void Montgomery_Params::square_this(BigInt& x,
secure_vector<word>& ws) const
{
const size_t output_size = 2*m_p_words + 2;
if(ws.size() < 2*output_size)
ws.resize(2*output_size);
word* z_data = &ws[0];
word* ws_data = &ws[output_size];
BOTAN_DEBUG_ASSERT(x.sig_words() <= m_p_words);
bigint_sqr(z_data, output_size,
x.data(), x.size(), std::min(m_p_words, x.size()),
ws_data, output_size);
bigint_monty_redc(z_data,
m_p.data(), m_p_words, m_p_dash,
ws_data, output_size);
if(x.size() < output_size)
x.grow_to(output_size);
copy_mem(x.mutable_data(), z_data, output_size);
}
BigInt Montgomery_Exponentation_State::exponentiation(const BigInt& k) const
{
const size_t exp_nibbles = (k.bits() + m_window_bits - 1) / m_window_bits;
BigInt x = m_R_mod;
const size_t z_size = 2*(m_p_words + 1);
BigInt z(BigInt::Positive, z_size);
secure_vector<word> workspace(z.size());
secure_vector<word> e(m_p_words);
for(size_t i = exp_nibbles; i > 0; --i)
{
for(size_t j = 0; j != m_window_bits; ++j)
{
bigint_monty_sqr(z, x, m_p.data(), m_p_words, m_mod_prime,
workspace.data());
x = z;
}
const uint32_t nibble = k.get_substring(m_window_bits*(i-1), m_window_bits);
BigInt::const_time_lookup(e, m_g, nibble);
bigint_mul(z.mutable_data(), z.size(),
x.data(), x.size(), x.sig_words(),
e.data(), m_p_words, m_p_words,
workspace.data());
bigint_monty_redc(z.mutable_data(),
m_p.data(), m_p_words, m_mod_prime,
workspace.data());
x = z;
}
x.grow_to(2*m_p_words + 1);
bigint_monty_redc(x.mutable_data(),
m_p.data(), m_p_words, m_mod_prime,
workspace.data());
return x;
}
void bigint_monty_sqr(word z[], size_t z_size,
const word x[], size_t x_size, size_t x_sw,
const word p[], size_t p_size, word p_dash,
word ws[])
{
bigint_sqr(&z[0], z_size, &ws[0],
&x[0], x_size, x_sw);
bigint_monty_redc(&z[0],
&p[0], p_size, p_dash,
&ws[0]);
}
BigInt Montgomery_Params::redc(const BigInt& x, secure_vector<word>& ws) const
{
const size_t output_size = 2*m_p_words + 2;
if(ws.size() < output_size)
ws.resize(output_size);
BigInt z = x;
z.grow_to(output_size);
bigint_monty_redc(z.mutable_data(),
m_p.data(), m_p_words, m_p_dash,
ws.data(), ws.size());
return z;
}
BigInt Montgomery_Params::sqr(const BigInt& x, secure_vector<word>& ws) const
{
const size_t output_size = 2*m_p_words + 2;
if(ws.size() < output_size)
ws.resize(output_size);
BigInt z(BigInt::Positive, output_size);
BOTAN_DEBUG_ASSERT(x.sig_words() <= m_p_words);
bigint_sqr(z.mutable_data(), z.size(),
x.data(), x.size(), std::min(m_p_words, x.size()),
ws.data(), ws.size());
bigint_monty_redc(z.mutable_data(),
m_p.data(), m_p_words, m_p_dash,
ws.data(), ws.size());
return z;
}
/*
* Compute the result
*/
BigInt Montgomery_Exponentiator::execute() const
{
const size_t exp_nibbles = (m_exp_bits + m_window_bits - 1) / m_window_bits;
BigInt x = m_R_mod;
const size_t z_size = 2*(m_mod_words + 1);
BigInt z(BigInt::Positive, z_size);
secure_vector<word> workspace(z.size());
for(size_t i = exp_nibbles; i > 0; --i)
{
for(size_t k = 0; k != m_window_bits; ++k)
{
bigint_monty_sqr(z, x, m_modulus.data(), m_mod_words, m_mod_prime,
workspace.data());
x = z;
}
const u32bit nibble = m_exp.get_substring(m_window_bits*(i-1), m_window_bits);
const BigInt& y = m_g[nibble];
bigint_monty_mul(z, x, y,
m_modulus.data(), m_mod_words, m_mod_prime,
workspace.data());
x = z;
}
x.grow_to(2*m_mod_words + 1);
bigint_monty_redc(x.mutable_data(),
m_modulus.data(), m_mod_words, m_mod_prime,
workspace.data());
return x;
}