/*

* 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/internal/pk_ops_impl.h>

#include <botan/internal/point_mul.h>

#include <botan/internal/keypair.h>

#include <botan/reducer.h>

#include <botan/internal/emsa.h>

#if defined(BOTAN_HAS_RFC6979_GENERATOR)

  #include <botan/internal/rfc6979.h>

#endif

namespace Botan {

namespace {

PointGFp 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;

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

      const PointGFp 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)

      PointGFp_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");

   }

}

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)) {}

Unexecuted instantiation: Botan::ECDSA_PublicKey::ECDSA_PublicKey(Botan::EC_Group const&, std::__1::vector<unsigned char, std::__1::allocator<unsigned char> > const&, Botan::BigInt const&, Botan::BigInt const&, unsigned char)

Unexecuted instantiation: Botan::ECDSA_PublicKey::ECDSA_PublicKey(Botan::EC_Group const&, std::__1::vector<unsigned char, std::__1::allocator<unsigned char> > const&, Botan::BigInt const&, Botan::BigInt const&, unsigned char)

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

         {

         PointGFp 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(!public_point().on_the_curve())

      return false;

   if(!strong)

      return true;

   return KeyPair::signature_consistency_check(rng, *this, "EMSA1(SHA-256)");

   }

namespace {

/**

* ECDSA signature operation

*/

class ECDSA_Signature_Operation final : public PK_Ops::Signature_with_EMSA

   {

   public:

      ECDSA_Signature_Operation(const ECDSA_PrivateKey& ecdsa,

                                const std::string& emsa,

                                RandomNumberGenerator& rng) :

         PK_Ops::Signature_with_EMSA(emsa),

         m_group(ecdsa.domain()),

         m_x(ecdsa.private_value())

         {

#if defined(BOTAN_HAS_RFC6979_GENERATOR)

         m_rfc6979.reset(new RFC6979_Nonce_Generator(this->hash_for_signature(), 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(); }

      size_t max_input_bits() const override { return m_group.get_order_bits(); }

      secure_vector<uint8_t> raw_sign(const uint8_t msg[], size_t msg_len,

                                      RandomNumberGenerator& rng) 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;

   };

secure_vector<uint8_t>

ECDSA_Signature_Operation::raw_sign(const uint8_t msg[], size_t msg_len,

                                    RandomNumberGenerator& rng)

   {

   BigInt m = 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_EMSA

   {

   public:

      ECDSA_Verification_Operation(const ECDSA_PublicKey& ecdsa,

                                   const std::string& emsa) :

         PK_Ops::Verification_with_EMSA(emsa),

         m_group(ecdsa.domain()),

         m_gy_mul(m_group.get_base_point(), ecdsa.public_point())

         {

         }

      size_t max_input_bits() const override { return m_group.get_order_bits(); }

      bool with_recovery() const override { return false; }

      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 PointGFp_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 PointGFp 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);

   }

}

std::unique_ptr<PK_Ops::Verification>

ECDSA_PublicKey::create_verification_op(const std::string& params,

                                        const std::string& 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::Signature>

ECDSA_PrivateKey::create_signature_op(RandomNumberGenerator& rng,

                                      const std::string& params,

                                      const std::string& provider) const

   {

   if(provider == "base" || provider.empty())

      return std::make_unique<ECDSA_Signature_Operation>(*this, params, rng);

   throw Provider_Not_Found(algo_name(), provider);

   }

}