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/*
* Montgomery Exponentiation
* (C) 1999-2010,2012,2018 Jack Lloyd
* 2016 Matthias Gierlings
*
* Botan is released under the Simplified BSD License (see license.txt)
*/
#include <botan/internal/monty_exp.h>
#include <botan/numthry.h>
#include <botan/reducer.h>
#include <botan/internal/mp_core.h>
namespace Botan {
class Montgomery_Exponentation_State
{
public:
Montgomery_Exponentation_State(const BigInt& g,
const BigInt& p,
const Modular_Reducer& mod_p,
size_t window_bits);
BigInt exponentiation(const BigInt& k) const;
private:
BigInt m_p;
BigInt m_R_mod;
BigInt m_R2_mod;
word m_mod_prime;
size_t m_p_words;
size_t m_window_bits;
std::vector<BigInt> m_g;
};
Montgomery_Exponentation_State::Montgomery_Exponentation_State(const BigInt& g,
const BigInt& p,
const Modular_Reducer& mod_p,
size_t window_bits) :
m_p(p),
m_p_words(p.sig_words()),
m_window_bits(window_bits)
{
if(p.is_positive() == false || p.is_even())
throw Invalid_Argument("Cannot use Montgomery reduction on even or negative integer");
if(window_bits > 12) // really even 8 is too large ...
throw Invalid_Argument("Montgomery window bits too large");
m_mod_prime = monty_inverse(m_p.word_at(0));
const BigInt r = BigInt::power_of_2(m_p_words * BOTAN_MP_WORD_BITS);
m_R_mod = mod_p.reduce(r);
m_R2_mod = mod_p.square(m_R_mod);
m_g.resize(1U << m_window_bits);
BigInt z(BigInt::Positive, 2 * (m_p_words + 1));
secure_vector<word> workspace(z.size());
m_g[0] = 1;
bigint_monty_mul(z, m_g[0], m_R2_mod,
m_p.data(), m_p_words, m_mod_prime,
workspace.data(), workspace.size());
m_g[0] = z;
m_g[1] = mod_p.reduce(g);
bigint_monty_mul(z, m_g[1], m_R2_mod,
m_p.data(), m_p_words, m_mod_prime,
workspace.data(), workspace.size());
m_g[1] = z;
const BigInt& x = m_g[1];
for(size_t i = 2; i != m_g.size(); ++i)
{
const BigInt& y = m_g[i-1];
bigint_monty_mul(z, x, y, m_p.data(), m_p_words, m_mod_prime,
workspace.data(), workspace.size());
m_g[i] = z;
m_g[i].shrink_to_fit();
m_g[i].grow_to(m_p_words);
}
}
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(), workspace.size());
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(), workspace.size());
bigint_monty_redc(z.mutable_data(),
m_p.data(), m_p_words, m_mod_prime,
workspace.data(), workspace.size());
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(), workspace.size());
return x;
}
std::shared_ptr<const Montgomery_Exponentation_State>
monty_precompute(const BigInt& g,
const BigInt& p,
const Modular_Reducer& mod_p,
size_t window_bits)
{
return std::make_shared<const Montgomery_Exponentation_State>(g, p, mod_p, window_bits);
}
BigInt monty_execute(const Montgomery_Exponentation_State& precomputed_state,
const BigInt& k)
{
return precomputed_state.exponentiation(k);
}
}
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