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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 = "Malformed ECP point detected") :
Exception(err) {}
};
/**
* This class represents one point on a curve of GF(p)
*/
class BOTAN_DLL PointGFp
{
public:
enum Compression_Type {
UNCOMPRESSED = 0,
COMPRESSED = 1,
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 BigInt& x, const BigInt& 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 z coordinate
*/
PointGFp(const CurveGFp& curve,
const BigInt& x,
const BigInt& y,
const BigInt& 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 this point
* @return *this
*/
PointGFp& negate();
/**
* Multiply the point by two
* @return *this
*/
PointGFp& mult2_in_place();
/**
* Set z coordinate to one.
* @return *this
*/
const PointGFp& set_z_to_one();
/**
* 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();
/**
* Return base curve of this point
* @result the curve over GF(p) of this point
*/
const CurveGFp& get_curve() const { return curve; }
/**
* get affine x coordinate
* @result affine x coordinate
*/
BigInt get_affine_x() const;
/**
* get affine y coordinate
* @result affine y coordinate
*/
BigInt get_affine_y() const;
/**
* get the jacobian projective x coordinate
* @result jacobian projective x coordinate
*/
const BigInt& get_jac_proj_x() const { return coord_x; }
/**
* get the jacobian projective y coordinate
* @result jacobian projective y coordinate
*/
const BigInt& get_jac_proj_y() const { return coord_y; }
/**
* get the jacobian projective z coordinate
* @result jacobian projective z coordinate
*/
const BigInt& get_jac_proj_z() const { return coord_z; }
/**
* 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);
/**
* Equality operator
*/
bool operator==(const PointGFp& other) const;
private:
GFpElement point_x() const { return GFpElement(curve.get_p(), coord_x); }
GFpElement point_y() const { return GFpElement(curve.get_p(), coord_y); }
GFpElement point_z() const { return GFpElement(curve.get_p(), coord_z); }
CurveGFp curve;
BigInt coord_x, coord_y, coord_z;
};
// relational operators
inline bool operator!=(const PointGFp& lhs, const PointGFp& rhs)
{
return !(rhs == lhs);
}
// 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 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(const MemoryRegion<byte>& os, const CurveGFp& curve);
// 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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