reducer.cpp

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/*
* Modular Reducer
* (C) 1999-2011,2018 Jack Lloyd
*
* Botan is released under the Simplified BSD License (see license.txt)
*/

#include <botan/reducer.h>
#include <botan/internal/ct_utils.h>
#include <botan/internal/mp_core.h>
#include <botan/divide.h>

namespace Botan {

/*
* Modular_Reducer Constructor
*/
Modular_Reducer::Modular_Reducer(const BigInt& mod)
   {
   if(mod < 0)
      throw Invalid_Argument("Modular_Reducer: modulus must be positive");

   // Left uninitialized if mod == 0
   m_mod_words = 0;

   if(mod > 0)
      {
      m_modulus = mod;
      m_mod_words = m_modulus.sig_words();

      // Compute mu = floor(2^{2k} / m)
      m_mu.set_bit(2 * BOTAN_MP_WORD_BITS * m_mod_words);
      m_mu = ct_divide(m_mu, m_modulus);
      }
   }

BigInt Modular_Reducer::reduce(const BigInt& x) const
   {
   BigInt r;
   secure_vector<word> ws;
   reduce(r, x, ws);
   return r;
   }

namespace {

/*
* Like if(cnd) x.rev_sub(...) but in const time
*/
void cnd_rev_sub(bool cnd, BigInt& x, const word y[], size_t y_sw, secure_vector<word>& ws)
   {
   if(x.sign() != BigInt::Positive)
      throw Invalid_State("BigInt::sub_rev requires this is positive");

   const size_t x_sw = x.sig_words();

   const size_t max_words = std::max(x_sw, y_sw);
   ws.resize(std::max(x_sw, y_sw));
   clear_mem(ws.data(), ws.size());
   x.grow_to(max_words);

   const int32_t relative_size = bigint_sub_abs(ws.data(), x.data(), x_sw, y, y_sw);

   x.cond_flip_sign((relative_size > 0) && cnd);
   bigint_cnd_swap(cnd, x.mutable_data(), ws.data(), max_words);
   }

}

void Modular_Reducer::reduce(BigInt& t1, const BigInt& x, secure_vector<word>& ws) const
   {
   if(&t1 == &x)
      throw Invalid_State("Modular_Reducer arguments cannot alias");
   if(m_mod_words == 0)
      throw Invalid_State("Modular_Reducer: Never initalized");

   const size_t x_sw = x.sig_words();

   if(x_sw > 2*m_mod_words)
      {
      // too big, fall back to slow boat division
      t1 = ct_modulo(x, m_modulus);
      return;
      }

   t1 = x;
   t1.set_sign(BigInt::Positive);
   t1 >>= (BOTAN_MP_WORD_BITS * (m_mod_words - 1));

   t1.mul(m_mu, ws);
   t1 >>= (BOTAN_MP_WORD_BITS * (m_mod_words + 1));

   // TODO add masked mul to avoid computing high bits
   t1.mul(m_modulus, ws);
   t1.mask_bits(BOTAN_MP_WORD_BITS * (m_mod_words + 1));

   t1.rev_sub(x.data(), std::min(x_sw, m_mod_words + 1), ws);

   /*
   * If t1 < 0 then we must add b^(k+1) where b = 2^w. To avoid a
   * side channel perform the addition unconditionally, with ws set
   * to either b^(k+1) or else 0.
   */
   const word t1_neg = t1.is_negative();

   if(ws.size() < m_mod_words + 2)
      ws.resize(m_mod_words + 2);
   clear_mem(ws.data(), ws.size());
   ws[m_mod_words + 1] = t1_neg;

   t1.add(ws.data(), m_mod_words + 2, BigInt::Positive);

   // Per HAC this step requires at most 2 subtractions
   t1.ct_reduce_below(m_modulus, ws, 2);

   cnd_rev_sub(t1.is_nonzero() && x.is_negative(), t1, m_modulus.data(), m_modulus.size(), ws);
   }

}