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/*
* Montgomery Exponentiation
* (C) 1999-2010 Jack Lloyd
*
* Distributed under the terms of the Botan license
*/
#include <botan/internal/def_powm.h>
#include <botan/numthry.h>
#include <botan/internal/mp_core.h>
namespace Botan {
namespace {
/*
* Compute -input^-1 mod 2^MP_WORD_BITS. We are assured that the
* inverse exists because input is odd (checked by checking that the
* modulus is odd in the Montgomery_Exponentiator constructor, and
* input is the low word of the modulus and thus also odd), and thus
* input and 2^n are relatively prime.
*/
word monty_inverse(word input)
{
word b = input;
word x2 = 1, x1 = 0, y2 = 0, y1 = 1;
// First iteration, a = n+1
word q = bigint_divop(1, 0, b);
word r = (MP_WORD_MAX - q*b) + 1;
word x = x2 - q*x1;
word y = y2 - q*y1;
word a = b;
b = r;
x2 = x1;
x1 = x;
y2 = y1;
y1 = y;
while(b > 0)
{
q = a / b;
r = a - q*b;
x = x2 - q*x1;
y = y2 - q*y1;
a = b;
b = r;
x2 = x1;
x1 = x;
y2 = y1;
y1 = y;
}
// Now invert in addition space
y2 = (MP_WORD_MAX - y2) + 1;
return y2;
}
}
/*
* Set the exponent
*/
void Montgomery_Exponentiator::set_exponent(const BigInt& exp)
{
m_exp = exp;
m_exp_bits = exp.bits();
}
/*
* Set the base
*/
void Montgomery_Exponentiator::set_base(const BigInt& base)
{
m_window_bits = Power_Mod::window_bits(m_exp.bits(), base.bits(), m_hints);
m_g.resize((1 << m_window_bits) - 1);
secure_vector<word> z(2 * (m_mod_words + 1));
secure_vector<word> workspace(z.size());
m_g[0] = (base >= m_modulus) ? (base % m_modulus) : base;
bigint_monty_mul(&z[0], z.size(),
m_g[0].data(), m_g[0].size(), m_g[0].sig_words(),
m_R2_mod.data(), m_R2_mod.size(), m_R2_mod.sig_words(),
m_modulus.data(), m_mod_words, m_mod_prime,
&workspace[0]);
m_g[0].assign(&z[0], m_mod_words + 1);
const BigInt& x = m_g[0];
const size_t x_sig = x.sig_words();
for(size_t i = 1; i != m_g.size(); ++i)
{
const BigInt& y = m_g[i-1];
const size_t y_sig = y.sig_words();
zeroise(z);
bigint_monty_mul(&z[0], z.size(),
x.data(), x.size(), x_sig,
y.data(), y.size(), y_sig,
m_modulus.data(), m_mod_words, m_mod_prime,
&workspace[0]);
m_g[i].assign(&z[0], m_mod_words + 1);
}
}
/*
* 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;
secure_vector<word> z(2 * (m_mod_words + 1));
secure_vector<word> workspace(2 * (m_mod_words + 1));
for(size_t i = exp_nibbles; i > 0; --i)
{
for(size_t k = 0; k != m_window_bits; ++k)
{
zeroise(z);
bigint_monty_sqr(&z[0], z.size(),
x.data(), x.size(), x.sig_words(),
m_modulus.data(), m_mod_words, m_mod_prime,
&workspace[0]);
x.assign(&z[0], m_mod_words + 1);
}
if(u32bit nibble = m_exp.get_substring(m_window_bits*(i-1), m_window_bits))
{
const BigInt& y = m_g[nibble-1];
zeroise(z);
bigint_monty_mul(&z[0], z.size(),
x.data(), x.size(), x.sig_words(),
y.data(), y.size(), y.sig_words(),
m_modulus.data(), m_mod_words, m_mod_prime,
&workspace[0]);
x.assign(&z[0], m_mod_words + 1);
}
}
x.grow_to(2*m_mod_words + 1);
bigint_monty_redc(&x[0], x.size(),
m_modulus.data(), m_mod_words, m_mod_prime,
&workspace[0]);
x.mask_bits(MP_WORD_BITS * (m_mod_words + 1));
return x;
}
/*
* Montgomery_Exponentiator Constructor
*/
Montgomery_Exponentiator::Montgomery_Exponentiator(const BigInt& mod,
Power_Mod::Usage_Hints hints) :
m_modulus(mod),
m_mod_words(m_modulus.sig_words()),
m_window_bits(1),
m_hints(hints)
{
// Montgomery reduction only works for positive odd moduli
if(!m_modulus.is_positive() || m_modulus.is_even())
throw Invalid_Argument("Montgomery_Exponentiator: invalid modulus");
m_mod_prime = monty_inverse(mod.word_at(0));
const BigInt r(BigInt::Power2, m_mod_words * BOTAN_MP_WORD_BITS);
m_R_mod = r % m_modulus;
m_R2_mod = (m_R_mod * m_R_mod) % m_modulus;
}
}
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