ec_point.h

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/*
* 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_EC_POINT_H_
#define BOTAN_EC_POINT_H_
 
#include <botan/curve_gfp.h>
#include <botan/exceptn.h>
#include <vector>
 
namespace Botan {
 
enum class EC_Point_Format {
   Uncompressed = 0,
   Compressed = 1,
   Hybrid = 2,
 
   UNCOMPRESSED BOTAN_DEPRECATED("Use EC_Point_Format::Uncompressed") = Uncompressed,
   COMPRESSED BOTAN_DEPRECATED("Use EC_Point_Format::Compressed") = Compressed,
   HYBRID BOTAN_DEPRECATED("Use EC_Point_Format::Hybrid") = Hybrid,
};
 
/**
* This class represents one point on a curve of GF(p)
*/
class BOTAN_PUBLIC_API(2, 0) EC_Point final {
   public:
      typedef EC_Point_Format Compression_Type;
      using enum EC_Point_Format;
 
      enum { WORKSPACE_SIZE = 8 };
 
      /**
      * Construct an uninitialized EC_Point
      */
      EC_Point() = default;
 
      /**
      * Construct the zero point
      * @param curve The base curve
      */
      explicit EC_Point(const CurveGFp& curve);
 
      /**
      * Copy constructor
      */
      EC_Point(const EC_Point&) = default;
 
      /**
      * Move Constructor
      */
      EC_Point(EC_Point&& other) { this->swap(other); }
 
      /**
      * Standard Assignment
      */
      EC_Point& operator=(const EC_Point&) = default;
 
      /**
      * Move Assignment
      */
      EC_Point& operator=(EC_Point&& other) {
         if(this != &other) {
            this->swap(other);
         }
         return (*this);
      }
 
      /**
      * Construct a point from its affine coordinates
      * Prefer EC_Group::point(x,y) for this operation.
      * @param curve the base curve
      * @param x affine x coordinate
      * @param y affine y coordinate
      */
      EC_Point(const CurveGFp& curve, const BigInt& x, const BigInt& y);
 
      /**
      * EC2OSP - elliptic curve to octet string primitive
      * @param format which format to encode using
      */
      std::vector<uint8_t> encode(EC_Point_Format format) const;
 
      /**
      * += Operator
      * @param rhs the EC_Point to add to the local value
      * @result resulting EC_Point
      */
      EC_Point& operator+=(const EC_Point& rhs);
 
      /**
      * -= Operator
      * @param rhs the EC_Point to subtract from the local value
      * @result resulting EC_Point
      */
      EC_Point& operator-=(const EC_Point& rhs);
 
      /**
      * *= Operator
      * @param scalar the EC_Point to multiply with *this
      * @result resulting EC_Point
      */
      EC_Point& operator*=(const BigInt& scalar);
 
      /**
      * Negate this point
      * @return *this
      */
      EC_Point& negate() {
         if(!is_zero()) {
            m_coord_y = m_curve.get_p() - m_coord_y;
         }
         return *this;
      }
 
      /**
      * 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;
 
      /**
      * Return the internal x coordinate
      *
      * Note this may be in Montgomery form
      */
      const BigInt& get_x() const { return m_coord_x; }
 
      /**
      * Return the internal y coordinate
      *
      * Note this may be in Montgomery form
      */
      const BigInt& get_y() const { return m_coord_y; }
 
      /**
      * Return the internal z coordinate
      *
      * Note this may be in Montgomery form
      */
      const BigInt& get_z() const { return m_coord_z; }
 
      void swap_coords(BigInt& new_x, BigInt& new_y, BigInt& new_z) {
         m_coord_x.swap(new_x);
         m_coord_y.swap(new_y);
         m_coord_z.swap(new_z);
      }
 
      /**
      * Force this point to affine coordinates
      */
      void force_affine();
 
      /**
      * Force all points on the list to affine coordinates
      */
      static void force_all_affine(std::vector<EC_Point>& points, secure_vector<word>& ws);
 
      bool is_affine() const;
 
      /**
      * Is this the point at infinity?
      * @result true, if this point is at infinity, false otherwise.
      */
      bool is_zero() const { return 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(EC_Point& other);
 
      friend void swap(EC_Point& x, EC_Point& y) { x.swap(y); }
 
      /**
      * Randomize the point representation
      * The actual value (get_affine_x, get_affine_y) does not change
      */
      void randomize_repr(RandomNumberGenerator& rng);
 
      /**
      * Randomize the point representation
      * The actual value (get_affine_x, get_affine_y) does not change
      */
      void randomize_repr(RandomNumberGenerator& rng, secure_vector<word>& ws);
 
      /**
      * Equality operator
      */
      bool operator==(const EC_Point& other) const;
 
      /**
      * Point addition
      * @param other the point to add to *this
      * @param workspace temp space, at least WORKSPACE_SIZE elements
      */
      void add(const EC_Point& other, std::vector<BigInt>& workspace) {
         BOTAN_ARG_CHECK(m_curve == other.m_curve, "cannot add points on different curves");
 
         const size_t p_words = m_curve.get_p_words();
 
         add(other.m_coord_x.data(),
             std::min(p_words, other.m_coord_x.size()),
             other.m_coord_y.data(),
             std::min(p_words, other.m_coord_y.size()),
             other.m_coord_z.data(),
             std::min(p_words, other.m_coord_z.size()),
             workspace);
      }
 
      /**
      * Point addition. Array version.
      *
      * @param x_words the words of the x coordinate of the other point
      * @param x_size size of x_words
      * @param y_words the words of the y coordinate of the other point
      * @param y_size size of y_words
      * @param z_words the words of the z coordinate of the other point
      * @param z_size size of z_words
      * @param workspace temp space, at least WORKSPACE_SIZE elements
      */
      void add(const word x_words[],
               size_t x_size,
               const word y_words[],
               size_t y_size,
               const word z_words[],
               size_t z_size,
               std::vector<BigInt>& workspace);
 
      /**
      * Point addition - mixed J+A
      * @param other affine point to add - assumed to be affine!
      * @param workspace temp space, at least WORKSPACE_SIZE elements
      */
      void add_affine(const EC_Point& other, std::vector<BigInt>& workspace) {
         BOTAN_ASSERT_NOMSG(m_curve == other.m_curve);
         BOTAN_DEBUG_ASSERT(other.is_affine());
 
         const size_t p_words = m_curve.get_p_words();
         add_affine(other.m_coord_x.data(),
                    std::min(p_words, other.m_coord_x.size()),
                    other.m_coord_y.data(),
                    std::min(p_words, other.m_coord_y.size()),
                    workspace);
      }
 
      /**
      * Point addition - mixed J+A. Array version.
      *
      * @param x_words the words of the x coordinate of the other point
      * @param x_size size of x_words
      * @param y_words the words of the y coordinate of the other point
      * @param y_size size of y_words
      * @param workspace temp space, at least WORKSPACE_SIZE elements
      */
      void add_affine(
         const word x_words[], size_t x_size, const word y_words[], size_t y_size, std::vector<BigInt>& workspace);
 
      /**
      * Point doubling
      * @param workspace temp space, at least WORKSPACE_SIZE elements
      */
      void mult2(std::vector<BigInt>& workspace);
 
      /**
      * Repeated point doubling
      * @param i number of doublings to perform
      * @param workspace temp space, at least WORKSPACE_SIZE elements
      */
      void mult2i(size_t i, std::vector<BigInt>& workspace);
 
      /**
      * Point addition
      * @param other the point to add to *this
      * @param workspace temp space, at least WORKSPACE_SIZE elements
      * @return other plus *this
      */
      EC_Point plus(const EC_Point& other, std::vector<BigInt>& workspace) const {
         EC_Point x = (*this);
         x.add(other, workspace);
         return x;
      }
 
      /**
      * Point doubling
      * @param workspace temp space, at least WORKSPACE_SIZE elements
      * @return *this doubled
      */
      EC_Point double_of(std::vector<BigInt>& workspace) const {
         EC_Point x = (*this);
         x.mult2(workspace);
         return x;
      }
 
      /**
      * Return the zero (aka infinite) point associated with this curve
      */
      EC_Point zero() const { return EC_Point(m_curve); }
 
      /**
      * Return base curve of this point
      * @result the curve over GF(p) of this point
      *
      * You should not need to use this
      */
      const CurveGFp& get_curve() const { return m_curve; }
 
   private:
      CurveGFp m_curve;
      BigInt m_coord_x, m_coord_y, m_coord_z;
};
 
/**
* Point multiplication operator
* @param scalar the scalar value
* @param point the point value
* @return scalar*point on the curve
*/
BOTAN_PUBLIC_API(2, 0) EC_Point operator*(const BigInt& scalar, const EC_Point& point);
 
/**
* ECC point multiexponentiation - not constant time!
* @param p1 a point
* @param z1 a scalar
* @param p2 a point
* @param z2 a scalar
* @result (p1 * z1 + p2 * z2)
*/
BOTAN_PUBLIC_API(2, 0)
EC_Point multi_exponentiate(const EC_Point& p1, const BigInt& z1, const EC_Point& p2, const BigInt& z2);
 
// relational operators
inline bool operator!=(const EC_Point& lhs, const EC_Point& rhs) {
   return !(rhs == lhs);
}
 
// arithmetic operators
inline EC_Point operator-(const EC_Point& lhs) {
   return EC_Point(lhs).negate();
}
 
inline EC_Point operator+(const EC_Point& lhs, const EC_Point& rhs) {
   EC_Point tmp(lhs);
   return tmp += rhs;
}
 
inline EC_Point operator-(const EC_Point& lhs, const EC_Point& rhs) {
   EC_Point tmp(lhs);
   return tmp -= rhs;
}
 
inline EC_Point operator*(const EC_Point& point, const BigInt& scalar) {
   return scalar * point;
}
 
/**
* Perform point decoding
* Use EC_Group::OS2ECP instead
*/
EC_Point BOTAN_PUBLIC_API(2, 0) OS2ECP(const uint8_t data[], size_t data_len, const CurveGFp& curve);
 
/**
* Perform point decoding
* Use EC_Group::OS2ECP instead
*
* @param data the encoded point
* @param data_len length of data in bytes
* @param curve_p the curve equation prime
* @param curve_a the curve equation a parameter
* @param curve_b the curve equation b parameter
*/
std::pair<BigInt, BigInt> BOTAN_UNSTABLE_API
OS2ECP(const uint8_t data[], size_t data_len, const BigInt& curve_p, const BigInt& curve_a, const BigInt& curve_b);
 
template <typename Alloc>
EC_Point OS2ECP(const std::vector<uint8_t, Alloc>& data, const CurveGFp& curve) {
   return OS2ECP(data.data(), data.size(), curve);
}
 
class EC_Point_Var_Point_Precompute;
 
// The name used for this type in older versions
typedef EC_Point PointGFp;
 
}  // namespace Botan
 
#endif