mceliece_key.cpp

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/*
 * (C) Copyright Projet SECRET, INRIA, Rocquencourt
 * (C) Bhaskar Biswas and  Nicolas Sendrier
 *
 * (C) 2014 cryptosource GmbH
 * (C) 2014 Falko Strenzke fstrenzke@cryptosource.de
 * (C) 2015 Jack Lloyd
 *
 * Botan is released under the Simplified BSD License (see license.txt)
 *
 */
 
#include <botan/mceliece.h>
 
#include <botan/ber_dec.h>
#include <botan/der_enc.h>
#include <botan/rng.h>
#include <botan/internal/bit_ops.h>
#include <botan/internal/code_based_util.h>
#include <botan/internal/loadstor.h>
#include <botan/internal/mce_internal.h>
#include <botan/internal/pk_ops_impl.h>
#include <botan/internal/polyn_gf2m.h>
 
namespace Botan {
 
McEliece_PrivateKey::McEliece_PrivateKey(const McEliece_PrivateKey&) = default;
McEliece_PrivateKey::McEliece_PrivateKey(McEliece_PrivateKey&&) noexcept = default;
McEliece_PrivateKey& McEliece_PrivateKey::operator=(const McEliece_PrivateKey&) = default;
McEliece_PrivateKey& McEliece_PrivateKey::operator=(McEliece_PrivateKey&&) noexcept = default;
McEliece_PrivateKey::~McEliece_PrivateKey() = default;
 
McEliece_PrivateKey::McEliece_PrivateKey(const polyn_gf2m& goppa_polyn,
                                         const std::vector<uint32_t>& parity_check_matrix_coeffs,
                                         const std::vector<polyn_gf2m>& square_root_matrix,
                                         const std::vector<gf2m>& inverse_support,
                                         const std::vector<uint8_t>& public_matrix) :
      McEliece_PublicKey(public_matrix, goppa_polyn.get_degree(), inverse_support.size()),
      m_g{goppa_polyn},
      m_sqrtmod(square_root_matrix),
      m_Linv(inverse_support),
      m_coeffs(parity_check_matrix_coeffs),
      m_codimension(static_cast<size_t>(ceil_log2(inverse_support.size())) * goppa_polyn.get_degree()),
      m_dimension(inverse_support.size() - m_codimension) {}
 
McEliece_PrivateKey::McEliece_PrivateKey(RandomNumberGenerator& rng, size_t code_length, size_t t) {
   uint32_t ext_deg = ceil_log2(code_length);
   *this = generate_mceliece_key(rng, ext_deg, code_length, t);
}
 
const polyn_gf2m& McEliece_PrivateKey::get_goppa_polyn() const {
   return m_g[0];
}
 
size_t McEliece_PublicKey::get_message_word_bit_length() const {
   size_t codimension = ceil_log2(m_code_length) * m_t;
   return m_code_length - codimension;
}
 
secure_vector<uint8_t> McEliece_PublicKey::random_plaintext_element(RandomNumberGenerator& rng) const {
   const size_t bits = get_message_word_bit_length();
 
   secure_vector<uint8_t> plaintext((bits + 7) / 8);
   rng.randomize(plaintext.data(), plaintext.size());
 
   // unset unused bits in the last plaintext byte
   if(uint32_t used = bits % 8) {
      const uint8_t mask = (1 << used) - 1;
      plaintext[plaintext.size() - 1] &= mask;
   }
 
   return plaintext;
}
 
AlgorithmIdentifier McEliece_PublicKey::algorithm_identifier() const {
   return AlgorithmIdentifier(object_identifier(), AlgorithmIdentifier::USE_EMPTY_PARAM);
}
 
std::vector<uint8_t> McEliece_PublicKey::public_key_bits() const {
   std::vector<uint8_t> output;
   DER_Encoder(output)
      .start_sequence()
      .start_sequence()
      .encode(static_cast<size_t>(get_code_length()))
      .encode(static_cast<size_t>(get_t()))
      .end_cons()
      .encode(m_public_matrix, ASN1_Type::OctetString)
      .end_cons();
   return output;
}
 
size_t McEliece_PublicKey::key_length() const {
   return m_code_length;
}
 
size_t McEliece_PublicKey::estimated_strength() const {
   return mceliece_work_factor(m_code_length, m_t);
}
 
McEliece_PublicKey::McEliece_PublicKey(std::span<const uint8_t> key_bits) {
   BER_Decoder dec(key_bits);
   size_t n;
   size_t t;
   dec.start_sequence()
      .start_sequence()
      .decode(n)
      .decode(t)
      .end_cons()
      .decode(m_public_matrix, ASN1_Type::OctetString)
      .end_cons();
   m_t = t;
   m_code_length = n;
}
 
secure_vector<uint8_t> McEliece_PrivateKey::private_key_bits() const {
   DER_Encoder enc;
   enc.start_sequence()
      .start_sequence()
      .encode(static_cast<size_t>(get_code_length()))
      .encode(static_cast<size_t>(get_t()))
      .end_cons()
      .encode(m_public_matrix, ASN1_Type::OctetString)
      .encode(m_g[0].encode(), ASN1_Type::OctetString);  // g as octet string
   enc.start_sequence();
   for(size_t i = 0; i < m_sqrtmod.size(); i++) {
      enc.encode(m_sqrtmod[i].encode(), ASN1_Type::OctetString);
   }
   enc.end_cons();
   secure_vector<uint8_t> enc_support;
 
   for(uint16_t Linv : m_Linv) {
      enc_support.push_back(get_byte<0>(Linv));
      enc_support.push_back(get_byte<1>(Linv));
   }
   enc.encode(enc_support, ASN1_Type::OctetString);
   secure_vector<uint8_t> enc_H;
   for(uint32_t coef : m_coeffs) {
      enc_H.push_back(get_byte<0>(coef));
      enc_H.push_back(get_byte<1>(coef));
      enc_H.push_back(get_byte<2>(coef));
      enc_H.push_back(get_byte<3>(coef));
   }
   enc.encode(enc_H, ASN1_Type::OctetString);
   enc.end_cons();
   return enc.get_contents();
}
 
bool McEliece_PrivateKey::check_key(RandomNumberGenerator& rng, bool /*unused*/) const {
   const secure_vector<uint8_t> plaintext = this->random_plaintext_element(rng);
 
   secure_vector<uint8_t> ciphertext;
   secure_vector<uint8_t> errors;
   mceliece_encrypt(ciphertext, errors, plaintext, *this, rng);
 
   secure_vector<uint8_t> plaintext_out;
   secure_vector<uint8_t> errors_out;
   mceliece_decrypt(plaintext_out, errors_out, ciphertext, *this);
 
   if(errors != errors_out || plaintext != plaintext_out) {
      return false;
   }
 
   return true;
}
 
McEliece_PrivateKey::McEliece_PrivateKey(std::span<const uint8_t> key_bits) {
   size_t n, t;
   secure_vector<uint8_t> enc_g;
   BER_Decoder dec_base(key_bits);
   BER_Decoder dec = dec_base.start_sequence()
                        .start_sequence()
                        .decode(n)
                        .decode(t)
                        .end_cons()
                        .decode(m_public_matrix, ASN1_Type::OctetString)
                        .decode(enc_g, ASN1_Type::OctetString);
 
   if(t == 0 || n == 0) {
      throw Decoding_Error("invalid McEliece parameters");
   }
 
   uint32_t ext_deg = ceil_log2(n);
   m_code_length = n;
   m_t = t;
   m_codimension = (ext_deg * t);
   m_dimension = (n - m_codimension);
 
   auto sp_field = std::make_shared<GF2m_Field>(ext_deg);
   m_g = {polyn_gf2m(enc_g, sp_field)};
   if(m_g[0].get_degree() != static_cast<int>(t)) {
      throw Decoding_Error("degree of decoded Goppa polynomial is incorrect");
   }
   BER_Decoder dec2 = dec.start_sequence();
   for(uint32_t i = 0; i < t / 2; i++) {
      secure_vector<uint8_t> sqrt_enc;
      dec2.decode(sqrt_enc, ASN1_Type::OctetString);
      while(sqrt_enc.size() < (t * 2)) {
         // ensure that the length is always t
         sqrt_enc.push_back(0);
         sqrt_enc.push_back(0);
      }
      if(sqrt_enc.size() != t * 2) {
         throw Decoding_Error("length of square root polynomial entry is too large");
      }
      m_sqrtmod.push_back(polyn_gf2m(sqrt_enc, sp_field));
   }
   secure_vector<uint8_t> enc_support;
   BER_Decoder dec3 = dec2.end_cons().decode(enc_support, ASN1_Type::OctetString);
   if(enc_support.size() % 2) {
      throw Decoding_Error("encoded support has odd length");
   }
   if(enc_support.size() / 2 != n) {
      throw Decoding_Error("encoded support has length different from code length");
   }
   for(uint32_t i = 0; i < n * 2; i += 2) {
      gf2m el = (enc_support[i] << 8) | enc_support[i + 1];
      m_Linv.push_back(el);
   }
   secure_vector<uint8_t> enc_H;
   dec3.decode(enc_H, ASN1_Type::OctetString).end_cons();
   if(enc_H.size() % 4) {
      throw Decoding_Error("encoded parity check matrix has length which is not a multiple of four");
   }
   if(enc_H.size() / 4 != bit_size_to_32bit_size(m_codimension) * m_code_length) {
      throw Decoding_Error("encoded parity check matrix has wrong length");
   }
 
   for(uint32_t i = 0; i < enc_H.size(); i += 4) {
      uint32_t coeff = (enc_H[i] << 24) | (enc_H[i + 1] << 16) | (enc_H[i + 2] << 8) | enc_H[i + 3];
      m_coeffs.push_back(coeff);
   }
}
 
bool McEliece_PrivateKey::operator==(const McEliece_PrivateKey& other) const {
   if(*static_cast<const McEliece_PublicKey*>(this) != *static_cast<const McEliece_PublicKey*>(&other)) {
      return false;
   }
   if(m_g != other.m_g) {
      return false;
   }
 
   if(m_sqrtmod != other.m_sqrtmod) {
      return false;
   }
   if(m_Linv != other.m_Linv) {
      return false;
   }
   if(m_coeffs != other.m_coeffs) {
      return false;
   }
 
   if(m_codimension != other.m_codimension || m_dimension != other.m_dimension) {
      return false;
   }
 
   return true;
}
 
std::unique_ptr<Public_Key> McEliece_PrivateKey::public_key() const {
   return std::make_unique<McEliece_PublicKey>(get_public_matrix(), get_t(), get_code_length());
}
 
bool McEliece_PublicKey::operator==(const McEliece_PublicKey& other) const {
   if(m_public_matrix != other.m_public_matrix) {
      return false;
   }
   if(m_t != other.m_t) {
      return false;
   }
   if(m_code_length != other.m_code_length) {
      return false;
   }
   return true;
}
 
namespace {
 
class MCE_KEM_Encryptor final : public PK_Ops::KEM_Encryption_with_KDF {
   public:
      MCE_KEM_Encryptor(const McEliece_PublicKey& key, std::string_view kdf) :
            KEM_Encryption_with_KDF(kdf), m_key(key) {}
 
   private:
      size_t raw_kem_shared_key_length() const override {
         const size_t err_sz = (m_key.get_code_length() + 7) / 8;
         const size_t ptext_sz = (m_key.get_message_word_bit_length() + 7) / 8;
         return ptext_sz + err_sz;
      }
 
      size_t encapsulated_key_length() const override { return (m_key.get_code_length() + 7) / 8; }
 
      void raw_kem_encrypt(secure_vector<uint8_t>& out_encapsulated_key,
                           secure_vector<uint8_t>& raw_shared_key,
                           RandomNumberGenerator& rng) override {
         secure_vector<uint8_t> plaintext = m_key.random_plaintext_element(rng);
 
         secure_vector<uint8_t> ciphertext, error_mask;
         mceliece_encrypt(ciphertext, error_mask, plaintext, m_key, rng);
 
         raw_shared_key.clear();
         raw_shared_key += plaintext;
         raw_shared_key += error_mask;
 
         out_encapsulated_key.swap(ciphertext);
      }
 
      const McEliece_PublicKey& m_key;
};
 
class MCE_KEM_Decryptor final : public PK_Ops::KEM_Decryption_with_KDF {
   public:
      MCE_KEM_Decryptor(const McEliece_PrivateKey& key, std::string_view kdf) :
            KEM_Decryption_with_KDF(kdf), m_key(key) {}
 
   private:
      size_t raw_kem_shared_key_length() const override {
         const size_t err_sz = (m_key.get_code_length() + 7) / 8;
         const size_t ptext_sz = (m_key.get_message_word_bit_length() + 7) / 8;
         return ptext_sz + err_sz;
      }
 
      secure_vector<uint8_t> raw_kem_decrypt(const uint8_t encap_key[], size_t len) override {
         secure_vector<uint8_t> plaintext, error_mask;
         mceliece_decrypt(plaintext, error_mask, encap_key, len, m_key);
 
         secure_vector<uint8_t> output;
         output.reserve(plaintext.size() + error_mask.size());
         output.insert(output.end(), plaintext.begin(), plaintext.end());
         output.insert(output.end(), error_mask.begin(), error_mask.end());
         return output;
      }
 
      const McEliece_PrivateKey& m_key;
};
 
}  // namespace
 
std::unique_ptr<PK_Ops::KEM_Encryption> McEliece_PublicKey::create_kem_encryption_op(std::string_view params,
                                                                                     std::string_view provider) const {
   if(provider == "base" || provider.empty()) {
      return std::make_unique<MCE_KEM_Encryptor>(*this, params);
   }
   throw Provider_Not_Found(algo_name(), provider);
}
 
std::unique_ptr<PK_Ops::KEM_Decryption> McEliece_PrivateKey::create_kem_decryption_op(RandomNumberGenerator& /*rng*/,
                                                                                      std::string_view params,
                                                                                      std::string_view provider) const {
   if(provider == "base" || provider.empty()) {
      return std::make_unique<MCE_KEM_Decryptor>(*this, params);
   }
   throw Provider_Not_Found(algo_name(), provider);
}
 
}  // namespace Botan