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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/internal/ct_utils.h>
#include <botan/internal/rounding.h>
#include <botan/numthry.h>
#include <botan/reducer.h>
#include <botan/monty.h>
namespace Botan {
class Montgomery_Exponentation_State
{
public:
Montgomery_Exponentation_State(std::shared_ptr<const Montgomery_Params> params,
const BigInt& g,
size_t window_bits);
BigInt exponentiation(const BigInt& k) const;
private:
std::shared_ptr<const Montgomery_Params> m_params;
std::vector<Montgomery_Int> m_g;
size_t m_window_bits;
};
Montgomery_Exponentation_State::Montgomery_Exponentation_State(std::shared_ptr<const Montgomery_Params> params,
const BigInt& g,
size_t window_bits) :
m_params(params),
m_window_bits(window_bits == 0 ? 4 : window_bits)
{
if(m_window_bits < 1 || m_window_bits > 12) // really even 8 is too large ...
throw Invalid_Argument("Invalid window bits for Montgomery exponentiation");
const size_t window_size = (1U << m_window_bits);
m_g.reserve(window_size);
m_g.push_back(Montgomery_Int(m_params, m_params->R1(), false));;
m_g.push_back(Montgomery_Int(m_params, g));
const Montgomery_Int& monty_g = m_g[1];
for(size_t i = 2; i != window_size; ++i)
{
m_g.push_back(monty_g * m_g[i - 1]);
}
// Resize each element to exactly p words
for(size_t i = 0; i != window_size; ++i)
{
m_g[i].fix_size();
}
}
namespace {
void const_time_lookup(secure_vector<word>& output,
const std::vector<Montgomery_Int>& g,
size_t nibble)
{
const size_t words = output.size();
clear_mem(output.data(), output.size());
for(size_t i = 0; i != g.size(); ++i)
{
const secure_vector<word>& vec = g[i].repr().get_word_vector();
BOTAN_ASSERT(vec.size() >= words,
"Word size as expected in const_time_lookup");
const word mask = CT::is_equal<word>(i, nibble);
for(size_t w = 0; w != words; ++w)
output[w] |= (mask & vec[w]);
}
}
}
BigInt Montgomery_Exponentation_State::exponentiation(const BigInt& scalar) const
{
const size_t exp_nibbles = (scalar.bits() + m_window_bits - 1) / m_window_bits;
Montgomery_Int x(m_params, m_params->R1(), false);
secure_vector<word> e_bits(m_params->p_words());
secure_vector<word> ws;
for(size_t i = exp_nibbles; i > 0; --i)
{
for(size_t j = 0; j != m_window_bits; ++j)
{
x.square_this(ws);
}
const uint32_t nibble = scalar.get_substring(m_window_bits*(i-1), m_window_bits);
const_time_lookup(e_bits, m_g, nibble);
x.mul_by(e_bits, ws);
}
return x.value();
}
std::shared_ptr<const Montgomery_Exponentation_State>
monty_precompute(std::shared_ptr<const Montgomery_Params> params,
const BigInt& g,
size_t window_bits)
{
return std::make_shared<const Montgomery_Exponentation_State>(params, g, window_bits);
}
BigInt monty_execute(const Montgomery_Exponentation_State& precomputed_state,
const BigInt& k)
{
return precomputed_state.exponentiation(k);
}
BigInt monty_multi_exp(std::shared_ptr<const Montgomery_Params> params_p,
const BigInt& x_bn,
const BigInt& z1,
const BigInt& y_bn,
const BigInt& z2)
{
if(z1.is_negative() || z2.is_negative())
throw Invalid_Argument("multi_exponentiate exponents must be positive");
const size_t z_bits = round_up(std::max(z1.bits(), z2.bits()), 2);
secure_vector<word> ws;
const Montgomery_Int one(params_p, params_p->R1(), false);
//const Montgomery_Int one(params_p, 1);
const Montgomery_Int x1(params_p, x_bn);
const Montgomery_Int x2 = x1.square(ws);
const Montgomery_Int x3 = x2.mul(x1, ws);
const Montgomery_Int y1(params_p, y_bn);
const Montgomery_Int y2 = y1.square(ws);
const Montgomery_Int y3 = y2.mul(y1, ws);
const Montgomery_Int y1x1 = y1.mul(x1, ws);
const Montgomery_Int y1x2 = y1.mul(x2, ws);
const Montgomery_Int y1x3 = y1.mul(x3, ws);
const Montgomery_Int y2x1 = y2.mul(x1, ws);
const Montgomery_Int y2x2 = y2.mul(x2, ws);
const Montgomery_Int y2x3 = y2.mul(x3, ws);
const Montgomery_Int y3x1 = y3.mul(x1, ws);
const Montgomery_Int y3x2 = y3.mul(x2, ws);
const Montgomery_Int y3x3 = y3.mul(x3, ws);
const Montgomery_Int* M[16] = {
&one,
&x1, // 0001
&x2, // 0010
&x3, // 0011
&y1, // 0100
&y1x1,
&y1x2,
&y1x3,
&y2, // 1000
&y2x1,
&y2x2,
&y2x3,
&y3, // 1100
&y3x1,
&y3x2,
&y3x3
};
Montgomery_Int H = one;
for(size_t i = 0; i != z_bits; i += 2)
{
if(i > 0)
{
H.square_this(ws);
H.square_this(ws);
}
const uint8_t z1_b = z1.get_substring(z_bits - i - 2, 2);
const uint8_t z2_b = z2.get_substring(z_bits - i - 2, 2);
const uint8_t z12 = (4*z2_b) + z1_b;
H.mul_by(*M[z12], ws);
}
return H.value();
}
}
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