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/*
* (C) 2015,2018 Jack Lloyd
*
* Botan is released under the Simplified BSD License (see license.txt)
*/
#include <botan/internal/point_mul.h>
#include <botan/rng.h>
#include <botan/internal/rounding.h>
namespace Botan {
Blinded_Point_Multiply::Blinded_Point_Multiply(const PointGFp& base,
const BigInt& order,
size_t h) :
m_ws(PointGFp::WORKSPACE_SIZE),
m_order(order)
{
BOTAN_UNUSED(h);
m_point_mul.reset(new PointGFp_Var_Point_Precompute(base));
}
Blinded_Point_Multiply::~Blinded_Point_Multiply()
{
/* for ~unique_ptr */
}
PointGFp Blinded_Point_Multiply::blinded_multiply(const BigInt& scalar,
RandomNumberGenerator& rng)
{
return m_point_mul->mul(scalar, rng, m_order, m_ws);
}
PointGFp_Base_Point_Precompute::PointGFp_Base_Point_Precompute(const PointGFp& base)
{
std::vector<BigInt> ws(PointGFp::WORKSPACE_SIZE);
const size_t p_bits = base.get_curve().get_p().bits();
/*
* Some of the curves (eg secp160k1) have an order slightly larger than
* the size of the prime modulus. In all cases they are at most 1 bit
* longer. The +1 compensates for this.
*/
const size_t T_bits = round_up(p_bits + PointGFp_SCALAR_BLINDING_BITS + 1, 2) / 2;
m_T.resize(3*T_bits);
m_T[0] = base;
m_T[1] = m_T[0];
m_T[1].mult2(ws);
m_T[2] = m_T[1];
m_T[2].add(m_T[0], ws);
for(size_t i = 1; i != T_bits; ++i)
{
m_T[3*i+0] = m_T[3*i - 2];
m_T[3*i+0].mult2(ws);
m_T[3*i+1] = m_T[3*i+0];
m_T[3*i+1].mult2(ws);
m_T[3*i+2] = m_T[3*i+1];
m_T[3*i+2].add(m_T[3*i+0], ws);
}
PointGFp::force_all_affine(m_T, ws[0].get_word_vector());
}
PointGFp PointGFp_Base_Point_Precompute::mul(const BigInt& k,
RandomNumberGenerator& rng,
const BigInt& group_order,
std::vector<BigInt>& ws) const
{
if(k.is_negative())
throw Invalid_Argument("PointGFp_Base_Point_Precompute scalar must be positive");
// Choose a small mask m and use k' = k + m*order (Coron's 1st countermeasure)
const BigInt mask(rng, PointGFp_SCALAR_BLINDING_BITS, false);
const BigInt scalar = k + group_order * mask;
size_t windows = round_up(scalar.bits(), 2) / 2;
BOTAN_ASSERT(windows <= m_T.size() / 3,
"Precomputed sufficient values for scalar mult");
if(ws.size() < PointGFp::WORKSPACE_SIZE)
ws.resize(PointGFp::WORKSPACE_SIZE);
PointGFp R = m_T[0].zero();
for(size_t i = 0; i != windows; ++i)
{
if(i == 4)
{
R.randomize_repr(rng, ws[0].get_word_vector());
}
const uint32_t w = scalar.get_substring(2*i, 2);
if(w > 0)
R.add_affine(m_T[3*i + w - 1], ws);
}
BOTAN_DEBUG_ASSERT(R.on_the_curve());
return R;
}
PointGFp_Var_Point_Precompute::PointGFp_Var_Point_Precompute(const PointGFp& point)
{
m_window_bits = 4;
m_U.resize(1U << m_window_bits);
m_U[0] = point.zero();
m_U[1] = point;
std::vector<BigInt> ws(PointGFp::WORKSPACE_SIZE);
for(size_t i = 2; i < m_U.size(); ++i)
{
m_U[i] = m_U[i-1];
m_U[i].add(point, ws);
}
}
void PointGFp_Var_Point_Precompute::randomize_repr(RandomNumberGenerator& rng)
{
for(size_t i = 1; i != m_U.size(); ++i)
m_U[i].randomize_repr(rng);
}
PointGFp PointGFp_Var_Point_Precompute::mul(const BigInt& k,
RandomNumberGenerator& rng,
const BigInt& group_order,
std::vector<BigInt>& ws) const
{
if(k.is_negative())
throw Invalid_Argument("PointGFp_Base_Point_Precompute scalar must be positive");
if(ws.size() < PointGFp::WORKSPACE_SIZE)
ws.resize(PointGFp::WORKSPACE_SIZE);
// Choose a small mask m and use k' = k + m*order (Coron's 1st countermeasure)
const BigInt mask(rng, PointGFp_SCALAR_BLINDING_BITS, false);
const BigInt scalar = k + group_order * mask;
const size_t scalar_bits = scalar.bits();
size_t windows = round_up(scalar_bits, m_window_bits) / m_window_bits;
PointGFp R = m_U[0];
if(windows > 0)
{
windows--;
const uint32_t nibble = scalar.get_substring(windows*m_window_bits, m_window_bits);
R.add(m_U[nibble], ws);
/*
Randomize after adding the first nibble as before the addition R
is zero, and we cannot effectively randomize the point
representation of the zero point.
*/
R.randomize_repr(rng);
while(windows)
{
for(size_t i = 0; i != m_window_bits; ++i)
R.mult2(ws);
const uint32_t inner_nibble = scalar.get_substring((windows-1)*m_window_bits, m_window_bits);
// cache side channel here, we are relying on blinding...
R.add(m_U[inner_nibble], ws);
windows--;
}
}
BOTAN_DEBUG_ASSERT(R.on_the_curve());
return R;
}
}
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