ecdsa.cpp

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/*
* ECDSA implementation
* (C) 2007 Manuel Hartl, FlexSecure GmbH
*     2007 Falko Strenzke, FlexSecure GmbH
*     2008-2010,2015,2016,2018,2024 Jack Lloyd
*     2016 René Korthaus
*
* Botan is released under the Simplified BSD License (see license.txt)
*/
 
#include <botan/ecdsa.h>
 
#include <botan/ec_group.h>
#include <botan/internal/keypair.h>
#include <botan/internal/pk_ops_impl.h>
 
#if defined(BOTAN_HAS_RFC6979_GENERATOR)
   #include <botan/internal/rfc6979.h>
#endif
 
namespace Botan {
 
namespace {
 
EC_AffinePoint recover_ecdsa_public_key(
   const EC_Group& group, const std::vector<uint8_t>& msg, const BigInt& r, const BigInt& s, uint8_t v) {
   if(group.has_cofactor()) {
      throw Invalid_Argument("ECDSA public key recovery only supported for prime order groups");
   }
 
   if(v >= 4) {
      throw Invalid_Argument("Unexpected v param for ECDSA public key recovery");
   }
 
   const BigInt& group_order = group.get_order();
 
   if(r <= 0 || r >= group_order || s <= 0 || s >= group_order) {
      throw Invalid_Argument("Out of range r/s cannot recover ECDSA public key");
   }
 
   const uint8_t y_odd = v % 2;
   const bool add_order = (v >> 1) == 0x01;
   const size_t p_bytes = group.get_p_bytes();
 
   BigInt x = r;
 
   if(add_order) {
      x += group_order;
   }
 
   if(x.bytes() <= p_bytes) {
      std::vector<uint8_t> X(p_bytes + 1);
 
      X[0] = 0x02 | y_odd;
      x.serialize_to(std::span{X}.subspan(1));
 
      if(auto R = EC_AffinePoint::deserialize(group, X)) {
         // Compute r_inv * (-eG + s*R)
         const auto ne = EC_Scalar::from_bytes_with_trunc(group, msg).negate();
         const auto ss = EC_Scalar::from_bigint(group, s);
 
         const auto r_inv = EC_Scalar::from_bigint(group, r).invert_vartime();
 
         const EC_Group::Mul2Table GR_mul(R.value());
         if(auto egsr = GR_mul.mul2_vartime(ne * r_inv, ss * r_inv)) {
            return egsr.value();
         }
      }
   }
 
   throw Decoding_Error("Failed to recover ECDSA public key from signature/msg pair");
}
 
}  // namespace
 
ECDSA_PublicKey::ECDSA_PublicKey(
   const EC_Group& group, const std::vector<uint8_t>& msg, const BigInt& r, const BigInt& s, uint8_t v) :
      EC_PublicKey(group, recover_ecdsa_public_key(group, msg, r, s, v)) {}
 
std::optional<size_t> ECDSA_PublicKey::_signature_element_size_for_DER_encoding() const {
   return domain().get_order_bytes();
}
 
std::unique_ptr<Private_Key> ECDSA_PublicKey::generate_another(RandomNumberGenerator& rng) const {
   return std::make_unique<ECDSA_PrivateKey>(rng, domain());
}
 
uint8_t ECDSA_PublicKey::recovery_param(const std::vector<uint8_t>& msg, const BigInt& r, const BigInt& s) const {
   const auto this_key = this->_public_ec_point().serialize_compressed();
 
   for(uint8_t v = 0; v != 4; ++v) {
      try {
         const auto R = recover_ecdsa_public_key(this->domain(), msg, r, s, v);
 
         if(R.serialize_compressed() == this_key) {
            return v;
         }
      } catch(Decoding_Error&) {
         // try the next v
      }
   }
 
   throw Internal_Error("Could not determine ECDSA recovery parameter");
}
 
std::unique_ptr<Public_Key> ECDSA_PrivateKey::public_key() const {
   return std::make_unique<ECDSA_PublicKey>(domain(), _public_ec_point());
}
 
bool ECDSA_PrivateKey::check_key(RandomNumberGenerator& rng, bool strong) const {
   if(!EC_PrivateKey::check_key(rng, strong)) {
      return false;
   }
 
   if(!strong) {
      return true;
   }
 
   return KeyPair::signature_consistency_check(rng, *this, "SHA-256");
}
 
namespace {
 
/**
* ECDSA signature operation
*/
class ECDSA_Signature_Operation final : public PK_Ops::Signature_with_Hash {
   public:
      ECDSA_Signature_Operation(const ECDSA_PrivateKey& ecdsa, std::string_view padding, RandomNumberGenerator& rng) :
            PK_Ops::Signature_with_Hash(padding),
            m_group(ecdsa.domain()),
            m_x(ecdsa._private_key()),
            m_b(EC_Scalar::random(m_group, rng)) {
#if defined(BOTAN_HAS_RFC6979_GENERATOR)
         m_rfc6979 = std::make_unique<RFC6979_Nonce_Generator>(
            this->rfc6979_hash_function(), m_group.get_order_bits(), ecdsa._private_key());
#endif
      }
 
      size_t signature_length() const override { return 2 * m_group.get_order_bytes(); }
 
      std::vector<uint8_t> raw_sign(std::span<const uint8_t> msg, RandomNumberGenerator& rng) override;
 
      AlgorithmIdentifier algorithm_identifier() const override;
 
   private:
      const EC_Group m_group;
      const EC_Scalar m_x;
 
#if defined(BOTAN_HAS_RFC6979_GENERATOR)
      std::unique_ptr<RFC6979_Nonce_Generator> m_rfc6979;
#endif
 
      EC_Scalar m_b;
};
 
AlgorithmIdentifier ECDSA_Signature_Operation::algorithm_identifier() const {
   const std::string full_name = "ECDSA/" + hash_function();
   const OID oid = OID::from_string(full_name);
   return AlgorithmIdentifier(oid, AlgorithmIdentifier::USE_EMPTY_PARAM);
}
 
std::vector<uint8_t> ECDSA_Signature_Operation::raw_sign(std::span<const uint8_t> msg, RandomNumberGenerator& rng) {
   const auto m = EC_Scalar::from_bytes_with_trunc(m_group, msg);
 
#if defined(BOTAN_HAS_RFC6979_GENERATOR)
   const auto k = m_rfc6979->nonce_for(m_group, m);
#else
   const auto k = EC_Scalar::random(m_group, rng);
#endif
 
   const auto r = EC_Scalar::gk_x_mod_order(k, rng);
 
   /*
   * Blind the inputs
   *
   * Here we are computing (x*r+m)/k
   *
   * Instead have a random b and compute (k*b)^-1
   *
   * Then compute (x*r+m) as (x*r*b + m*b)
   *
   * Finally (x*r*b + m*b)/(k*b) = (x*r+m)/k
   *
   * This effectively blinds both the inversion as well as the various scalar
   * multiplications. All of these operations should be constant-time anyway but
   * blinding is very cheap and may help if either the compiler introduces
   * variable-time behavior, or for the case of EM/power side channel attacks [1].
   *
   * [1] But note that such attacks are currently outside of Botan's threat model.
   *
   */
   const auto k_inv = (m_b * k).invert();
 
   const auto xr_m = ((m_x * m_b) * r) + (m * m_b);
 
   const auto s = (k_inv * xr_m);
 
   // Generate the next blinding value via modular squaring
   m_b.square_self();
 
   // With overwhelming probability, a bug rather than actual zero r/s
   if(r.is_zero() || s.is_zero()) {
      throw Internal_Error("During ECDSA signature generated zero r/s");
   }
 
   return EC_Scalar::serialize_pair(r, s);
}
 
/**
* ECDSA verification operation
*/
class ECDSA_Verification_Operation final : public PK_Ops::Verification_with_Hash {
   public:
      ECDSA_Verification_Operation(const ECDSA_PublicKey& ecdsa, std::string_view padding) :
            PK_Ops::Verification_with_Hash(padding), m_group(ecdsa.domain()), m_gy_mul(ecdsa._public_ec_point()) {}
 
      ECDSA_Verification_Operation(const ECDSA_PublicKey& ecdsa, const AlgorithmIdentifier& alg_id) :
            PK_Ops::Verification_with_Hash(alg_id, "ECDSA", true),
            m_group(ecdsa.domain()),
            m_gy_mul(ecdsa._public_ec_point()) {}
 
      bool verify(std::span<const uint8_t> msg, std::span<const uint8_t> sig) override;
 
   private:
      const EC_Group m_group;
      const EC_Group::Mul2Table m_gy_mul;
};
 
bool ECDSA_Verification_Operation::verify(std::span<const uint8_t> msg, std::span<const uint8_t> sig) {
   if(auto rs = EC_Scalar::deserialize_pair(m_group, sig)) {
      const auto& [r, s] = rs.value();
 
      if(r.is_nonzero() && s.is_nonzero()) {
         const auto m = EC_Scalar::from_bytes_with_trunc(m_group, msg);
 
         const auto w = s.invert_vartime();
 
         // Check if r == x_coord(g*w*m + y*w*r) % n
         return m_gy_mul.mul2_vartime_x_mod_order_eq(r, w, m, r);
      }
   }
 
   return false;
}
 
}  // namespace
 
std::unique_ptr<PK_Ops::Verification> ECDSA_PublicKey::create_verification_op(std::string_view params,
                                                                              std::string_view provider) const {
   if(provider == "base" || provider.empty()) {
      return std::make_unique<ECDSA_Verification_Operation>(*this, params);
   }
 
   throw Provider_Not_Found(algo_name(), provider);
}
 
std::unique_ptr<PK_Ops::Verification> ECDSA_PublicKey::create_x509_verification_op(
   const AlgorithmIdentifier& signature_algorithm, std::string_view provider) const {
   if(provider == "base" || provider.empty()) {
      return std::make_unique<ECDSA_Verification_Operation>(*this, signature_algorithm);
   }
 
   throw Provider_Not_Found(algo_name(), provider);
}
 
std::unique_ptr<PK_Ops::Signature> ECDSA_PrivateKey::create_signature_op(RandomNumberGenerator& rng,
                                                                         std::string_view params,
                                                                         std::string_view provider) const {
   if(provider == "base" || provider.empty()) {
      return std::make_unique<ECDSA_Signature_Operation>(*this, params, rng);
   }
 
   throw Provider_Not_Found(algo_name(), provider);
}
 
}  // namespace Botan