#pragma once

#include <iostream>
#include <cstdint>

//The GF(2^8) field used in AES

class GF28{
	int value;

	static int reduce(int v,int m);

public:
	static const int modulus=0x11b;

	static uint8_t multiply(uint8_t x,uint8_t y); //for when the class is overkill

	GF28();
	explicit GF28(int v);

	explicit operator uint8_t() const;

	GF28& operator+=(GF28 o);
	GF28& operator-=(GF28 o);
	GF28& operator<<=(int n); //multiplication by x^n

	GF28 operator+(GF28 o) const;
	GF28 operator-(GF28 o) const;
	GF28 operator*(GF28 o) const;
	GF28 operator<<(int n) const; //multiplication by x^n

	bool operator==(GF28 o) const;

	GF28 inverse() const;

	friend std::ostream& operator<<(std::ostream&,GF28);
};

std::ostream& operator<<(std::ostream &os,GF28 p);