-add-1998-cmo-2

   simplified with Z2 = 1

   */

   const BigInt& p = m_curve.get_p();

   m_curve.sqr(T3, m_coord_z, ws); // z1^2

   m_curve.mul(T4, x_words, x_size, T3, ws); // x2*z1^2

   m_curve.mul(T2, m_coord_z, T3, ws); // z1^3

   m_curve.mul(T0, y_words, y_size, T2, ws); // y2*z1^3

   T4.mod_sub(m_coord_x, p, sub_ws); // x2*z1^2 - x1*z2^2

   T0.mod_sub(m_coord_y, p, sub_ws);

   if(T4.is_zero())

      {

      if(T0.is_zero())

         {

         mult2(ws_bn);

         return;

         }

      // setting to zero:

      m_coord_x.clear();

      m_coord_y = m_curve.get_1_rep();

      m_coord_z.clear();

      return;

      }

   m_curve.sqr(T2, T4, ws);

   m_curve.mul(T3, m_coord_x, T2, ws);

   m_curve.mul(T1, T2, T4, ws);

   m_curve.sqr(m_coord_x, T0, ws);

   m_coord_x.mod_sub(T1, p, sub_ws);

   m_coord_x.mod_sub(T3, p, sub_ws);

   m_coord_x.mod_sub(T3, p, sub_ws);

   T3.mod_sub(m_coord_x, p, sub_ws);

   m_curve.mul(T2, T0, T3, ws);

   m_curve.mul(T0, m_coord_y, T1, ws);

   T2.mod_sub(T0, p, sub_ws);

   m_coord_y.swap(T2);

   m_curve.mul(T0, m_coord_z, T4, ws);

   m_coord_z.swap(T0);

   }

void PointGFp::add(const word x_words[], size_t x_size,

                   const word y_words[], size_t y_size,

                   const word z_words[], size_t z_size,

                   std::vector<BigInt>& ws_bn)

   {

   if(all_zeros(x_words, x_size) & all_zeros(z_words, z_size))

      return;

   if(is_zero())

      {

      m_coord_x.set_words(x_words, x_size);

      m_coord_y.set_words(y_words, y_size);

      m_coord_z.set_words(z_words, z_size);

      return;

      }

   resize_ws(ws_bn, m_curve.get_ws_size());

   secure_vector<word>& ws = ws_bn[0].get_word_vector();

   secure_vector<word>& sub_ws = ws_bn[1].get_word_vector();

   BigInt& T0 = ws_bn[2];

   BigInt& T1 = ws_bn[3];

   BigInt& T2 = ws_bn[4];

   BigInt& T3 = ws_bn[5];

   BigInt& T4 = ws_bn[6];

   BigInt& T5 = ws_bn[7];

   /*

   https://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html#addition-add-1998-cmo-2

   */

   const BigInt& p = m_curve.get_p();

   m_curve.sqr(T0, z_words, z_size, ws); // z2^2

   m_curve.mul(T1, m_coord_x, T0, ws); // x1*z2^2

   m_curve.mul(T3, z_words, z_size, T0, ws); // z2^3

   m_curve.mul(T2, m_coord_y, T3, ws); // y1*z2^3

   m_curve.sqr(T3, m_coord_z, ws); // z1^2

   m_curve.mul(T4, x_words, x_size, T3, ws); // x2*z1^2

   m_curve.mul(T5, m_coord_z, T3, ws); // z1^3

   m_curve.mul(T0, y_words, y_size, T5, ws); // y2*z1^3

   T4.mod_sub(T1, p, sub_ws); // x2*z1^2 - x1*z2^2

   T0.mod_sub(T2, p, sub_ws);

   if(T4.is_zero())

      {

      if(T0.is_zero())

         {

         mult2(ws_bn);

         return;

         }

      // setting to zero:

      m_coord_x.clear();

      m_coord_y = m_curve.get_1_rep();

      m_coord_z.clear();

      return;

      }

   m_curve.sqr(T5, T4, ws);

   m_curve.mul(T3, T1, T5, ws);

   m_curve.mul(T1, T5, T4, ws);

   m_curve.sqr(m_coord_x, T0, ws);

   m_coord_x.mod_sub(T1, p, sub_ws);

   m_coord_x.mod_sub(T3, p, sub_ws);

   m_coord_x.mod_sub(T3, p, sub_ws);

   T3.mod_sub(m_coord_x, p, sub_ws);

   m_curve.mul(m_coord_y, T0, T3, ws);

   m_curve.mul(T3, T2, T1, ws);

   m_coord_y.mod_sub(T3, p, sub_ws);

   m_curve.mul(T3, z_words, z_size, m_coord_z, ws);

   m_curve.mul(m_coord_z, T3, T4, ws);

   }

void PointGFp::mult2i(size_t iterations, std::vector<BigInt>& ws_bn)

   {

   if(iterations == 0)

      return;

   if(m_coord_y.is_zero())

      {

      *this = PointGFp(m_curve); // setting myself to zero

      return;

      }

   /*

   TODO we can save 2 squarings per iteration by computing

   a*Z^4 using values cached from previous iteration

   */

   for(size_t i = 0; i != iterations; ++i)

      mult2(ws_bn);

   }

// *this *= 2

void PointGFp::mult2(std::vector<BigInt>& ws_bn)

   {

   if(is_zero())

      return;

   if(m_coord_y.is_zero())

      {

      *this = PointGFp(m_curve); // setting myself to zero

      return;

      }

   resize_ws(ws_bn, m_curve.get_ws_size());

   secure_vector<word>& ws = ws_bn[0].get_word_vector();

   secure_vector<word>& sub_ws = ws_bn[1].get_word_vector();

   BigInt& T0 = ws_bn[2];

   BigInt& T1 = ws_bn[3];

   BigInt& T2 = ws_bn[4];

   BigInt& T3 = ws_bn[5];

   BigInt& T4 = ws_bn[6];

   /*

   https://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html#doubling-dbl-1986-cc

   */

   const BigInt& p = m_curve.get_p();

   m_curve.sqr(T0, m_coord_y, ws);

   m_curve.mul(T1, m_coord_x, T0, ws);

   T1.mod_mul(4, p, sub_ws);

   if(m_curve.a_is_zero())

      {

      // if a == 0 then 3*x^2 + a*z^4 is just 3*x^2

      m_curve.sqr(T4, m_coord_x, ws); // x^2

      T4.mod_mul(3, p, sub_ws); // 3*x^2

      }

   else if(m_curve.a_is_minus_3())

      {

      /*

      if a == -3 then

        3*x^2 + a*z^4 == 3*x^2 - 3*z^4 == 3*(x^2-z^4) == 3*(x-z^2)*(x+z^2)

      */

      m_curve.sqr(T3, m_coord_z, ws); // z^2

      // (x-z^2)

      T2 = m_coord_x;

      T2.mod_sub(T3, p, sub_ws);

      // (x+z^2)

      T3.mod_add(m_coord_x, p, sub_ws);

      m_curve.mul(T4, T2, T3, ws); // (x-z^2)*(x+z^2)

      T4.mod_mul(3, p, sub_ws); // 3*(x-z^2)*(x+z^2)

      }

   else

      {

      m_curve.sqr(T3, m_coord_z, ws); // z^2

      m_curve.sqr(T4, T3, ws); // z^4

      m_curve.mul(T3, m_curve.get_a_rep(), T4, ws); // a*z^4

      m_curve.sqr(T4, m_coord_x, ws); // x^2

      T4.mod_mul(3, p, sub_ws);

      T4.mod_add(T3, p, sub_ws); // 3*x^2 + a*z^4

      }

   m_curve.sqr(T2, T4, ws);

   T2.mod_sub(T1, p, sub_ws);

   T2.mod_sub(T1, p, sub_ws);

   m_curve.sqr(T3, T0, ws);

   T3.mod_mul(8, p, sub_ws);

   T1.mod_sub(T2, p, sub_ws);

   m_curve.mul(T0, T4, T1, ws);

   T0.mod_sub(T3, p, sub_ws);

   m_coord_x.swap(T2);

   m_curve.mul(T2, m_coord_y, m_coord_z, ws);

   T2.mod_mul(2, p, sub_ws);

   m_coord_y.swap(T0);

   m_coord_z.swap(T2);

   }

// arithmetic operators

PointGFp& PointGFp::operator+=(const PointGFp& rhs)

   {

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

   add(rhs, ws);

   return *this;

   }

PointGFp& PointGFp::operator-=(const PointGFp& rhs)

   {

   PointGFp minus_rhs = PointGFp(rhs).negate();

   if(is_zero())

      *this = minus_rhs;

   else

      *this += minus_rhs;

   return *this;

   }

PointGFp& PointGFp::operator*=(const BigInt& scalar)

   {

   *this = scalar * *this;

   return *this;

   }

PointGFp operator*(const BigInt& scalar, const PointGFp& point)

   {

   BOTAN_DEBUG_ASSERT(point.on_the_curve());

   const size_t scalar_bits = scalar.bits();

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

   PointGFp R[2] = { point.zero(), 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_DEBUG_ASSERT(R[0].on_the_curve());

   return R[0];

   }

//static

void PointGFp::force_all_affine(std::vector<PointGFp>& points,

                                secure_vector<word>& ws)

   {

   if(points.size() <= 1)

      {

      for(size_t i = 0; i != points.size(); ++i)

         points[i].force_affine();

      return;

      }

   /*

   For >= 2 points use Montgomery's trick

   See Algorithm 2.26 in "Guide to Elliptic Curve Cryptography"

   (Hankerson, Menezes, Vanstone)

   TODO is it really necessary to save all k points in c?

   */

   const CurveGFp& curve = points[0].m_curve;

   const BigInt& rep_1 = curve.get_1_rep();

   if(ws.size() < curve.get_ws_size())

      ws.resize(curve.get_ws_size());

   std::vector<BigInt> c(points.size());

   c[0] = points[0].m_coord_z;

   for(size_t i = 1; i != points.size(); ++i)

      {

      curve.mul(c[i], c[i-1], points[i].m_coord_z, ws);

      }

   BigInt s_inv = curve.invert_element(c[c.size()-1], ws);

   BigInt z_inv, z2_inv, z3_inv;

   for(size_t i = points.size() - 1; i != 0; i--)

      {

      PointGFp& point = points[i];

      curve.mul(z_inv, s_inv, c[i-1], ws);

      s_inv = curve.mul_to_tmp(s_inv, point.m_coord_z, ws);

      curve.sqr(z2_inv, z_inv, ws);

      curve.mul(z3_inv, z2_inv, z_inv, ws);

      point.m_coord_x = curve.mul_to_tmp(point.m_coord_x, z2_inv, ws);

      point.m_coord_y = curve.mul_to_tmp(point.m_coord_y, z3_inv, ws);

      point.m_coord_z = rep_1;

      }

   curve.sqr(z2_inv, s_inv, ws);

   curve.mul(z3_inv, z2_inv, s_inv, ws);

   points[0].m_coord_x = curve.mul_to_tmp(points[0].m_coord_x, z2_inv, ws);

   points[0].m_coord_y = curve.mul_to_tmp(points[0].m_coord_y, z3_inv, ws);

   points[0].m_coord_z = rep_1;

   }

void PointGFp::force_affine()

   {

   if(is_zero())

      throw Invalid_State("Cannot convert zero ECC point to affine");

   secure_vector<word> ws;

   const BigInt z_inv = m_curve.invert_element(m_coord_z, ws);

   const BigInt z2_inv = m_curve.sqr_to_tmp(z_inv, ws);

   const BigInt z3_inv = m_curve.mul_to_tmp(z_inv, z2_inv, ws);

   m_coord_x = m_curve.mul_to_tmp(m_coord_x, z2_inv, ws);

   m_coord_y = m_curve.mul_to_tmp(m_coord_y, z3_inv, ws);

   m_coord_z = m_curve.get_1_rep();

   }

bool PointGFp::is_affine() const

   {

   return m_curve.is_one(m_coord_z);

   }

BigInt PointGFp::get_affine_x() const

   {

   if(is_zero())

      throw Illegal_Transformation("Cannot convert zero point to affine");

   secure_vector<word> monty_ws;

   if(is_affine())

      return m_curve.from_rep_to_tmp(m_coord_x, monty_ws);

   BigInt z2 = m_curve.sqr_to_tmp(m_coord_z, monty_ws);

   z2 = m_curve.invert_element(z2, monty_ws);

   BigInt r;

   m_curve.mul(r, m_coord_x, z2, monty_ws);

   m_curve.from_rep(r, monty_ws);

   return r;

   }

BigInt PointGFp::get_affine_y() const

   {

   if(is_zero())

      throw Illegal_Transformation("Cannot convert zero point to affine");

   secure_vector<word> monty_ws;

   if(is_affine())

      return m_curve.from_rep_to_tmp(m_coord_y, monty_ws);

   const BigInt z2 = m_curve.sqr_to_tmp(m_coord_z, monty_ws);

   const BigInt z3 = m_curve.mul_to_tmp(m_coord_z, z2, monty_ws);

   const BigInt z3_inv = m_curve.invert_element(z3, monty_ws);

   BigInt r;

   m_curve.mul(r, m_coord_y, z3_inv, monty_ws);

   m_curve.from_rep(r, monty_ws);

   return r;

   }

bool PointGFp::on_the_curve() const

   {

   /*

   Is the point still on the curve?? (If everything is correct, the

   point is always on its curve; then the function will return true.

   If somehow the state is corrupted, which suggests a fault attack

   (or internal computational error), then return false.

   */

   if(is_zero())

      return true;

   secure_vector<word> monty_ws;

   const BigInt y2 = m_curve.from_rep_to_tmp(m_curve.sqr_to_tmp(m_coord_y, monty_ws), monty_ws);

   const BigInt x3 = m_curve.mul_to_tmp(m_coord_x, m_curve.sqr_to_tmp(m_coord_x, monty_ws), monty_ws);

   const BigInt ax = m_curve.mul_to_tmp(m_coord_x, m_curve.get_a_rep(), monty_ws);

   const BigInt z2 = m_curve.sqr_to_tmp(m_coord_z, monty_ws);

   if(m_coord_z == z2) // Is z equal to 1 (in Montgomery form)?

      {

      if(y2 != m_curve.from_rep_to_tmp(x3 + ax + m_curve.get_b_rep(), monty_ws))

         return false;

      }

   const BigInt z3 = m_curve.mul_to_tmp(m_coord_z, z2, monty_ws);

   const BigInt ax_z4 = m_curve.mul_to_tmp(ax, m_curve.sqr_to_tmp(z2, monty_ws), monty_ws);

   const BigInt b_z6 = m_curve.mul_to_tmp(m_curve.get_b_rep(), m_curve.sqr_to_tmp(z3, monty_ws), monty_ws);

   if(y2 != m_curve.from_rep_to_tmp(x3 + ax_z4 + b_z6, monty_ws))

      return false;

   return true;

   }

// swaps the states of *this and other, does not throw!

void PointGFp::swap(PointGFp& other)

   {

   m_curve.swap(other.m_curve);

   m_coord_x.swap(other.m_coord_x);

   m_coord_y.swap(other.m_coord_y);

   m_coord_z.swap(other.m_coord_z);

   }

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

std::vector<uint8_t> PointGFp::encode(PointGFp::Compression_Type format) const

   {

   if(is_zero())

      return std::vector<uint8_t>(1); // single 0 byte

   const size_t p_bytes = m_curve.get_p().bytes();

   const BigInt x = get_affine_x();

   const BigInt y = get_affine_y();

   std::vector<uint8_t> result;

   if(format == PointGFp::UNCOMPRESSED)

      {

      result.resize(1 + 2*p_bytes);

      result[0] = 0x04;

      BigInt::encode_1363(&result[1], p_bytes, x);

      BigInt::encode_1363(&result[1+p_bytes], p_bytes, y);

      }

   else if(format == PointGFp::COMPRESSED)

      {

      result.resize(1 + p_bytes);

      result[0] = 0x02 | static_cast<uint8_t>(y.get_bit(0));

      BigInt::encode_1363(&result[1], p_bytes, x);

      }

   else if(format == PointGFp::HYBRID)

      {

      result.resize(1 + 2*p_bytes);

      result[0] = 0x06 | static_cast<uint8_t>(y.get_bit(0));

      BigInt::encode_1363(&result[1], p_bytes, x);

      BigInt::encode_1363(&result[1+p_bytes], p_bytes, y);

      }

   else

      throw Invalid_Argument("EC2OSP illegal point encoding");

   return result;

   }

namespace {

BigInt decompress_point(bool yMod2,

                        const BigInt& x,

                        const BigInt& curve_p,

                        const BigInt& curve_a,

                        const BigInt& curve_b)

   {

   BigInt xpow3 = x * x * x;

   BigInt g = curve_a * x;

   g += xpow3;

   g += curve_b;

   g = g % curve_p;

   BigInt z = ressol(g, curve_p);

   if(z < 0)

      throw Illegal_Point("error during EC point decompression");

   if(z.get_bit(0) != yMod2)

      z = curve_p - z;

   return z;

   }

}

PointGFp OS2ECP(const uint8_t data[], size_t data_len,

                const CurveGFp& curve)

   {

   // Should we really be doing this?

   if(data_len <= 1)

      return PointGFp(curve); // return zero

   std::pair<BigInt, BigInt> xy = OS2ECP(data, data_len, curve.get_p(), curve.get_a(), curve.get_b());

   PointGFp point(curve, xy.first, xy.second);

   if(!point.on_the_curve())

      throw Illegal_Point("OS2ECP: Decoded point was not on the curve");

   return point;

   }

std::pair<BigInt, BigInt> OS2ECP(const uint8_t data[], size_t data_len,

                                 const BigInt& curve_p,

                                 const BigInt& curve_a,

                                 const BigInt& curve_b)

   {

   if(data_len <= 1)

      throw Decoding_Error("OS2ECP invalid point");

   const uint8_t pc = data[0];

   BigInt x, y;

   if(pc == 2 || pc == 3)

      {

      //compressed form

      x = BigInt::decode(&data[1], data_len - 1);

      const bool y_mod_2 = ((pc & 0x01) == 1);

      y = decompress_point(y_mod_2, x, curve_p, curve_a, curve_b);

      }

   else if(pc == 4)

      {

      const size_t l = (data_len - 1) / 2;

      // uncompressed form

      x = BigInt::decode(&data[1], l);

      y = BigInt::decode(&data[l+1], l);

      }

   else if(pc == 6 || pc == 7)

      {

      const size_t l = (data_len - 1) / 2;

      // hybrid form

      x = BigInt::decode(&data[1], l);

      y = BigInt::decode(&data[l+1], l);

      const bool y_mod_2 = ((pc & 0x01) == 1);

      if(decompress_point(y_mod_2, x, curve_p, curve_a, curve_b) != y)

         throw Illegal_Point("OS2ECP: Decoding error in hybrid format");

      }

   else

      throw Invalid_Argument("OS2ECP: Unknown format type " + std::to_string(pc));

   return std::make_pair(x, y);

   }

}