ec_inner_data.cpp

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/*
* (C) 2024 Jack Lloyd
*
* Botan is released under the Simplified BSD License (see license.txt)
*/
 
#include <botan/internal/ec_inner_data.h>
 
#include <botan/der_enc.h>
#include <botan/internal/ec_inner_pc.h>
#include <botan/internal/fmt.h>
#include <botan/internal/pcurves.h>
#include <algorithm>
 
#if defined(BOTAN_HAS_LEGACY_EC_POINT)
   #include <botan/internal/ec_inner_bn.h>
   #include <botan/internal/point_mul.h>
#endif
 
#if defined(BOTAN_HAS_XMD)
   #include <botan/internal/xmd.h>
#endif
 
namespace Botan {
 
EC_Group_Data::~EC_Group_Data() = default;
 
// Note this constructor *does not* initialize m_curve, m_base_point or m_base_mult
EC_Group_Data::EC_Group_Data(const BigInt& p,
                             const BigInt& a,
                             const BigInt& b,
                             const BigInt& g_x,
                             const BigInt& g_y,
                             const BigInt& order,
                             const BigInt& cofactor,
                             const OID& oid,
                             EC_Group_Source source) :
      m_p(p),
      m_a(a),
      m_b(b),
      m_g_x(g_x),
      m_g_y(g_y),
      m_order(order),
      m_cofactor(cofactor),
#if defined(BOTAN_HAS_LEGACY_EC_POINT)
      m_mod_field(Barrett_Reduction::for_public_modulus(p)),
      m_mod_order(Barrett_Reduction::for_public_modulus(order)),
      m_monty(m_p, m_mod_field),
#endif
      m_oid(oid),
      m_p_words(p.sig_words()),
      m_p_bits(p.bits()),
      m_order_bits(order.bits()),
      m_order_bytes((m_order_bits + 7) / 8),
      m_a_is_minus_3(a == p - 3),
      m_a_is_zero(a.is_zero()),
      m_has_cofactor(m_cofactor != 1),
      m_order_is_less_than_p(m_order < p),
      m_source(source) {
   // TODO(Botan4) we can assume/assert the OID is set
   if(!m_oid.empty()) {
      DER_Encoder der(m_der_named_curve);
      der.encode(m_oid);
 
      const std::string name = m_oid.human_name_or_empty();
      if(!name.empty()) {
         // returns nullptr if unknown or not supported
         m_pcurve = PCurve::PrimeOrderCurve::for_named_curve(name);
      }
      if(m_pcurve) {
         m_engine = EC_Group_Engine::Optimized;
      }
   }
 
   // Try a generic pcurves instance
   if(!m_pcurve && !m_has_cofactor) {
      m_pcurve = PCurve::PrimeOrderCurve::from_params(p, a, b, g_x, g_y, order);
      if(m_pcurve) {
         m_engine = EC_Group_Engine::Generic;
      }
      // possibly still null here, if parameters unsuitable or if the
      // pcurves_generic module wasn't included in the build
   }
 
#if defined(BOTAN_HAS_LEGACY_EC_POINT)
   secure_vector<word> ws;
   m_a_r = m_monty.mul(a, m_monty.R2(), ws);
   m_b_r = m_monty.mul(b, m_monty.R2(), ws);
   if(!m_pcurve) {
      m_engine = EC_Group_Engine::Legacy;
   }
#else
   if(!m_pcurve) {
      if(m_oid.empty()) {
         throw Not_Implemented("EC_Group this group is not supported in this build configuration");
      } else {
         throw Not_Implemented(
            fmt("EC_Group the group {} is not supported in this build configuration", oid.to_string()));
      }
   }
#endif
}
 
std::shared_ptr<EC_Group_Data> EC_Group_Data::create(const BigInt& p,
                                                     const BigInt& a,
                                                     const BigInt& b,
                                                     const BigInt& g_x,
                                                     const BigInt& g_y,
                                                     const BigInt& order,
                                                     const BigInt& cofactor,
                                                     const OID& oid,
                                                     EC_Group_Source source) {
   auto group = std::make_shared<EC_Group_Data>(p, a, b, g_x, g_y, order, cofactor, oid, source);
 
#if defined(BOTAN_HAS_LEGACY_EC_POINT)
   group->m_curve = CurveGFp(group.get());
   group->m_base_point = EC_Point(group->m_curve, g_x, g_y);
   if(!group->m_pcurve) {
      group->m_base_mult = std::make_unique<EC_Point_Base_Point_Precompute>(group->m_base_point, group->m_mod_order);
   }
#endif
 
   return group;
}
 
bool EC_Group_Data::params_match(const BigInt& p,
                                 const BigInt& a,
                                 const BigInt& b,
                                 const BigInt& g_x,
                                 const BigInt& g_y,
                                 const BigInt& order,
                                 const BigInt& cofactor) const {
   if(p != this->p()) {
      return false;
   }
   if(a != this->a()) {
      return false;
   }
   if(b != this->b()) {
      return false;
   }
   if(order != this->order()) {
      return false;
   }
   if(cofactor != this->cofactor()) {
      return false;
   }
   if(g_x != this->g_x()) {
      return false;
   }
   if(g_y != this->g_y()) {
      return false;
   }
 
   return true;
}
 
bool EC_Group_Data::params_match(const BigInt& p,
                                 const BigInt& a,
                                 const BigInt& b,
                                 std::span<const uint8_t> base_pt,
                                 const BigInt& order,
                                 const BigInt& cofactor) const {
   if(p != this->p()) {
      return false;
   }
   if(a != this->a()) {
      return false;
   }
   if(b != this->b()) {
      return false;
   }
   if(order != this->order()) {
      return false;
   }
   if(cofactor != this->cofactor()) {
      return false;
   }
 
   const size_t field_len = this->p_bytes();
 
   if(base_pt.size() == 1 + field_len && (base_pt[0] == 0x02 || base_pt[0] == 0x03)) {
      // compressed
 
      const auto g_x = m_g_x.serialize(field_len);
      const auto g_y = m_g_y.is_odd();
 
      const auto sec1_x = base_pt.subspan(1, field_len);
      const bool sec1_y = (base_pt[0] == 0x03);
 
      if(!std::ranges::equal(sec1_x, g_x)) {
         return false;
      }
 
      if(sec1_y != g_y) {
         return false;
      }
 
      return true;
   } else if(base_pt.size() == 1 + 2 * field_len && base_pt[0] == 0x04) {
      const auto g_x = m_g_x.serialize(field_len);
      const auto g_y = m_g_y.serialize(field_len);
 
      const auto sec1_x = base_pt.subspan(1, field_len);
      const auto sec1_y = base_pt.subspan(1 + field_len, field_len);
 
      if(!std::ranges::equal(sec1_x, g_x)) {
         return false;
      }
 
      if(!std::ranges::equal(sec1_y, g_y)) {
         return false;
      }
 
      return true;
   } else {
      throw Decoding_Error("Invalid base point encoding in explicit group");
   }
}
 
bool EC_Group_Data::params_match(const EC_Group_Data& other) const {
   return params_match(other.p(), other.a(), other.b(), other.g_x(), other.g_y(), other.order(), other.cofactor());
}
 
void EC_Group_Data::set_oid(const OID& oid) {
   BOTAN_ARG_CHECK(!oid.empty(), "OID should be set");
   BOTAN_STATE_CHECK(m_oid.empty() && m_der_named_curve.empty());
   m_oid = oid;
 
   DER_Encoder der(m_der_named_curve);
   der.encode(m_oid);
}
 
std::unique_ptr<EC_Scalar_Data> EC_Group_Data::scalar_from_bytes_with_trunc(std::span<const uint8_t> bytes) const {
   const size_t bit_length = 8 * bytes.size();
 
   if(bit_length < order_bits()) {
      // No shifting required, but might still need to reduce by modulus
      return this->scalar_from_bytes_mod_order(bytes);
   } else {
      const size_t shift = bit_length - order_bits();
 
      const size_t new_length = bytes.size() - (shift / 8);
      const size_t bit_shift = shift % 8;
 
      if(bit_shift == 0) {
         // Easy case just read different bytes
         return this->scalar_from_bytes_mod_order(bytes.first(new_length));
      } else {
         std::vector<uint8_t> sbytes(new_length);
 
         uint8_t carry = 0;
         for(size_t i = 0; i != new_length; ++i) {
            const uint8_t w = bytes[i];
            sbytes[i] = (w >> bit_shift) | carry;
            carry = w << (8 - bit_shift);
         }
 
         return this->scalar_from_bytes_mod_order(sbytes);
      }
   }
}
 
std::unique_ptr<EC_Scalar_Data> EC_Group_Data::scalar_from_bytes_mod_order(std::span<const uint8_t> bytes) const {
   if(bytes.size() > 2 * order_bytes()) {
      return {};
   }
 
   if(m_pcurve) {
      if(auto s = m_pcurve->scalar_from_wide_bytes(bytes)) {
         return std::make_unique<EC_Scalar_Data_PC>(shared_from_this(), std::move(*s));
      } else {
         return {};
      }
   } else {
#if defined(BOTAN_HAS_LEGACY_EC_POINT)
      return std::make_unique<EC_Scalar_Data_BN>(shared_from_this(), m_mod_order.reduce(BigInt(bytes)));
#else
      throw Not_Implemented("Legacy EC interfaces disabled in this build configuration");
#endif
   }
}
 
std::unique_ptr<EC_Scalar_Data> EC_Group_Data::scalar_random(RandomNumberGenerator& rng) const {
   if(m_pcurve) {
      return std::make_unique<EC_Scalar_Data_PC>(shared_from_this(), m_pcurve->random_scalar(rng));
   } else {
#if defined(BOTAN_HAS_LEGACY_EC_POINT)
      return std::make_unique<EC_Scalar_Data_BN>(shared_from_this(),
                                                 BigInt::random_integer(rng, BigInt::one(), m_order));
#else
      throw Not_Implemented("Legacy EC interfaces disabled in this build configuration");
#endif
   }
}
 
std::unique_ptr<EC_Scalar_Data> EC_Group_Data::scalar_one() const {
   if(m_pcurve) {
      return std::make_unique<EC_Scalar_Data_PC>(shared_from_this(), m_pcurve->scalar_one());
   } else {
#if defined(BOTAN_HAS_LEGACY_EC_POINT)
      return std::make_unique<EC_Scalar_Data_BN>(shared_from_this(), BigInt::one());
#else
      throw Not_Implemented("Legacy EC interfaces disabled in this build configuration");
#endif
   }
}
 
std::unique_ptr<EC_Scalar_Data> EC_Group_Data::scalar_from_bigint(const BigInt& bn) const {
   if(bn <= 0 || bn >= m_order) {
      return {};
   }
 
   if(m_pcurve) {
      return this->scalar_deserialize(bn.serialize(m_order_bytes));
   } else {
#if defined(BOTAN_HAS_LEGACY_EC_POINT)
      return std::make_unique<EC_Scalar_Data_BN>(shared_from_this(), bn);
#else
      throw Not_Implemented("Legacy EC interfaces disabled in this build configuration");
#endif
   }
}
 
std::unique_ptr<EC_Scalar_Data> EC_Group_Data::gk_x_mod_order(const EC_Scalar_Data& scalar,
                                                              RandomNumberGenerator& rng) const {
   if(m_pcurve) {
      const auto& k = EC_Scalar_Data_PC::checked_ref(scalar);
      auto gk_x_mod_order = m_pcurve->base_point_mul_x_mod_order(k.value(), rng);
      return std::make_unique<EC_Scalar_Data_PC>(shared_from_this(), gk_x_mod_order);
   } else {
#if defined(BOTAN_HAS_LEGACY_EC_POINT)
      const auto& k = EC_Scalar_Data_BN::checked_ref(scalar);
      BOTAN_STATE_CHECK(m_base_mult != nullptr);
      std::vector<BigInt> ws;
      const auto pt = m_base_mult->mul(k.value(), rng, m_order, ws);
 
      if(pt.is_zero()) {
         return std::make_unique<EC_Scalar_Data_BN>(shared_from_this(), BigInt::zero());
      } else {
         return std::make_unique<EC_Scalar_Data_BN>(shared_from_this(), m_mod_order.reduce(pt.get_affine_x()));
      }
#else
      throw Not_Implemented("Legacy EC interfaces disabled in this build configuration");
#endif
   }
}
 
std::unique_ptr<EC_Scalar_Data> EC_Group_Data::scalar_deserialize(std::span<const uint8_t> bytes) const {
   if(bytes.size() != m_order_bytes) {
      return nullptr;
   }
 
   if(m_pcurve) {
      if(auto s = m_pcurve->deserialize_scalar(bytes)) {
         return std::make_unique<EC_Scalar_Data_PC>(shared_from_this(), *s);
      } else {
         return nullptr;
      }
   } else {
#if defined(BOTAN_HAS_LEGACY_EC_POINT)
      BigInt r(bytes);
 
      if(r.is_zero() || r >= m_order) {
         return nullptr;
      }
 
      return std::make_unique<EC_Scalar_Data_BN>(shared_from_this(), std::move(r));
#else
      throw Not_Implemented("Legacy EC interfaces disabled in this build configuration");
#endif
   }
}
 
std::unique_ptr<EC_AffinePoint_Data> EC_Group_Data::point_deserialize(std::span<const uint8_t> bytes) const {
   // The deprecated "hybrid" point format
   // TODO(Botan4) remove this
   if(bytes.size() >= 1 + 2 * 4 && (bytes[0] == 0x06 || bytes[0] == 0x07)) {
      const bool hdr_y_is_even = bytes[0] == 0x06;
      const bool y_is_even = (bytes.back() & 0x01) == 0;
 
      if(hdr_y_is_even == y_is_even) {
         std::vector<uint8_t> sec1(bytes.begin(), bytes.end());
         sec1[0] = 0x04;
         return this->point_deserialize(sec1);
      }
   }
 
   try {
      if(m_pcurve) {
         if(auto pt = m_pcurve->deserialize_point(bytes)) {
            return std::make_unique<EC_AffinePoint_Data_PC>(shared_from_this(), std::move(*pt));
         } else {
            return {};
         }
      } else {
#if defined(BOTAN_HAS_LEGACY_EC_POINT)
         auto pt = Botan::OS2ECP(bytes, m_curve);
         return std::make_unique<EC_AffinePoint_Data_BN>(shared_from_this(), std::move(pt));
#else
         throw Not_Implemented("Legacy EC interfaces disabled in this build configuration");
#endif
      }
   } catch(...) {
      return {};
   }
}
 
namespace {
 
std::function<void(std::span<uint8_t>)> h2c_expand_message(std::string_view hash_fn,
                                                           std::span<const uint8_t> input,
                                                           std::span<const uint8_t> domain_sep) {
   /*
   * This could be extended to support expand_message_xof or a MHF like Argon2
   */
 
   if(hash_fn.starts_with("SHAKE")) {
      throw Not_Implemented("Hash to curve currently does not support expand_message_xof");
   }
 
   return [=](std::span<uint8_t> uniform_bytes) {
#if defined(BOTAN_HAS_XMD)
      expand_message_xmd(hash_fn, uniform_bytes, input, domain_sep);
#else
      BOTAN_UNUSED(hash_fn, uniform_bytes, input, domain_sep);
      throw Not_Implemented("Hash to curve is not implemented due to XMD being disabled");
#endif
   };
}
 
}  // namespace
 
std::unique_ptr<EC_AffinePoint_Data> EC_Group_Data::point_hash_to_curve_ro(std::string_view hash_fn,
                                                                           std::span<const uint8_t> input,
                                                                           std::span<const uint8_t> domain_sep) const {
   if(m_pcurve) {
      auto pt = m_pcurve->hash_to_curve_ro(h2c_expand_message(hash_fn, input, domain_sep));
      return std::make_unique<EC_AffinePoint_Data_PC>(shared_from_this(), m_pcurve->point_to_affine(pt));
   } else {
      throw Not_Implemented("Hash to curve is not implemented for this curve");
   }
}
 
std::unique_ptr<EC_AffinePoint_Data> EC_Group_Data::point_hash_to_curve_nu(std::string_view hash_fn,
                                                                           std::span<const uint8_t> input,
                                                                           std::span<const uint8_t> domain_sep) const {
   if(m_pcurve) {
      auto pt = m_pcurve->hash_to_curve_nu(h2c_expand_message(hash_fn, input, domain_sep));
      return std::make_unique<EC_AffinePoint_Data_PC>(shared_from_this(), std::move(pt));
   } else {
      throw Not_Implemented("Hash to curve is not implemented for this curve");
   }
}
 
std::unique_ptr<EC_AffinePoint_Data> EC_Group_Data::point_g_mul(const EC_Scalar_Data& scalar,
                                                                RandomNumberGenerator& rng) const {
   if(m_pcurve) {
      const auto& k = EC_Scalar_Data_PC::checked_ref(scalar);
      auto pt = m_pcurve->point_to_affine(m_pcurve->mul_by_g(k.value(), rng));
      return std::make_unique<EC_AffinePoint_Data_PC>(shared_from_this(), std::move(pt));
   } else {
#if defined(BOTAN_HAS_LEGACY_EC_POINT)
      const auto& group = scalar.group();
      const auto& bn = EC_Scalar_Data_BN::checked_ref(scalar);
 
      BOTAN_STATE_CHECK(group->m_base_mult != nullptr);
      std::vector<BigInt> ws;
      auto pt = group->m_base_mult->mul(bn.value(), rng, m_order, ws);
      return std::make_unique<EC_AffinePoint_Data_BN>(shared_from_this(), std::move(pt));
#else
      throw Not_Implemented("Legacy EC interfaces disabled in this build configuration");
#endif
   }
}
 
std::unique_ptr<EC_AffinePoint_Data> EC_Group_Data::mul_px_qy(const EC_AffinePoint_Data& p,
                                                              const EC_Scalar_Data& x,
                                                              const EC_AffinePoint_Data& q,
                                                              const EC_Scalar_Data& y,
                                                              RandomNumberGenerator& rng) const {
   if(m_pcurve) {
      auto pt = m_pcurve->mul_px_qy(EC_AffinePoint_Data_PC::checked_ref(p).value(),
                                    EC_Scalar_Data_PC::checked_ref(x).value(),
                                    EC_AffinePoint_Data_PC::checked_ref(q).value(),
                                    EC_Scalar_Data_PC::checked_ref(y).value(),
                                    rng);
 
      if(pt) {
         return std::make_unique<EC_AffinePoint_Data_PC>(shared_from_this(), m_pcurve->point_to_affine(*pt));
      } else {
         return nullptr;
      }
   } else {
#if defined(BOTAN_HAS_LEGACY_EC_POINT)
      std::vector<BigInt> ws;
      const auto& group = p.group();
 
      // TODO this could be better!
      const EC_Point_Var_Point_Precompute p_mul(p.to_legacy_point(), rng, ws);
      const EC_Point_Var_Point_Precompute q_mul(q.to_legacy_point(), rng, ws);
 
      const auto order = group->order() * group->cofactor();  // See #3800
 
      auto px = p_mul.mul(EC_Scalar_Data_BN::checked_ref(x).value(), rng, order, ws);
      auto qy = q_mul.mul(EC_Scalar_Data_BN::checked_ref(y).value(), rng, order, ws);
 
      auto px_qy = px + qy;
 
      if(!px_qy.is_zero()) {
         px_qy.force_affine();
         return std::make_unique<EC_AffinePoint_Data_BN>(shared_from_this(), std::move(px_qy));
      } else {
         return nullptr;
      }
#else
      throw Not_Implemented("Legacy EC interfaces disabled in this build configuration");
#endif
   }
}
 
std::unique_ptr<EC_AffinePoint_Data> EC_Group_Data::affine_add(const EC_AffinePoint_Data& p,
                                                               const EC_AffinePoint_Data& q) const {
   if(m_pcurve) {
      auto pt = m_pcurve->point_add(EC_AffinePoint_Data_PC::checked_ref(p).value(),
                                    EC_AffinePoint_Data_PC::checked_ref(q).value());
 
      return std::make_unique<EC_AffinePoint_Data_PC>(shared_from_this(), m_pcurve->point_to_affine(pt));
   } else {
#if defined(BOTAN_HAS_LEGACY_EC_POINT)
      auto pt = p.to_legacy_point() + q.to_legacy_point();
      return std::make_unique<EC_AffinePoint_Data_BN>(shared_from_this(), std::move(pt));
#else
      throw Not_Implemented("Legacy EC interfaces disabled in this build configuration");
#endif
   }
}
 
std::unique_ptr<EC_AffinePoint_Data> EC_Group_Data::affine_neg(const EC_AffinePoint_Data& p) const {
   if(m_pcurve) {
      auto pt = m_pcurve->point_negate(EC_AffinePoint_Data_PC::checked_ref(p).value());
      return std::make_unique<EC_AffinePoint_Data_PC>(shared_from_this(), pt);
   } else {
#if defined(BOTAN_HAS_LEGACY_EC_POINT)
      auto pt = p.to_legacy_point();
      pt.negate();  // negates in place
      return std::make_unique<EC_AffinePoint_Data_BN>(shared_from_this(), std::move(pt));
#else
      throw Not_Implemented("Legacy EC interfaces disabled in this build configuration");
#endif
   }
}
 
std::unique_ptr<EC_Mul2Table_Data> EC_Group_Data::make_mul2_table(const EC_AffinePoint_Data& h) const {
   if(m_pcurve) {
      return std::make_unique<EC_Mul2Table_Data_PC>(h);
   } else {
#if defined(BOTAN_HAS_LEGACY_EC_POINT)
      const EC_AffinePoint_Data_BN g(shared_from_this(), this->base_point());
      return std::make_unique<EC_Mul2Table_Data_BN>(g, h);
#else
      throw Not_Implemented("Legacy EC interfaces disabled in this build configuration");
#endif
   }
}
 
}  // namespace Botan