path: root/src/lib/math/ec_gfp/point_gfp.h

/*
* Point arithmetic on elliptic curves over GF(p)
*
* (C) 2007 Martin Doering, Christoph Ludwig, Falko Strenzke
*     2008-2011,2014,2015 Jack Lloyd
*
* Botan is released under the Simplified BSD License (see license.txt)
*/

#ifndef BOTAN_POINT_GFP_H__
#define BOTAN_POINT_GFP_H__

#include <botan/curve_gfp.h>
#include <vector>

namespace Botan {

/**
* Exception thrown if you try to convert a zero point to an affine
* coordinate
*/
struct BOTAN_DLL Illegal_Transformation : public Exception
   {
   explicit Illegal_Transformation(const std::string& err =
                          "Requested transformation is not possible") :
      Exception(err) {}
   };

/**
* Exception thrown if some form of illegal point is decoded
*/
struct BOTAN_DLL Illegal_Point : public Exception
   {
   explicit 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() = default;

      /**
      * Construct the zero point
      * @param curve The base curve
      */
      explicit PointGFp(const CurveGFp& curve);

      static PointGFp zero_of(const CurveGFp& curve)
         {
         return PointGFp(curve);
         }

      /**
      * Copy constructor
      */
      PointGFp(const PointGFp&) = default;

      /**
      * Move Constructor
      */
      PointGFp(PointGFp&& other)
         {
         this->swap(other);
         }

      /**
      * Standard Assignment
      */
      PointGFp& operator=(const PointGFp&) = default;

      /**
      * Move Assignment
      */
      PointGFp& operator=(PointGFp&& other)
         {
         if(this != &other)
            this->swap(other);
         return (*this);
         }

      /**
      * 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);

      /**
      * += 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
      * @param scalar the PointGFp to multiply with *this
      * @result resulting PointGFp
      */

      PointGFp& operator*=(const BigInt& scalar);

      /**
      * Multiplication Operator
      * @param scalar the scalar value
      * @param point the point value
      * @return scalar*point on the curve
      */
      friend BOTAN_DLL PointGFp operator*(const BigInt& scalar, const PointGFp& point);

      /**
      * Multiexponentiation
      * @param p1 a point
      * @param z1 a scalar
      * @param p2 a point
      * @param z2 a scalar
      * @result (p1 * z1 + p2 * z2)
      */
      friend BOTAN_DLL PointGFp multi_exponentiate(
        const PointGFp& p1, const BigInt& z1,
        const PointGFp& p2, const BigInt& z2);

      /**
      * Negate this point
      * @return *this
      */
      PointGFp& negate()
         {
         if(!is_zero())
            m_coord_y = m_curve.get_p() - m_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 m_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 (m_coord_x.is_zero() && m_coord_z.is_zero()); }

      /**
      * Checks whether the point is to be found on the underlying
      * curve; used to prevent fault attacks.
      * @return if the point is on the curve
      */
      bool on_the_curve() const;

      /**
      * swaps the states of *this and other, does not throw!
      * @param other the object to swap values with
      */
      void swap(PointGFp& other);

      /**
      * Randomize the point representation
      * The actual value (get_affine_x, get_affine_y) does not change
      */
      void randomize_repr(RandomNumberGenerator& rng);

      /**
      * Equality operator
      */
      bool operator==(const PointGFp& other) const;
   private:
      friend class Blinded_Point_Multiply;

      BigInt curve_mult(const BigInt& x, const BigInt& y) const
         {
         BigInt z;
         m_curve.mul(z, x, y, m_monty_ws);
         return z;
         }

      void curve_mult(BigInt& z, const BigInt& x, const BigInt& y) const
         {
         m_curve.mul(z, x, y, m_monty_ws);
         }

      BigInt curve_sqr(const BigInt& x) const
         {
         BigInt z;
         m_curve.sqr(z, x, m_monty_ws);
         return z;
         }

      void curve_sqr(BigInt& z, const BigInt& x) const
         {
         m_curve.sqr(z, x, m_monty_ws);
         }

      /**
      * Point addition
      * @param workspace temp space, at least 11 elements
      */
      void add(const PointGFp& other, std::vector<BigInt>& workspace);

      /**
      * Point doubling
      * @param workspace temp space, at least 9 elements
      */
      void mult2(std::vector<BigInt>& workspace);

      CurveGFp m_curve;
      BigInt m_coord_x, m_coord_y, m_coord_z;
      mutable secure_vector<word> m_monty_ws; // workspace for Montgomery
   };

// 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 PointGFp& point, const BigInt& scalar)
   {
   return scalar * point;
   }

// encoding and decoding
secure_vector<uint8_t> BOTAN_DLL EC2OSP(const PointGFp& point, uint8_t format);

PointGFp BOTAN_DLL OS2ECP(const uint8_t data[], size_t data_len,
                          const CurveGFp& curve);

template<typename Alloc>
PointGFp OS2ECP(const std::vector<uint8_t, Alloc>& data, const CurveGFp& curve)
   { return OS2ECP(data.data(), data.size(), curve); }

/**

*/
class BOTAN_DLL Blinded_Point_Multiply
   {
   public:
      Blinded_Point_Multiply(const PointGFp& base, const BigInt& order, size_t h = 0);

      PointGFp blinded_multiply(const BigInt& scalar, RandomNumberGenerator& rng);
   private:
      const size_t m_h;
      const BigInt& m_order;
      std::vector<BigInt> m_ws;
      std::vector<PointGFp> m_U;
   };

}

namespace std {

template<>
inline void swap<Botan::PointGFp>(Botan::PointGFp& x, Botan::PointGFp& y)
   { x.swap(y); }

}

#endif