ecdsa.cpp

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/*
* ECDSA implemenation
* (C) 2007 Manuel Hartl, FlexSecure GmbH
*     2007 Falko Strenzke, FlexSecure GmbH
*     2008-2010,2015,2016,2018 Jack Lloyd
*     2016 René Korthaus
*
* Botan is released under the Simplified BSD License (see license.txt)
*/
 
#include <botan/ecdsa.h>
 
#include <botan/reducer.h>
#include <botan/internal/keypair.h>
#include <botan/internal/pk_ops_impl.h>
#include <botan/internal/point_mul.h>
 
#if defined(BOTAN_HAS_RFC6979_GENERATOR)
   #include <botan/internal/rfc6979.h>
#endif
 
namespace Botan {
 
namespace {
 
EC_Point 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.get_cofactor() != 1) {
      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 uint8_t add_order = v >> 1;
   const size_t p_bytes = group.get_p_bytes();
 
   try {
      const BigInt e = BigInt::from_bytes_with_max_bits(msg.data(), msg.size(), group.get_order_bits());
      const BigInt r_inv = group.inverse_mod_order(r);
 
      BigInt x = r + add_order * group_order;
 
      std::vector<uint8_t> X(p_bytes + 1);
 
      X[0] = 0x02 | y_odd;
      x.serialize_to(std::span{X}.subspan(1));
 
      const EC_Point R = group.OS2ECP(X);
 
      if((R * group_order).is_zero() == false) {
         throw Decoding_Error("Unable to recover ECDSA public key");
      }
 
      // Compute r_inv * (s*R - eG)
      EC_Point_Multi_Point_Precompute RG_mul(R, group.get_base_point());
      const BigInt ne = group.mod_order(group_order - e);
      return r_inv * RG_mul.multi_exp(s, ne);
   } catch(...) {
      // continue on and throw
   }
 
   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::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 {
   for(uint8_t v = 0; v != 4; ++v) {
      try {
         EC_Point R = recover_ecdsa_public_key(this->domain(), msg, r, s, v);
 
         if(R == this->public_point()) {
            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_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_value()) {
#if defined(BOTAN_HAS_RFC6979_GENERATOR)
         m_rfc6979 = std::make_unique<RFC6979_Nonce_Generator>(this->rfc6979_hash_function(), m_group.get_order(), m_x);
#endif
 
         m_b = m_group.random_scalar(rng);
         m_b_inv = m_group.inverse_mod_order(m_b);
      }
 
      size_t signature_length() const override { return 2 * m_group.get_order_bytes(); }
 
      secure_vector<uint8_t> raw_sign(const uint8_t msg[], size_t msg_len, RandomNumberGenerator& rng) override;
 
      AlgorithmIdentifier algorithm_identifier() const override;
 
   private:
      const EC_Group m_group;
      const BigInt m_x;
 
#if defined(BOTAN_HAS_RFC6979_GENERATOR)
      std::unique_ptr<RFC6979_Nonce_Generator> m_rfc6979;
#endif
 
      std::vector<BigInt> m_ws;
 
      BigInt m_b, m_b_inv;
};
 
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);
}
 
secure_vector<uint8_t> ECDSA_Signature_Operation::raw_sign(const uint8_t msg[],
                                                           size_t msg_len,
                                                           RandomNumberGenerator& rng) {
   BigInt m = m_group.mod_order(BigInt::from_bytes_with_max_bits(msg, msg_len, m_group.get_order_bits()));
 
#if defined(BOTAN_HAS_RFC6979_GENERATOR)
   const BigInt k = m_rfc6979->nonce_for(m);
#else
   const BigInt k = m_group.random_scalar(rng);
#endif
 
   const BigInt r = m_group.mod_order(m_group.blinded_base_point_multiply_x(k, rng, m_ws));
 
   const BigInt k_inv = m_group.inverse_mod_order(k);
 
   /*
   * Blind the input message and compute x*r+m as (x*r*b + m*b)/b
   */
   m_b = m_group.square_mod_order(m_b);
   m_b_inv = m_group.square_mod_order(m_b_inv);
 
   m = m_group.multiply_mod_order(m_b, m_group.mod_order(m));
   const BigInt xr_m = m_group.mod_order(m_group.multiply_mod_order(m_x, m_b, r) + m);
 
   const BigInt s = m_group.multiply_mod_order(k_inv, xr_m, m_b_inv);
 
   // 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 BigInt::encode_fixed_length_int_pair(r, s, m_group.get_order_bytes());
}
 
/**
* 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(m_group.get_base_point(), ecdsa.public_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(m_group.get_base_point(), ecdsa.public_point()) {}
 
      bool verify(const uint8_t msg[], size_t msg_len, const uint8_t sig[], size_t sig_len) override;
 
   private:
      const EC_Group m_group;
      const EC_Point_Multi_Point_Precompute m_gy_mul;
};
 
bool ECDSA_Verification_Operation::verify(const uint8_t msg[], size_t msg_len, const uint8_t sig[], size_t sig_len) {
   if(sig_len != m_group.get_order_bytes() * 2) {
      return false;
   }
 
   const BigInt e = BigInt::from_bytes_with_max_bits(msg, msg_len, m_group.get_order_bits());
 
   const BigInt r(sig, sig_len / 2);
   const BigInt s(sig + sig_len / 2, sig_len / 2);
 
   // Cannot be negative here since we just decoded from binary
   if(r.is_zero() || s.is_zero()) {
      return false;
   }
 
   if(r >= m_group.get_order() || s >= m_group.get_order()) {
      return false;
   }
 
   const BigInt w = m_group.inverse_mod_order(s);
 
   const BigInt u1 = m_group.multiply_mod_order(m_group.mod_order(e), w);
   const BigInt u2 = m_group.multiply_mod_order(r, w);
   const EC_Point R = m_gy_mul.multi_exp(u1, u2);
 
   if(R.is_zero()) {
      return false;
   }
 
   const BigInt v = m_group.mod_order(R.get_affine_x());
   return (v == r);
}
 
}  // 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