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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/internal/pk_ops_impl.h>
#include <botan/internal/point_mul.h>
#include <botan/keypair.h>
#include <botan/reducer.h>
#include <botan/emsa.h>
#if defined(BOTAN_HAS_RFC6979_GENERATOR)
#include <botan/rfc6979.h>
#endif
#if defined(BOTAN_HAS_OPENSSL)
#include <botan/internal/openssl.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 uint8_t y_odd = v % 2;
const uint8_t add_order = v >> 1;
const BigInt& group_order = group.get_order();
const size_t p_bytes = group.get_p_bytes();
try
{
const BigInt e(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)) {}
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");
}
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(hash_for_emsa(emsa), 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(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(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);
if(r <= 0 || r >= m_group.get_order() || s <= 0 || 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 defined(BOTAN_HAS_OPENSSL)
if(provider == "openssl" || provider.empty())
{
try
{
return make_openssl_ecdsa_ver_op(*this, params);
}
catch(Lookup_Error& e)
{
if(provider == "openssl")
throw;
}
}
#endif
if(provider == "base" || provider.empty())
return std::unique_ptr<PK_Ops::Verification>(new 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 defined(BOTAN_HAS_OPENSSL)
if(provider == "openssl" || provider.empty())
{
try
{
return make_openssl_ecdsa_sig_op(*this, params);
}
catch(Lookup_Error& e)
{
if(provider == "openssl")
throw;
}
}
#endif
if(provider == "base" || provider.empty())
return std::unique_ptr<PK_Ops::Signature>(new ECDSA_Signature_Operation(*this, params, rng));
throw Provider_Not_Found(algo_name(), provider);
}
}