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/*
* Montgomery Exponentiation
* (C) 1999-2007 Jack Lloyd
*
* Distributed under the terms of the Botan license
*/
#include <botan/def_powm.h>
#include <botan/numthry.h>
#include <botan/mp_core.h>
namespace Botan {
namespace {
/*
* Try to choose a good window size
*/
u32bit choose_window_bits(u32bit exp_bits, u32bit,
Power_Mod::Usage_Hints hints)
{
static const u32bit wsize[][2] = {
{ 2048, 4 }, { 1024, 3 }, { 256, 2 }, { 128, 1 }, { 0, 0 }
};
u32bit window_bits = 1;
if(exp_bits)
{
for(u32bit j = 0; wsize[j][0]; ++j)
{
if(exp_bits >= wsize[j][0])
{
window_bits += wsize[j][1];
break;
}
}
}
if(hints & Power_Mod::BASE_IS_FIXED)
window_bits += 2;
if(hints & Power_Mod::EXP_IS_LARGE)
++window_bits;
return window_bits;
}
/*
* Montgomery Reduction
*/
inline void montgomery_reduce(BigInt& out, MemoryRegion<word>& z_buf,
const BigInt& x_bn, u32bit x_size, word u)
{
const word* x = x_bn.data();
word* z = z_buf.begin();
u32bit z_size = z_buf.size();
bigint_monty_redc(z, z_size, x, x_size, u);
out.get_reg().set(z + x_size, x_size + 1);
}
}
/*
* Set the exponent
*/
void Montgomery_Exponentiator::set_exponent(const BigInt& exp)
{
this->exp = exp;
exp_bits = exp.bits();
}
/*
* Set the base
*/
void Montgomery_Exponentiator::set_base(const BigInt& base)
{
window_bits = choose_window_bits(exp.bits(), base.bits(), hints);
g.resize((1 << window_bits) - 1);
SecureVector<word> z(2 * (mod_words + 1));
SecureVector<word> workspace(z.size());
g[0] = (base >= modulus) ? (base % modulus) : base;
bigint_mul(z.begin(), z.size(), workspace,
g[0].data(), g[0].size(), g[0].sig_words(),
R2.data(), R2.size(), R2.sig_words());
montgomery_reduce(g[0], z, modulus, mod_words, mod_prime);
const BigInt& x = g[0];
const u32bit x_sig = x.sig_words();
for(u32bit j = 1; j != g.size(); ++j)
{
const BigInt& y = g[j-1];
const u32bit y_sig = y.sig_words();
z.clear();
bigint_mul(z.begin(), z.size(), workspace,
x.data(), x.size(), x_sig,
y.data(), y.size(), y_sig);
montgomery_reduce(g[j], z, modulus, mod_words, mod_prime);
}
}
/*
* Compute the result
*/
BigInt Montgomery_Exponentiator::execute() const
{
const u32bit exp_nibbles = (exp_bits + window_bits - 1) / window_bits;
BigInt x = R_mod;
SecureVector<word> z(2 * (mod_words + 1));
SecureVector<word> workspace(2 * (mod_words + 1));
for(u32bit j = exp_nibbles; j > 0; --j)
{
for(u32bit k = 0; k != window_bits; ++k)
{
z.clear();
bigint_sqr(z.begin(), z.size(), workspace,
x.data(), x.size(), x.sig_words());
montgomery_reduce(x, z, modulus, mod_words, mod_prime);
}
u32bit nibble = exp.get_substring(window_bits*(j-1), window_bits);
if(nibble)
{
const BigInt& y = g[nibble-1];
z.clear();
bigint_mul(z.begin(), z.size(), workspace,
x.data(), x.size(), x.sig_words(),
y.data(), y.size(), y.sig_words());
montgomery_reduce(x, z, modulus, mod_words, mod_prime);
}
}
z.clear();
z.copy(x.data(), x.size());
montgomery_reduce(x, z, modulus, mod_words, mod_prime);
return x;
}
/*
* Montgomery_Exponentiator Constructor
*/
Montgomery_Exponentiator::Montgomery_Exponentiator(const BigInt& mod,
Power_Mod::Usage_Hints hints)
{
if(!mod.is_positive())
throw Exception("Montgomery_Exponentiator: modulus must be positive");
if(mod.is_even())
throw Exception("Montgomery_Exponentiator: modulus must be odd");
window_bits = 0;
this->hints = hints;
modulus = mod;
mod_words = modulus.sig_words();
BigInt mod_prime_bn(BigInt::Power2, MP_WORD_BITS);
mod_prime = (mod_prime_bn - inverse_mod(modulus, mod_prime_bn)).word_at(0);
R_mod = BigInt(BigInt::Power2, MP_WORD_BITS * mod_words);
R_mod %= modulus;
R2 = BigInt(BigInt::Power2, 2 * MP_WORD_BITS * mod_words);
R2 %= modulus;
}
}
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