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/*
* Elliptic curves over GF(p) Montgomery Representation
* (C) 2014,2015 Jack Lloyd
* 2016 Matthias Gierlings
*
* Botan is released under the Simplified BSD License (see license.txt)
*/
#include <botan/curve_gfp.h>
#include <botan/curve_nistp.h>
#include <botan/internal/mp_core.h>
#include <botan/internal/mp_asmi.h>
namespace Botan {
namespace {
class CurveGFp_Montgomery final : 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, x, y, m_p.data(), m_p_words, m_p_dash, ws.data());
}
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 x_sw = x.sig_words();
BOTAN_ASSERT(x_sw <= m_p_words, "Input in range");
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, x, m_p.data(), m_p_words, m_p_dash,
ws.data());
}
class CurveGFp_NIST : public CurveGFp_Repr
{
public:
CurveGFp_NIST(size_t p_bits, const BigInt& a, const BigInt& b) :
m_a(a), m_b(b), m_p_words((p_bits + BOTAN_MP_WORD_BITS - 1) / BOTAN_MP_WORD_BITS)
{
}
const BigInt& get_a() const override { return m_a; }
const BigInt& get_b() const override { return m_b; }
size_t get_p_words() const override { return m_p_words; }
const BigInt& get_a_rep() const override { return m_a; }
const BigInt& get_b_rep() const override { return m_b; }
void to_curve_rep(BigInt& x, secure_vector<word>& ws) const override
{ redc(x, ws); }
void from_curve_rep(BigInt& x, secure_vector<word>& ws) const override
{ redc(x, ws); }
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:
virtual void redc(BigInt& x, secure_vector<word>& ws) const = 0;
// Curve parameters
BigInt m_a, m_b;
size_t m_p_words; // cache of m_p.sig_words()
};
void CurveGFp_NIST::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 p_words = get_p_words();
const size_t output_size = 2*p_words + 1;
ws.resize(2*(p_words+2));
z.grow_to(output_size);
z.clear();
bigint_mul(z, x, y, ws.data());
this->redc(z, ws);
}
void CurveGFp_NIST::curve_sqr(BigInt& z, const BigInt& x,
secure_vector<word>& ws) const
{
if(x.is_zero())
{
z = 0;
return;
}
const size_t p_words = get_p_words();
const size_t output_size = 2*p_words + 1;
ws.resize(2*(p_words+2));
z.grow_to(output_size);
z.clear();
bigint_sqr(z.mutable_data(), output_size, ws.data(),
x.data(), x.size(), x.sig_words());
this->redc(z, ws);
}
#if defined(BOTAN_HAS_NIST_PRIME_REDUCERS_W32)
/**
* The NIST P-192 curve
*/
class CurveGFp_P192 final : public CurveGFp_NIST
{
public:
CurveGFp_P192(const BigInt& a, const BigInt& b) : CurveGFp_NIST(192, a, b) {}
const BigInt& get_p() const override { return prime_p192(); }
private:
void redc(BigInt& x, secure_vector<word>& ws) const override { redc_p192(x, ws); }
};
/**
* The NIST P-224 curve
*/
class CurveGFp_P224 final : public CurveGFp_NIST
{
public:
CurveGFp_P224(const BigInt& a, const BigInt& b) : CurveGFp_NIST(224, a, b) {}
const BigInt& get_p() const override { return prime_p224(); }
private:
void redc(BigInt& x, secure_vector<word>& ws) const override { redc_p224(x, ws); }
};
/**
* The NIST P-256 curve
*/
class CurveGFp_P256 final : public CurveGFp_NIST
{
public:
CurveGFp_P256(const BigInt& a, const BigInt& b) : CurveGFp_NIST(256, a, b) {}
const BigInt& get_p() const override { return prime_p256(); }
private:
void redc(BigInt& x, secure_vector<word>& ws) const override { redc_p256(x, ws); }
};
/**
* The NIST P-384 curve
*/
class CurveGFp_P384 final : public CurveGFp_NIST
{
public:
CurveGFp_P384(const BigInt& a, const BigInt& b) : CurveGFp_NIST(384, a, b) {}
const BigInt& get_p() const override { return prime_p384(); }
private:
void redc(BigInt& x, secure_vector<word>& ws) const override { redc_p384(x, ws); }
};
#endif
/**
* The NIST P-521 curve
*/
class CurveGFp_P521 final : public CurveGFp_NIST
{
public:
CurveGFp_P521(const BigInt& a, const BigInt& b) : CurveGFp_NIST(521, a, b) {}
const BigInt& get_p() const override { return prime_p521(); }
private:
void redc(BigInt& x, secure_vector<word>& ws) const override { redc_p521(x, ws); }
};
}
std::shared_ptr<CurveGFp_Repr>
CurveGFp::choose_repr(const BigInt& p, const BigInt& a, const BigInt& b)
{
#if defined(BOTAN_HAS_NIST_PRIME_REDUCERS_W32)
if(p == prime_p192())
return std::shared_ptr<CurveGFp_Repr>(new CurveGFp_P192(a, b));
if(p == prime_p224())
return std::shared_ptr<CurveGFp_Repr>(new CurveGFp_P224(a, b));
if(p == prime_p256())
return std::shared_ptr<CurveGFp_Repr>(new CurveGFp_P256(a, b));
if(p == prime_p384())
return std::shared_ptr<CurveGFp_Repr>(new CurveGFp_P384(a, b));
#endif
if(p == prime_p521())
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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