dl_group.cpp

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/*
* Discrete Logarithm Parameters
* (C) 1999-2008,2015,2018 Jack Lloyd
*
* Botan is released under the Simplified BSD License (see license.txt)
*/
 
#include <botan/dl_group.h>
#include <botan/numthry.h>
#include <botan/reducer.h>
#include <botan/internal/primality.h>
#include <botan/internal/monty.h>
#include <botan/internal/divide.h>
#include <botan/der_enc.h>
#include <botan/ber_dec.h>
#include <botan/pem.h>
#include <botan/internal/workfactor.h>
#include <botan/internal/monty_exp.h>
#include <botan/internal/fmt.h>
#include <string_view>
 
namespace Botan {
 
class DL_Group_Data final
   {
   public:
      DL_Group_Data(const BigInt& p, const BigInt& q, const BigInt& g, DL_Group_Source source) :
         m_p(p), m_q(q), m_g(g),
         m_mod_p(p),
         m_mod_q(q),
         m_monty_params(std::make_shared<Montgomery_Params>(m_p, m_mod_p)),
         m_monty(monty_precompute(m_monty_params, m_g, /*window bits=*/4)),
         m_p_bits(p.bits()),
         m_q_bits(q.bits()),
         m_estimated_strength(dl_work_factor(m_p_bits)),
         m_exponent_bits(dl_exponent_size(m_p_bits)),
         m_source(source)
         {
         }
 
      ~DL_Group_Data() = default;
 
      DL_Group_Data(const DL_Group_Data& other) = delete;
      DL_Group_Data(DL_Group_Data&& other) = delete;
      DL_Group_Data& operator=(const DL_Group_Data& other) = delete;
      DL_Group_Data& operator=(DL_Group_Data&& other) = delete;
 
      const BigInt& p() const { return m_p; }
      const BigInt& q() const { return m_q; }
      const BigInt& g() const { return m_g; }
 
      BigInt mod_p(const BigInt& x) const { return m_mod_p.reduce(x); }
 
      BigInt multiply_mod_p(const BigInt& x, const BigInt& y) const
         {
         return m_mod_p.multiply(x, y);
         }
 
      BigInt mod_q(const BigInt& x) const { return m_mod_q.reduce(x); }
 
      BigInt multiply_mod_q(const BigInt& x, const BigInt& y) const
         {
         return m_mod_q.multiply(x, y);
         }
 
      BigInt square_mod_q(const BigInt& x) const
         {
         return m_mod_q.square(x);
         }
 
      std::shared_ptr<const Montgomery_Params> monty_params_p() const
         { return m_monty_params; }
 
      size_t p_bits() const { return m_p_bits; }
      size_t q_bits() const { return m_q_bits; }
      size_t p_bytes() const { return (m_p_bits + 7) / 8; }
      size_t q_bytes() const { return (m_q_bits + 7) / 8; }
 
      size_t estimated_strength() const { return m_estimated_strength; }
 
      size_t exponent_bits() const { return m_exponent_bits; }
 
      BigInt power_g_p(const BigInt& k, size_t max_k_bits) const
         {
         return monty_execute(*m_monty, k, max_k_bits);
         }
 
      BigInt power_g_p_vartime(const BigInt& k) const
         {
         return monty_execute_vartime(*m_monty, k);
         }
 
      BigInt power_b_p(const BigInt& b, const BigInt& k, size_t max_k_bits) const
         {
         return monty_exp(m_monty_params, b, k, max_k_bits);
         }
 
      BigInt power_b_p_vartime(const BigInt& b, const BigInt& k) const
         {
         return monty_exp_vartime(m_monty_params, b, k);
         }
 
      bool q_is_set() const { return m_q_bits > 0; }
 
      void assert_q_is_set(std::string_view function) const
         {
         if(q_is_set() == false)
            throw Invalid_State(fmt("DL_Group::{}: q is not set for this group", function));
         }
 
      DL_Group_Source source() const { return m_source; }
 
   private:
      BigInt m_p;
      BigInt m_q;
      BigInt m_g;
      Modular_Reducer m_mod_p;
      Modular_Reducer m_mod_q;
      std::shared_ptr<const Montgomery_Params> m_monty_params;
      std::shared_ptr<const Montgomery_Exponentation_State> m_monty;
      size_t m_p_bits;
      size_t m_q_bits;
      size_t m_estimated_strength;
      size_t m_exponent_bits;
      DL_Group_Source m_source;
   };
 
//static
std::shared_ptr<DL_Group_Data> DL_Group::BER_decode_DL_group(const uint8_t data[], size_t data_len,
                                                             DL_Group_Format format,
                                                             DL_Group_Source source)
   {
   BigInt p, q, g;
 
   BER_Decoder decoder(data, data_len);
   BER_Decoder ber = decoder.start_sequence();
 
   if(format == DL_Group_Format::ANSI_X9_57)
      {
      ber.decode(p)
         .decode(q)
         .decode(g)
         .verify_end();
      }
   else if(format == DL_Group_Format::ANSI_X9_42)
      {
      ber.decode(p)
         .decode(g)
         .decode(q)
         .discard_remaining();
      }
   else if(format == DL_Group_Format::PKCS_3)
      {
      // q is left as zero
      ber.decode(p)
         .decode(g)
         .discard_remaining();
      }
   else
      throw Invalid_Argument("Unknown DL_Group encoding");
 
   return std::make_shared<DL_Group_Data>(p, q, g, source);
   }
 
//static
std::shared_ptr<DL_Group_Data>
DL_Group::load_DL_group_info(const char* p_str,
                             const char* q_str,
                             const char* g_str)
   {
   const BigInt p(p_str);
   const BigInt q(q_str);
   const BigInt g(g_str);
 
   return std::make_shared<DL_Group_Data>(p, q, g, DL_Group_Source::Builtin);
   }
 
//static
std::shared_ptr<DL_Group_Data>
DL_Group::load_DL_group_info(const char* p_str,
                             const char* g_str)
   {
   const BigInt p(p_str);
   const BigInt q = (p - 1) / 2;
   const BigInt g(g_str);
 
   return std::make_shared<DL_Group_Data>(p, q, g, DL_Group_Source::Builtin);
   }
 
namespace {
 
DL_Group_Format pem_label_to_dl_format(std::string_view label)
   {
   if(label == "DH PARAMETERS")
      return DL_Group_Format::PKCS_3;
   else if(label == "DSA PARAMETERS")
      return DL_Group_Format::ANSI_X9_57;
   else if(label == "X942 DH PARAMETERS" || label == "X9.42 DH PARAMETERS")
      return DL_Group_Format::ANSI_X9_42;
   else
      throw Decoding_Error(fmt("DL_Group: Unknown PEM label '{}'", label));
   }
 
}
 
/*
* DL_Group Constructor
*/
DL_Group::DL_Group(std::string_view str)
   {
   // Either a name or a PEM block, try name first
   m_data = DL_group_info(str);
 
   if(m_data == nullptr)
      {
      try
         {
         std::string label;
         const std::vector<uint8_t> ber = unlock(PEM_Code::decode(str, label));
         DL_Group_Format format = pem_label_to_dl_format(label);
 
         m_data = BER_decode_DL_group(ber.data(), ber.size(), format, DL_Group_Source::ExternalSource);
         }
      catch(...) {}
      }
 
   if(m_data == nullptr)
      throw Invalid_Argument(fmt("DL_Group: Unknown group '{}'", str));
   }
 
namespace {
 
/*
* Create generator of the q-sized subgroup (DSA style generator)
*/
BigInt make_dsa_generator(const BigInt& p, const BigInt& q)
   {
   BigInt e, r;
   vartime_divide(p - 1, q, e, r);
 
   if(e == 0 || r > 0)
      throw Invalid_Argument("make_dsa_generator q does not divide p-1");
 
   for(size_t i = 0; i != PRIME_TABLE_SIZE; ++i)
      {
      // TODO precompute!
      BigInt g = power_mod(BigInt::from_word(PRIMES[i]), e, p);
      if(g > 1)
         return g;
      }
 
   throw Internal_Error("DL_Group: Couldn't create a suitable generator");
   }
 
}
 
/*
* DL_Group Constructor
*/
DL_Group::DL_Group(RandomNumberGenerator& rng,
                   PrimeType type, size_t pbits, size_t qbits)
   {
   if(pbits < 1024)
      throw Invalid_Argument(fmt("DL_Group: requested prime size {} is too small", pbits));
 
   if(qbits >= pbits)
      throw Invalid_Argument(fmt("DL_Group: requested q size {} is too big for p {}", qbits, pbits));
 
   if(type == Strong)
      {
      if(qbits != 0 && qbits != pbits - 1)
         throw Invalid_Argument("Cannot create strong-prime DL_Group with specified q bits");
 
      const BigInt p = random_safe_prime(rng, pbits);
      const BigInt q = (p - 1) / 2;
 
      /*
      Always choose a generator that is quadratic reside mod p,
      this forces g to be a generator of the subgroup of size q.
      */
      BigInt g = BigInt::from_word(2);
      if(jacobi(g, p) != 1)
         {
         // prime table does not contain 2
         for(size_t i = 0; i < PRIME_TABLE_SIZE; ++i)
            {
            g = BigInt::from_word(PRIMES[i]);
            if(jacobi(g, p) == 1)
               break;
            }
         }
 
      m_data = std::make_shared<DL_Group_Data>(p, q, g, DL_Group_Source::RandomlyGenerated);
      }
   else if(type == Prime_Subgroup)
      {
      if(qbits == 0)
         qbits = dl_exponent_size(pbits);
 
      const BigInt q = random_prime(rng, qbits);
      Modular_Reducer mod_2q(2*q);
      BigInt X;
      BigInt p;
      while(p.bits() != pbits || !is_prime(p, rng, 128, true))
         {
         X.randomize(rng, pbits);
         p = X - mod_2q.reduce(X) + 1;
         }
 
      const BigInt g = make_dsa_generator(p, q);
      m_data = std::make_shared<DL_Group_Data>(p, q, g, DL_Group_Source::RandomlyGenerated);
      }
   else if(type == DSA_Kosherizer)
      {
      if(qbits == 0)
         qbits = ((pbits <= 1024) ? 160 : 256);
 
      BigInt p, q;
      generate_dsa_primes(rng, p, q, pbits, qbits);
      const BigInt g = make_dsa_generator(p, q);
      m_data = std::make_shared<DL_Group_Data>(p, q, g, DL_Group_Source::RandomlyGenerated);
      }
   else
      {
      throw Invalid_Argument("DL_Group unknown PrimeType");
      }
   }
 
/*
* DL_Group Constructor
*/
DL_Group::DL_Group(RandomNumberGenerator& rng,
                   const std::vector<uint8_t>& seed,
                   size_t pbits, size_t qbits)
   {
   BigInt p, q;
 
   if(!generate_dsa_primes(rng, p, q, pbits, qbits, seed))
      throw Invalid_Argument("DL_Group: The seed given does not generate a DSA group");
 
   BigInt g = make_dsa_generator(p, q);
 
   m_data = std::make_shared<DL_Group_Data>(p, q, g, DL_Group_Source::RandomlyGenerated);
   }
 
/*
* DL_Group Constructor
*/
DL_Group::DL_Group(const BigInt& p, const BigInt& g)
   {
   m_data = std::make_shared<DL_Group_Data>(p, BigInt::zero(), g, DL_Group_Source::ExternalSource);
   }
 
/*
* DL_Group Constructor
*/
DL_Group::DL_Group(const BigInt& p, const BigInt& q, const BigInt& g)
   {
   m_data = std::make_shared<DL_Group_Data>(p, q, g, DL_Group_Source::ExternalSource);
   }
 
const DL_Group_Data& DL_Group::data() const
   {
   if(m_data)
      return *m_data;
 
   throw Invalid_State("DL_Group uninitialized");
   }
 
bool DL_Group::verify_public_element(const BigInt& y) const
   {
   const BigInt& p = get_p();
   const BigInt& q = get_q();
 
   if(y <= 1 || y >= p)
      return false;
 
   if(q.is_zero() == false)
      {
      if(data().power_b_p_vartime(y, q) != 1)
         return false;
      }
 
   return true;
   }
 
bool DL_Group::verify_private_element(const BigInt& x) const
   {
   const BigInt& p = get_p();
   const BigInt& q = get_q();
 
   if(x <= 1 || x >= p)
      return false;
 
   if(q > 0 && x > q)
      return false;
 
   return true;
   }
 
bool DL_Group::verify_element_pair(const BigInt& y, const BigInt& x) const
   {
   const BigInt& p = get_p();
 
   if(y <= 1 || y >= p || x <= 1 || x >= p)
      return false;
 
   if(y != this->power_g_p(x))
      return false;
 
   return true;
   }
 
/*
* Verify the parameters
*/
bool DL_Group::verify_group(RandomNumberGenerator& rng,
                            bool strong) const
   {
   const bool from_builtin = (source() == DL_Group_Source::Builtin);
 
   if(!strong && from_builtin)
      return true;
 
   const BigInt& p = get_p();
   const BigInt& q = get_q();
   const BigInt& g = get_g();
 
   if(g < 2 || p < 3 || q < 0)
      return false;
 
   const size_t test_prob = 128;
   const bool is_randomly_generated = (source() != DL_Group_Source::ExternalSource);
 
   if(!is_prime(p, rng, test_prob, is_randomly_generated))
      {
      return false;
      }
 
   if(q != 0)
      {
      if((p - 1) % q != 0)
         {
         return false;
         }
      if(data().power_g_p_vartime(q) != 1)
         {
         return false;
         }
      if(!is_prime(q, rng, test_prob, is_randomly_generated))
         {
         return false;
         }
      }
   else
      {
      if(!from_builtin && !is_randomly_generated)
         {
         // If we got this p,g from some unknown source, try to verify
         // that the group order is not too absurdly small.
 
         const size_t upper_bound = strong ? 1000 : 100;
 
         for(size_t i = 2; i != upper_bound; ++i)
            {
            if(data().power_g_p_vartime(BigInt::from_word(i)) == 1)
               {
               return false;
               }
            }
         }
      }
 
   return true;
   }
 
/*
* Return the prime
*/
const BigInt& DL_Group::get_p() const
   {
   return data().p();
   }
 
/*
* Return the generator
*/
const BigInt& DL_Group::get_g() const
   {
   return data().g();
   }
 
/*
* Return the subgroup
*/
const BigInt& DL_Group::get_q() const
   {
   return data().q();
   }
 
std::shared_ptr<const Montgomery_Params> DL_Group::monty_params_p() const
   {
   return data().monty_params_p();
   }
 
bool DL_Group::has_q() const
   {
   return data().q_is_set();
   }
 
size_t DL_Group::p_bits() const
   {
   return data().p_bits();
   }
 
size_t DL_Group::p_bytes() const
   {
   return data().p_bytes();
   }
 
size_t DL_Group::q_bits() const
   {
   data().assert_q_is_set("q_bits");
   return data().q_bits();
   }
 
size_t DL_Group::q_bytes() const
   {
   data().assert_q_is_set("q_bytes");
   return data().q_bytes();
   }
 
size_t DL_Group::estimated_strength() const
   {
   return data().estimated_strength();
   }
 
size_t DL_Group::exponent_bits() const
   {
   return data().exponent_bits();
   }
 
BigInt DL_Group::inverse_mod_p(const BigInt& x) const
   {
   // precompute??
   return inverse_mod(x, get_p());
   }
 
BigInt DL_Group::mod_p(const BigInt& x) const
   {
   return data().mod_p(x);
   }
 
BigInt DL_Group::multiply_mod_p(const BigInt& x, const BigInt& y) const
   {
   return data().multiply_mod_p(x, y);
   }
 
BigInt DL_Group::inverse_mod_q(const BigInt& x) const
   {
   data().assert_q_is_set("inverse_mod_q");
   // precompute??
   return inverse_mod(x, get_q());
   }
 
BigInt DL_Group::mod_q(const BigInt& x) const
   {
   data().assert_q_is_set("mod_q");
   return data().mod_q(x);
   }
 
BigInt DL_Group::multiply_mod_q(const BigInt& x, const BigInt& y) const
   {
   data().assert_q_is_set("multiply_mod_q");
   return data().multiply_mod_q(x, y);
   }
 
BigInt DL_Group::multiply_mod_q(const BigInt& x, const BigInt& y, const BigInt& z) const
   {
   data().assert_q_is_set("multiply_mod_q");
   return data().multiply_mod_q(data().multiply_mod_q(x, y), z);
   }
 
BigInt DL_Group::square_mod_q(const BigInt& x) const
   {
   data().assert_q_is_set("square_mod_q");
   return data().square_mod_q(x);
   }
 
BigInt DL_Group::multi_exponentiate(const BigInt& x, const BigInt& y, const BigInt& z) const
   {
   return monty_multi_exp(data().monty_params_p(), get_g(), x, y, z);
   }
 
BigInt DL_Group::power_g_p(const BigInt& x) const
   {
   return data().power_g_p(x, x.bits());
   }
 
BigInt DL_Group::power_g_p(const BigInt& x, size_t max_x_bits) const
   {
   return data().power_g_p(x, max_x_bits);
   }
 
BigInt DL_Group::power_b_p(const BigInt& b, const BigInt& x) const
   {
   return this->power_b_p(b, x, data().p_bits());
   }
 
BigInt DL_Group::power_b_p(const BigInt& b, const BigInt& x, size_t max_x_bits) const
   {
   return data().power_b_p(b, x, max_x_bits);
   }
 
DL_Group_Source DL_Group::source() const
   {
   return data().source();
   }
 
/*
* DER encode the parameters
*/
std::vector<uint8_t> DL_Group::DER_encode(DL_Group_Format format) const
   {
   if(get_q().is_zero() && (format != DL_Group_Format::PKCS_3))
      throw Encoding_Error("Cannot encode DL_Group in ANSI formats when q param is missing");
 
   std::vector<uint8_t> output;
   DER_Encoder der(output);
 
   if(format == DL_Group_Format::ANSI_X9_57)
      {
      der.start_sequence()
            .encode(get_p())
            .encode(get_q())
            .encode(get_g())
         .end_cons();
      }
   else if(format == DL_Group_Format::ANSI_X9_42)
      {
      der.start_sequence()
            .encode(get_p())
            .encode(get_g())
            .encode(get_q())
         .end_cons();
      }
   else if(format == DL_Group_Format::PKCS_3)
      {
      der.start_sequence()
            .encode(get_p())
            .encode(get_g())
         .end_cons();
      }
   else
      throw Invalid_Argument("Unknown DL_Group encoding");
 
   return output;
   }
 
/*
* PEM encode the parameters
*/
std::string DL_Group::PEM_encode(DL_Group_Format format) const
   {
   const std::vector<uint8_t> encoding = DER_encode(format);
 
   if(format == DL_Group_Format::PKCS_3)
      return PEM_Code::encode(encoding, "DH PARAMETERS");
   else if(format == DL_Group_Format::ANSI_X9_57)
      return PEM_Code::encode(encoding, "DSA PARAMETERS");
   else if(format == DL_Group_Format::ANSI_X9_42)
      return PEM_Code::encode(encoding, "X9.42 DH PARAMETERS");
   else
      throw Invalid_Argument("Unknown DL_Group encoding");
   }
 
DL_Group::DL_Group(const uint8_t ber[], size_t ber_len, DL_Group_Format format)
   {
   m_data = BER_decode_DL_group(ber, ber_len, format, DL_Group_Source::ExternalSource);
   }
 
void DL_Group::BER_decode(const std::vector<uint8_t>& ber, DL_Group_Format format)
   {
   m_data = BER_decode_DL_group(ber.data(), ber.size(), format, DL_Group_Source::ExternalSource);
   }
 
//static
DL_Group DL_Group::DL_Group_from_PEM(std::string_view pem)
   {
   std::string label;
   const std::vector<uint8_t> ber = unlock(PEM_Code::decode(pem, label));
   DL_Group_Format format = pem_label_to_dl_format(label);
   return DL_Group(ber, format);
   }
 
}