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/*
* Arithmetic for point groups of elliptic curves over GF(p)
*
* (C) 2007 Martin Doering, Christoph Ludwig, Falko Strenzke
* 2008-2010 Jack Lloyd
*
* Distributed under the terms of the Botan license
*/
#ifndef BOTAN_POINT_GFP_H__
#define BOTAN_POINT_GFP_H__
#include <botan/curve_gfp.h>
#include <vector>
namespace Botan {
struct BOTAN_DLL Illegal_Point : public Exception
{
Illegal_Point(const std::string& err = "") : Exception(err) {}
};
/**
* This class represents one point on a curve of GF(p)
*/
class BOTAN_DLL PointGFp
{
public:
/**
* uncompressed encoding byte value
*/
static const int UNCOMPRESSED = 0;
/**
* compressed encoding byte value
*/
static const int COMPRESSED = 1;
/**
* hybrid encoding byte value
*/
static const int HYBRID = 2;
/**
* Construct the point O
* @param curve The base curve
*/
PointGFp(const CurveGFp& curve);
/**
* Construct a point given its affine coordinates
* @param curve the base curve
* @param x affine x coordinate
* @param y affine y coordinate
*/
PointGFp(const CurveGFp& curve,
const GFpElement& x,
const GFpElement& y);
/**
* Construct a point given its jacobian projective coordinates
* @param curve the base curve
* @param x jacobian projective x coordinate
* @param y jacobian projective y coordinate
* @param z jacobian projective y coordinate
*/
PointGFp(const CurveGFp& curve,
const GFpElement& x,
const GFpElement& y,
const GFpElement& z);
//PointGFp(const PointGFp& other) = default;
//PointGFp& operator=(const PointGFp& other) = default;
/**
* += Operator
* @param rhs the PointGFp to add to the local value
* @result resulting PointGFp
*/
PointGFp& operator+=(const PointGFp& rhs);
/**
* -= Operator
* @param rhs the PointGFp to subtract from the local value
* @result resulting PointGFp
*/
PointGFp& operator-=(const PointGFp& rhs);
/**
* *= Operator
* This function turns on the the special reduction multiplication
* itself for fast computation, turns it off again when finished.
* @param scalar the PointGFp to multiply with *this
* @result resulting PointGFp
*/
PointGFp& operator*=(const BigInt& scalar);
/**
* Negate internal value(*this *= -1 )
* @return *this
*/
PointGFp& negate();
/**
* Multiply the point by two(*this *= 2 )
* @return *this
*/
PointGFp& mult2_in_place();
/**
* Set z coordinate to one.
* @return *this
*/
const PointGFp& set_z_to_one() const;
/**
* Return a point
* where the coordinates are transformed
* so that z equals one,
* thus x and y have just the affine values.
* @result *this
*/
PointGFp get_z_to_one() const;
/**
* Return base curve of this point
* @result the curve over GF(p) of this point
*/
const CurveGFp& get_curve() const { return mC; }
/**
* get affine x coordinate
* @result affine x coordinate
*/
GFpElement get_affine_x() const;
/**
* get affine y coordinate
* @result affine y coordinate
*/
GFpElement get_affine_y() const;
/**
* get the jacobian projective x coordinate
* @result jacobian projective x coordinate
*/
GFpElement get_jac_proj_x() const;
/**
* get the jacobian projective y coordinate
* @result jacobian projective y coordinate
*/
GFpElement get_jac_proj_y() const;
/**
* get the jacobian projective z coordinate
* @result jacobian projective z coordinate
*/
GFpElement get_jac_proj_z() const;
/**
* Is this the point at infinity?
* @result true, if this point is at infinity, false otherwise.
*/
bool is_zero() const;
/**
* Checks whether the point is to be found on the underlying curve.
* Throws an Invalid_Point exception in case of detecting that the point
* does not satisfy the curve equation.
* To be used to ensure against fault attacks.
*/
void check_invariants() const;
/**
* swaps the states of *this and other, does not throw!
* @param other the object to swap values with
*/
void swap(PointGFp& other);
static GFpElement decompress(bool yMod2, GFpElement const& x, const CurveGFp& curve);
private:
CurveGFp mC;
mutable GFpElement mX; // NOTE: these values must be mutable (affine<->proj)
mutable GFpElement mY;
mutable GFpElement mZ;
};
// relational operators
bool BOTAN_DLL operator==(const PointGFp& lhs, const PointGFp& rhs);
inline bool operator!=(const PointGFp& lhs, const PointGFp& rhs )
{
return !operator==(lhs, rhs);
}
// arithmetic operators
PointGFp BOTAN_DLL operator+(const PointGFp& lhs, const PointGFp& rhs);
PointGFp BOTAN_DLL operator-(const PointGFp& lhs, const PointGFp& rhs);
PointGFp BOTAN_DLL operator-(const PointGFp& lhs);
PointGFp BOTAN_DLL operator*(const BigInt& scalar, const PointGFp& point);
PointGFp BOTAN_DLL operator*(const PointGFp& point, const BigInt& scalar);
PointGFp BOTAN_DLL mult2(const PointGFp& point);
PointGFp BOTAN_DLL create_random_point(RandomNumberGenerator& rng,
const CurveGFp& curve);
// encoding and decoding
SecureVector<byte> BOTAN_DLL EC2OSP(const PointGFp& point, byte format);
PointGFp BOTAN_DLL OS2ECP(MemoryRegion<byte> const& os, const CurveGFp& curve);
/* Should these be private? */
SecureVector<byte>
BOTAN_DLL encode_uncompressed(const PointGFp& point);
SecureVector<byte> BOTAN_DLL encode_hybrid(const PointGFp& point);
SecureVector<byte> BOTAN_DLL encode_compressed(const PointGFp& point);
// swaps the states of point1 and point2, does not throw!
// cf. Meyers, Item 25
inline
void swap(PointGFp& point1, PointGFp& point2 )
{
point1.swap(point2);
}
} // namespace Botan
namespace std {
// swaps the states of point1 and point2, does not throw!
// cf. Meyers, Item 25
template<> inline void
swap<Botan::PointGFp>(Botan::PointGFp& x, Botan::PointGFp& y) { x.swap(y); }
} // namespace std
#endif
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