randombit / botan / 5079590438

EC_Point::EC_Point(const CurveGFp& curve) : m_curve(curve), m_coord_x(0), m_coord_y(curve.get_1_rep()), m_coord_z(0) {

}

EC_Point::EC_Point(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 EC_Point affine x");

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

      throw Invalid_Argument("Invalid EC_Point 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 EC_Point::randomize_repr(RandomNumberGenerator& rng) {

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

   randomize_repr(rng, ws);

}

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

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

   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);

}

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

   BOTAN_ASSERT(ws_bn.size() >= EC_Point::WORKSPACE_SIZE, "Expected size for EC_Point workspace");

   for(auto& ws : ws_bn)

      if(ws.size() < cap_size)

         ws.get_word_vector().resize(cap_size);

}

void EC_Point::add_affine(

   if((CT::all_zeros(x_words, x_size) & CT::all_zeros(y_words, y_size)).is_set()) {

   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];

   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;

      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 EC_Point::add(const word x_words[],

   if((CT::all_zeros(x_words, x_size) & CT::all_zeros(z_words, z_size)).is_set())

   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];

   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;

      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 EC_Point::mult2i(size_t iterations, std::vector<BigInt>& ws_bn) {

   if(iterations == 0)

   if(m_coord_y.is_zero()) {

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

      mult2(ws_bn);

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

   if(is_zero())

   if(m_coord_y.is_zero()) {

   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];

   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()) {

      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()) {

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

      T2 = m_coord_x;

      T2.mod_sub(T3, p, sub_ws);

      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)

      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);

EC_Point& EC_Point::operator+=(const EC_Point& rhs) {

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

   add(rhs, ws);

   return *this;

}

EC_Point& EC_Point::operator-=(const EC_Point& rhs) {

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

   if(is_zero())

      *this += minus_rhs;

   return *this;

}

EC_Point& EC_Point::operator*=(const BigInt& scalar) {

   *this = scalar * *this;

   return *this;

EC_Point operator*(const BigInt& scalar, const EC_Point& point) {

   BOTAN_DEBUG_ASSERT(point.on_the_curve());

   const size_t scalar_bits = scalar.bits();

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

   EC_Point 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())

   BOTAN_DEBUG_ASSERT(R[0].on_the_curve());

   return R[0];

}

void EC_Point::force_all_affine(std::vector<EC_Point>& points, secure_vector<word>& ws) {

   if(points.size() <= 1) {

   for(auto& point : points) {

      if(point.is_zero())

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

   const BigInt& rep_1 = curve.get_1_rep();

   if(ws.size() < 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--) {

      EC_Point& 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 EC_Point::force_affine() {

   if(is_zero())

   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 EC_Point::is_affine() const { return m_curve.is_one(m_coord_z); }

BigInt EC_Point::get_affine_x() const {

   if(is_zero())

      throw Invalid_State("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 EC_Point::get_affine_y() const {

   if(is_zero())

      throw Invalid_State("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 EC_Point::on_the_curve() const {

   if(is_zero())

   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))

   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;

}

void EC_Point::swap(EC_Point& 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 EC_Point::operator==(const EC_Point& other) const {

   if(m_curve != other.m_curve)

   if(is_zero())

      return other.is_zero();

   return (get_affine_x() == other.get_affine_x() && get_affine_y() == other.get_affine_y());

std::vector<uint8_t> EC_Point::encode(EC_Point_Format 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 == EC_Point_Format::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 == EC_Point_Format::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 == EC_Point_Format::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);

   return result;

}

BigInt decompress_point(

   BigInt xpow3 = x * x * x;

   BigInt g = curve_a * x;

   g += xpow3;

   g += curve_b;

   g = g % curve_p;

   BigInt z = sqrt_modulo_prime(g, curve_p);

   if(z < 0)

      throw Decoding_Error("Error during EC point decompression");

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

      z = curve_p - z;

   return z;

}

EC_Point OS2ECP(const uint8_t data[], size_t data_len, const CurveGFp& curve) {

   if(data_len <= 1)

      return EC_Point(curve);  // return zero

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

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

   if(!point.on_the_curve())

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

   return point;

}

std::pair<BigInt, BigInt> OS2ECP(

   if(data_len <= 1)

   const uint8_t pc = data[0];

   BigInt x, y;

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

      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;

      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;

      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 Decoding_Error("OS2ECP: Decoding error in hybrid format");

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

   return std::make_pair(x, y);

}