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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_Transformation : public Exception
{
Illegal_Transformation(const std::string& err =
"Requested transformation is not possible") :
Exception(err) {}
};
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 an uninitialized PointGFp
*/
PointGFp() {}
/**
* Construct the zero point
* @param curve The base curve
*/
PointGFp(const CurveGFp& curve);
/**
* Construct a point from 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);
//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()
{
if(!is_zero())
coord_y = curve.get_p() - coord_y;
return *this;
}
/**
* 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;
/**
* Is this the point at infinity?
* @result true, if this point is at infinity, false otherwise.
*/
bool is_zero() const
{ return (coord_x.is_zero() && coord_z.is_zero()); }
/**
* 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:
class Workspace
{
public:
Workspace(u32bit p_words) :
ws_monty(2*p_words+1), ws_bn(12) {}
SecureVector<word> ws_monty;
std::vector<BigInt> ws_bn;
};
/**
* Montgomery multiplication/reduction
* @param x first multiplicand
* @param y second multiplicand
* @param workspace temp space
*/
BigInt monty_mult(const BigInt& x, const BigInt& y,
MemoryRegion<word>& workspace);
/**
* Montgomery squaring/reduction
* @param x multiplicand
* @param workspace temp space
*/
BigInt monty_sqr(const BigInt& x,
MemoryRegion<word>& workspace);
/**
* Point addition
*/
void add(const PointGFp& other, Workspace& workspace);
/**
* Point doubling
* @param workspace temp space
*/
void mult2(Workspace& workspace);
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
inline PointGFp operator-(const PointGFp& lhs)
{
return PointGFp(lhs).negate();
}
inline PointGFp operator+(const PointGFp& lhs, const PointGFp& rhs)
{
PointGFp tmp(lhs);
return tmp += rhs;
}
inline PointGFp operator-(const PointGFp& lhs, const PointGFp& rhs)
{
PointGFp tmp(lhs);
return tmp -= rhs;
}
inline PointGFp operator*(const BigInt& scalar, const PointGFp& point)
{
PointGFp result(point);
return result *= scalar;
}
inline PointGFp operator*(const PointGFp& point, const BigInt& scalar)
{
PointGFp result(point);
return result *= scalar;
}
// encoding and decoding
SecureVector<byte> BOTAN_DLL EC2OSP(const PointGFp& point, byte format);
PointGFp BOTAN_DLL OS2ECP(const byte data[], u32bit data_len,
const CurveGFp& curve);
inline PointGFp OS2ECP(const MemoryRegion<byte>& data, const CurveGFp& curve)
{ return OS2ECP(&data[0], data.size(), curve); }
}
namespace std {
template<>
inline void swap<Botan::PointGFp>(Botan::PointGFp& x, Botan::PointGFp& y)
{ x.swap(y); }
}
#endif
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