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/*
* Elliptic curves over GF(p) Montgomery Representation
* (C) 2014 Jack Lloyd
*
* Distributed under the terms of the Botan license
*/
#include <botan/curve_gfp.h>
#include <botan/internal/curve_nistp.h>
#include <botan/internal/mp_core.h>
namespace Botan {
namespace {
class CurveGFp_Montgomery : public CurveGFp_Repr
{
public:
CurveGFp_Montgomery(const BigInt& p, const BigInt& a, const BigInt& b) :
m_p(p), m_a(a), m_b(b),
m_p_words(m_p.sig_words()),
m_p_dash(monty_inverse(m_p.word_at(0)))
{
const BigInt r = BigInt::power_of_2(m_p_words * BOTAN_MP_WORD_BITS);
m_r2 = (r * r) % p;
m_a_r = (m_a * r) % p;
m_b_r = (m_b * r) % p;
}
const BigInt& get_a() const override { return m_a; }
const BigInt& get_b() const override { return m_b; }
const BigInt& get_p() const override { return m_p; }
const BigInt& get_a_rep() const override { return m_a_r; }
const BigInt& get_b_rep() const override { return m_b_r; }
size_t get_p_words() const override { return m_p_words; }
void to_curve_rep(BigInt& x, secure_vector<word>& ws) const override;
void from_curve_rep(BigInt& x, secure_vector<word>& ws) const override;
void curve_mul(BigInt& z, const BigInt& x, const BigInt& y,
secure_vector<word>& ws) const override;
void curve_sqr(BigInt& z, const BigInt& x,
secure_vector<word>& ws) const override;
private:
BigInt m_p, m_a, m_b;
size_t m_p_words; // cache of m_p.sig_words()
// Montgomery parameters
BigInt m_r2, m_a_r, m_b_r;
word m_p_dash;
};
void CurveGFp_Montgomery::to_curve_rep(BigInt& x, secure_vector<word>& ws) const
{
const BigInt tx = x;
curve_mul(x, tx, m_r2, ws);
}
void CurveGFp_Montgomery::from_curve_rep(BigInt& x, secure_vector<word>& ws) const
{
const BigInt tx = x;
curve_mul(x, tx, 1, ws);
}
void CurveGFp_Montgomery::curve_mul(BigInt& z, const BigInt& x, const BigInt& y,
secure_vector<word>& ws) const
{
if(x.is_zero() || y.is_zero())
{
z = 0;
return;
}
const size_t output_size = 2*m_p_words + 1;
ws.resize(2*(m_p_words+2));
z.grow_to(output_size);
z.clear();
bigint_monty_mul(z.mutable_data(), output_size,
x.data(), x.size(), x.sig_words(),
y.data(), y.size(), y.sig_words(),
m_p.data(), m_p_words, m_p_dash,
&ws[0]);
}
void CurveGFp_Montgomery::curve_sqr(BigInt& z, const BigInt& x,
secure_vector<word>& ws) const
{
if(x.is_zero())
{
z = 0;
return;
}
const size_t output_size = 2*m_p_words + 1;
ws.resize(2*(m_p_words+2));
z.grow_to(output_size);
z.clear();
bigint_monty_sqr(z.mutable_data(), output_size,
x.data(), x.size(), x.sig_words(),
m_p.data(), m_p_words, m_p_dash,
&ws[0]);
}
}
// Default implementation
void CurveGFp_Repr::normalize(BigInt& x, secure_vector<word>& ws, size_t /*bound*/) const
{
const BigInt& p = get_p();
while(x.is_negative())
x += p;
const size_t p_words = get_p_words();
const word* prime = p.data();
x.grow_to(p_words + 1);
if(ws.size() < p_words + 1)
ws.resize(p_words + 1);
//FIXME: take into account bound if > 0
while(true)
{
if(bigint_sub3(&ws[0], x.data(), p_words, prime, p_words)) // borrow?
break;
x.swap_reg(ws);
}
}
std::shared_ptr<CurveGFp_Repr>
CurveGFp::choose_repr(const BigInt& p, const BigInt& a, const BigInt& b)
{
if(p == CurveGFp_P521::prime())
return std::shared_ptr<CurveGFp_Repr>(new CurveGFp_P521(a, b));
return std::shared_ptr<CurveGFp_Repr>(new CurveGFp_Montgomery(p, a, b));
}
}
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