srp6.cpp

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/*
* SRP-6a (RFC 5054 compatatible)
* (C) 2011,2012,2019,2020 Jack Lloyd
*
* Botan is released under the Simplified BSD License (see license.txt)
*/
 
#include <botan/srp6.h>
#include <botan/hash.h>
#include <botan/dl_group.h>
#include <botan/numthry.h>
#include <botan/internal/fmt.h>
 
namespace Botan {
 
namespace {
 
BigInt hash_seq(HashFunction& hash_fn,
                size_t pad_to,
                const BigInt& in1,
                const BigInt& in2)
   {
   hash_fn.update(BigInt::encode_1363(in1, pad_to));
   hash_fn.update(BigInt::encode_1363(in2, pad_to));
 
   return BigInt::decode(hash_fn.final());
   }
 
BigInt compute_x(HashFunction& hash_fn,
                 std::string_view identifier,
                 std::string_view password,
                 const std::vector<uint8_t>& salt)
   {
   hash_fn.update(identifier);
   hash_fn.update(":");
   hash_fn.update(password);
 
   secure_vector<uint8_t> inner_h = hash_fn.final();
 
   hash_fn.update(salt);
   hash_fn.update(inner_h);
 
   secure_vector<uint8_t> outer_h = hash_fn.final();
 
   return BigInt::decode(outer_h);
   }
 
}
 
std::string srp6_group_identifier(const BigInt& N, const BigInt& g)
   {
   /*
   This function assumes that only one 'standard' SRP parameter set has
   been defined for a particular bitsize. As of this writing that is the case.
   */
   try
      {
      std::string group_name = "modp/srp/" + std::to_string(N.bits());
 
      DL_Group group(group_name);
 
      if(group.get_p() == N && group.get_g() == g)
         return group_name;
      }
   catch(...)
      {
      }
 
   // If we didn't return, the group was unknown or did not match
   throw Invalid_Argument("Invalid or unknown SRP group parameters");
   }
 
std::pair<BigInt, SymmetricKey>
srp6_client_agree(std::string_view identifier,
                  std::string_view password,
                  std::string_view group_id,
                  std::string_view hash_id,
                  const std::vector<uint8_t>& salt,
                  const BigInt& B,
                  RandomNumberGenerator& rng)
   {
   DL_Group group(group_id);
   const size_t a_bits = group.exponent_bits();
 
   return srp6_client_agree(identifier, password, group, hash_id, salt, B, a_bits, rng);
   }
 
std::pair<BigInt, SymmetricKey>
srp6_client_agree(std::string_view identifier,
                  std::string_view password,
                  const DL_Group& group,
                  std::string_view hash_id,
                  const std::vector<uint8_t>& salt,
                  const BigInt& B,
                  const size_t a_bits,
                  RandomNumberGenerator& rng)
   {
   BOTAN_ARG_CHECK(a_bits <= group.p_bits(), "Invalid a_bits");
 
   const BigInt& g = group.get_g();
   const BigInt& p = group.get_p();
 
   const size_t p_bytes = group.p_bytes();
 
   if(B <= 0 || B >= p)
      throw Decoding_Error("Invalid SRP parameter from server");
 
   auto hash_fn = HashFunction::create_or_throw(hash_id);
   if(8*hash_fn->output_length() >= group.p_bits())
      throw Invalid_Argument(fmt("Hash function {} too large for SRP6 with this group",
                                 hash_fn->name()));
 
   const BigInt k = hash_seq(*hash_fn, p_bytes, p, g);
 
   const BigInt a(rng, a_bits);
 
   const BigInt A = group.power_g_p(a, a_bits);
 
   const BigInt u = hash_seq(*hash_fn, p_bytes, A, B);
 
   const BigInt x = compute_x(*hash_fn, identifier, password, salt);
 
   const BigInt g_x_p = group.power_g_p(x, hash_fn->output_length()*8);
 
   const BigInt B_k_g_x_p = group.mod_p(B - group.multiply_mod_p(k, g_x_p));
 
   const BigInt a_ux = a + u*x;
 
   const size_t max_aux_bits =
      std::max<size_t>(a_bits + 1,
                       2*8*hash_fn->output_length());
   BOTAN_ASSERT_NOMSG(max_aux_bits >= a_ux.bits());
 
   const BigInt S = group.power_b_p(B_k_g_x_p, a_ux, max_aux_bits);
 
   const SymmetricKey Sk(BigInt::encode_1363(S, p_bytes));
 
   return std::make_pair(A, Sk);
   }
 
BigInt srp6_generate_verifier(std::string_view identifier,
                              std::string_view password,
                              const std::vector<uint8_t>& salt,
                              std::string_view group_id,
                              std::string_view hash_id)
   {
   DL_Group group(group_id);
   return srp6_generate_verifier(identifier, password, salt, group, hash_id);
   }
 
BigInt srp6_generate_verifier(std::string_view identifier,
                              std::string_view password,
                              const std::vector<uint8_t>& salt,
                              const DL_Group& group,
                              std::string_view hash_id)
   {
   auto hash_fn = HashFunction::create_or_throw(hash_id);
   if(8*hash_fn->output_length() >= group.p_bits())
      throw Invalid_Argument(fmt("Hash function {} too large for SRP6 with this group",
                                 hash_fn->name()));
 
   const BigInt x = compute_x(*hash_fn, identifier, password, salt);
   return group.power_g_p(x, hash_fn->output_length() * 8);
   }
 
BigInt SRP6_Server_Session::step1(const BigInt& v,
                                  std::string_view group_id,
                                  std::string_view hash_id,
                                  RandomNumberGenerator& rng)
   {
   DL_Group group(group_id);
   const size_t b_bits = group.exponent_bits();
   return this->step1(v, group, hash_id, b_bits, rng);
   }
 
BigInt SRP6_Server_Session::step1(const BigInt& v,
                                  const DL_Group& group,
                                  std::string_view hash_id,
                                  size_t b_bits,
                                  RandomNumberGenerator& rng)
   {
   BOTAN_ARG_CHECK(b_bits <= group.p_bits(), "Invalid b_bits");
 
   m_group = group;
 
   const BigInt& g = group.get_g();
   const BigInt& p = group.get_p();
 
   m_v = v;
   m_b = BigInt(rng, b_bits);
   m_hash_id = hash_id;
 
   auto hash_fn = HashFunction::create_or_throw(hash_id);
   if(8*hash_fn->output_length() >= group.p_bits())
      throw Invalid_Argument(fmt("Hash function {} too large for SRP6 with this group",
                                 hash_fn->name()));
 
   const BigInt k = hash_seq(*hash_fn, m_group.p_bytes(), p, g);
   m_B = group.mod_p(v*k + group.power_g_p(m_b, b_bits));
 
   return m_B;
   }
 
SymmetricKey SRP6_Server_Session::step2(const BigInt& A)
   {
   if(A <= 0 || A >= m_group.get_p())
      throw Decoding_Error("Invalid SRP parameter from client");
 
   auto hash_fn = HashFunction::create_or_throw(m_hash_id);
   if(8*hash_fn->output_length() >= m_group.p_bits())
      throw Invalid_Argument(fmt("Hash function {} too large for SRP6 with this group",
                                 hash_fn->name()));
 
   const BigInt u = hash_seq(*hash_fn, m_group.p_bytes(), A, m_B);
 
   const BigInt vup = m_group.power_b_p(m_v, u, m_group.p_bits());
   const BigInt S = m_group.power_b_p(m_group.multiply_mod_p(A, vup), m_b, m_group.p_bits());
 
   return SymmetricKey(BigInt::encode_1363(S, m_group.p_bytes()));
   }
 
}