Elliptic Curve

素域上椭圆曲线E(Fp)E(F_p)E(Fp)的C++实现

EC.hEC.hEC.h

#pragma once#include <iostream>#include <NTL/ZZ.h>       // integers
#include <NTL/ZZ_p.h> // integers mod pusing namespace std;
using namespace NTL;#pragma comment(lib, "NTL")typedef char int8;
typedef int int32;
typedef long long int64;
typedef unsigned char uint8;
typedef unsigned int  uint32;
typedef unsigned long long uint64;// 换行
#define pn puts("")// 异常
#define ErrorInfo(format, ...) {\printf("File:%s, Line:%d, Function:%s, ",\__FILE__, __LINE__ , __FUNCTION__);\printf(format, ##__VA_ARGS__);}/*E(F_p)上椭圆曲线点
*/
struct Point
{uint8 PC;  //标识。无穷远点PC=00，点的未压缩表示PC=04ZZ x;       //横坐标ZZ y;      //纵坐标
};//打印
ostream& operator<<(ostream& cout, Point& P);/*Elliptic curve素域上椭圆曲线，E(F_p)y^2 = x^3 + ax + b
*/
class EC
{
private:ZZ p;ZZ a;ZZ b;public:/*椭圆曲线初始化*/void init(ZZ& p, ZZ& a, ZZ& b);/*判断是否是椭圆曲线上的点*/bool IsECPoint(Point& op1);/*加法*/void Add(Point& res, Point& op1, Point& op2);/*倍点*/void Double(Point& res, Point& op1);/*多倍点*/void Multiple(Point& res, ZZ& k, Point& op1);/*打印EC参数*/void Param();};

EC.cppEC.cppEC.cpp

#include "EC.h"ostream& operator<<(ostream& cout, Point& P)
{printf("struct Point\n\tPC = %02x\n", P.PC);if (P.PC != 0){cout << "\tx = " << P.x; pn;cout << "\ty = " << P.y; pn;}return cout;
}void EC::init(ZZ&p, ZZ& a, ZZ& b)
{if ((4 * PowerMod(a%p, 3, p) + 27 * PowerMod(b%p, 2, p)) % p == 0){ErrorInfo("%s\n", "4*a^3 + 27*b^2 = 0 mod p");return;}this->p = p;this->a = a;this->b = b;
}bool EC::IsECPoint(Point& op1)
{if (op1.PC == 0)return 1;elsereturn PowerMod(op1.y, 2, p) == (PowerMod(op1.x, 3, p) + a * op1.x + b) % p;
}void EC::Add(Point& res, Point& op1, Point& op2)
{if (op1.PC == 0 || op2.PC == 0){if (op1.PC != 0){res = op1;return;}if (op2.PC != 0){res = op2;return;}res.PC = 0;return;}if (op1.x == op2.x){if (op1.y == op2.y)Double(res, op1);else if (op1.y + op2.y == p)res.PC = 0;elseErrorInfo("%s\n", "x1 == x2, but y1 != y2 and y1 != -y2");}else{res.PC = 4;ZZ xx = op2.x + (p - op1.x);if (xx >= p)xx -= p;ZZ lambda = ((op2.y + (p - op1.y))*InvMod(xx, p)) % p;ZZ x = (PowerMod(lambda, 2, p) + (p - op1.x) + (p - op2.x)) % p;res.y = (lambda*(op1.x - x) + (p - op1.y)) % p;res.x = x;}
}void EC::Double(Point& res, Point& op1)
{if (op1.PC == 0){res.PC = 0;return;}if (op1.y == 0){ErrorInfo("%s\n", "y1 == 0");}else{res.PC = 4;ZZ yy = 2 * op1.y;if (yy >= p)yy -= p;ZZ lambda = ((3 * PowerMod(op1.x, 2, p) + a)*InvMod(yy, p)) % p;ZZ x = (PowerMod(lambda, 2, p) + 2 * (p - op1.x)) % p;res.y = (lambda*(op1.x - x) + (p - op1.y)) % p;res.x = x;}
}void EC::Multiple(Point& res, ZZ& k, Point& op1)
{if (op1.PC == 0){res.PC = 0;return;}Point op = op1;ZZ kk = k;res.PC = 0;while (kk > 0){if ((kk & 1) == 1)Add(res, res, op);Double(op, op);kk >>= 1;}
}void EC::Param()
{cout << "class EC\n";cout << "\ta=" << a; pn;cout << "\tb=" << b; pn;cout << "\tp=" << p; pn; pn;
}

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Elliptic Curve

素域上椭圆曲线E(Fp)E(F_p)E(Fp)的C++实现

EC.hEC.hEC.h

EC.cppEC.cppEC.cpp

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Elliptic Curve

素域上椭圆曲线E(Fp)E(F_p)E(Fp​)的C++实现

EC.hEC.hEC.h

EC.cppEC.cppEC.cpp

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最新文章

热门文章

素域上椭圆曲线E(Fp)E(F_p)E(Fp)的C++实现