elliptic_curve.hpp

/**
* Ðåàë³çàö³ÿ êëàñ³â òî÷êè, êîîðäèíàòè ÿêî¿ íàëåæàòü äåÿêîìó ê³ëüöþ ëèøê³â, 
* òà åë³ïòè÷íî¿ êðèâî¿ íàä ïîëåì ëèøê³â
* ðîçä³ë 2.4 êóðñîâî¿
*/
#include <cstdint>
#include <string>
#include "modular_arithmetic.hpp"

#ifndef ELLIPTIC_CURVE_H
#define ELLIPTIC_CURVE_H


/**
* Òî÷êà, êîîðäèíàòè ÿêî¿ x òà y íàëåæàòü äåÿêîìó ê³ëüöþ ëèøê³â.
* ßêùî áóëåâà çì³ííà is_infinity = true, òî öå íåñê³í÷åííî â³ääàëåíà òî÷êà
*/
class Point
{
private:
	Galois x, y;
	bool is_infinity;

public:
	Point() {}

	Point(Galois x, Galois y);

	/**
	* Êîíñòðóêòîð äëÿ ñòâîðåííÿ íåñê³í÷åííî â³ääàëåíî¿ òî÷êè.
	* is_infinity ìຠäîð³âíþâàòè true. Ïðè false êîðåêòíà ðîáîòà íå ãàðàíòóºòüñÿ.
	*/
	Point(bool is_infinity);

	bool operator== (const Point& other);

	bool operator!= (const Point& other);

	Point operator- ();

	/**
	* Ïîâåðòຠtrue ÿêùî òî÷êà º íåñê³í÷åííî â³ääàëåíîþ, false - â ³íøîìó âèïàäêó
	*/
	bool isinfty();

	/**
	* Ïîâåðòຠêîîðäèíàòó x
	*/
	Galois get_x();

	/**
	* Ïîâåðòຠêîîðäèíàòó y
	*/
	Galois get_y();

	/**
	* Ïîâåðòຠñòðîêîâå ïðåäñòàâëåííÿ
	* ßêùî òî÷êà ñê³í÷åííà, òî âîíî ìàòèìå âèãëÿä (x, y). ßêùî íåñê³í÷åííî â³ääàëåíà - (infty).
	*/
	std::string get_str();
};


/**
* Åë³ïòè÷íà êðèâà, ÿêà ìຠâèãëÿä y^2 = x^3 + a*x + b.
* Äëÿ êîðåêòíî¿ ðîáîòè ìåòîä³â double_point, add_points, sub_points ïàðàìåòð q, 
* ÿêèé âèçíà÷ຠÿêîìó ê³ëüöþ ëèøê³â ìàþòü íàëåæàòè êîîðäèíàòè òî÷îê êðèâî¿, ìຠáóòè ïðîñòèì
*/
class EllipticCurve
{
private:
	Galois a, b;
	int_fast64_t q;

public:
	EllipticCurve(int_fast64_t a, int_fast64_t b, int_fast64_t q);
	EllipticCurve();

	/**
	* Ïîâåðòຠtrue ÿêùî òî÷êà P íàëåæèòü êðèâ³é, false - â ³íøîìó âèïàäêó
	*/
	bool is_point_on_curve(Point& P);

	/**
	* Ïîäâîºííÿ òî÷êè P íà åë³ïòè÷í³é êðèâ³é
	*/
	Point double_point(Point& P);

	/**
	* Äîäàâàííÿ òî÷îê P òà Q íà åë³ïòè÷í³é êðèâ³é
	*/
	Point add_points(Point& P, Point& Q);

	/**
	* ³äí³ìàííÿ òî÷îê P òà Q íà åë³ïòè÷í³é êðèâ³é
	*/
	Point sub_points(Point& P, Point& Q);

	/**
	* Ïîâåðòຠïîðÿäîê òî÷êè r, äå r * P = (infty)
	*/
	int_fast64_t order(Point& P);

	/**
	* Ïîâåðòຠçíà÷åííÿ ïàðàìåòðà q
	*/
	int_fast64_t get_mod();

	/**
	* Ïîâåðòຠçíà÷åííÿ êîåô³ö³ºíòà a
	*/
	Galois get_a();

	/**
	* Ïîâåðòຠçíà÷åííÿ êîåô³ö³ºíòà b
	*/
	Galois get_b();
};


#endif