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/*************************************************
* Modular Exponentiation Source File *
* (C) 1999-2005 The Botan Project *
*************************************************/
#include <botan/numthry.h>
#include <vector>
namespace Botan {
namespace {
/*************************************************
* Exponentiation Window Size *
*************************************************/
u32bit window_size(u32bit exp_bits)
{
struct mapping { u32bit bits; u32bit window_size; };
static const mapping wsize[] = {
{ 2048, 7 },
{ 1024, 6 },
{ 256, 5 },
{ 128, 4 },
{ 64, 3 },
{ 0, 0 }
};
for(u32bit j = 0; wsize[j].bits; j++)
{
if(exp_bits >= wsize[j].bits)
return wsize[j].window_size;
}
return 1;
}
/*************************************************
* Left-to-Right Binary Modular Exponentiation *
*************************************************/
BigInt power_mod_l2r(const BigInt& basex, const BigInt& exp,
ModularReducer* reducer)
{
const BigInt base = reducer->convert_in(basex);
const u32bit exp_bits = exp.bits();
BigInt x = reducer->convert_in(1);
for(u32bit j = exp_bits; j > 0; j--)
{
x = reducer->square(x);
if(exp.get_bit(j-1))
x = reducer->multiply(x, base);
}
return reducer->convert_out(x);
}
/*************************************************
* Modular Exponentiation with g = 2 *
*************************************************/
BigInt power_mod_g2(const BigInt& exp, ModularReducer* reducer)
{
if(reducer->must_convert())
throw Internal_Error("power_mod_g2: Can't use this reducer");
const u32bit exp_bits = exp.bits();
BigInt x = 1;
for(u32bit j = exp_bits; j > 0; j--)
{
x = reducer->square(x);
if(exp.get_bit(j-1))
{
x <<= 1;
x = reducer->reduce(x);
}
}
return x;
}
/*************************************************
* Window Modular Exponentiation *
*************************************************/
BigInt power_mod_window(const BigInt& base, const BigInt& exp,
ModularReducer* reducer, u32bit window_bits)
{
if(window_bits < 2)
throw Internal_Error("power_mod_window: Window size too small");
std::vector<BigInt> g((1 << window_bits) - 1);
g[0] = reducer->convert_in(base);
for(u32bit j = 1; j != g.size(); j++)
g[j] = reducer->multiply(g[j-1], g[0]);
const u32bit exp_nibbles = (exp.bits() + window_bits - 1) / window_bits;
BigInt x = reducer->convert_in(1);
for(u32bit j = exp_nibbles; j > 0; j--)
{
for(u32bit k = 0; k != window_bits; k++)
x = reducer->square(x);
u32bit nibble = exp.get_nibble(j-1, window_bits);
if(nibble)
x = reducer->multiply(x, g[nibble-1]);
}
return reducer->convert_out(x);
}
}
/*************************************************
* Modular Exponentiation *
*************************************************/
BigInt power_mod(const BigInt& base, const BigInt& exp, const BigInt& mod)
{
ModularReducer* reducer = get_reducer(mod);
BigInt x = power_mod(base, exp, reducer);
delete reducer;
return x;
}
/*************************************************
* Modular Exponentiation Algorithm Dispatch *
*************************************************/
BigInt power_mod(const BigInt& base, const BigInt& exp,
ModularReducer* reducer)
{
if(base.is_negative())
throw Invalid_Argument("power_mod: base must be positive");
if(exp.is_negative())
throw Invalid_Argument("power_mod: exponent must be positive");
if(exp.is_zero())
return 1;
const u32bit window_bits = window_size(exp.bits());
if(base == 2 && !reducer->must_convert())
return power_mod_g2(exp, reducer);
if(window_bits > 1)
return power_mod_window(base, exp, reducer, window_bits);
return power_mod_l2r(base, exp, reducer);
}
}
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