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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>
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();
m_modulus_2 = Botan::square(m_modulus);
m_mu = BigInt::power_of_2(2 * BOTAN_MP_WORD_BITS * m_mod_words) / m_modulus;
}
}
/*
* Barrett Reduction
*/
BigInt Modular_Reducer::reduce(const BigInt& x) const
{
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 - 1) && x.cmp(m_modulus_2, false) >= 0)
{
// too big, fall back to normal division
return (x % m_modulus);
}
secure_vector<word> ws;
BigInt 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);
t1.reduce_below(m_modulus, ws);
if(x.is_negative() && t1.is_nonzero())
{
t1.rev_sub(m_modulus.data(), m_modulus.size(), ws);
}
return t1;
}
}
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