Rsa.cpp

#include "Rsa.h"
#include<iostream>
#include<sstream>
#include<ctime>
#include<cstdlib>

using std::cout;
using std::endl;
using std::ostringstream;

Rsa::Rsa()
{
}

Rsa::~Rsa()
{
}

void Rsa::init(unsigned int n)
{
	srand(time(NULL));
	//产生大素数p、q
	_p=createPrime(n,10);
	_q=createPrime(n,10);
	//计算N
	N=_p*_q;
	//计算出欧拉数
	_ol=(_p-1)*(_q-1);
	//加密指数e
	createExp(_ol);
	//d
}

BigInt Rsa::createOddNum(unsigned int n)
{//生成长度为n的奇数
	n=n/4;
	static unsigned char hex_table[]={'0','1','2','3','4','5','6','7','8','9','A','B','C','D','E','F'};
	if(n)
	{
		ostringstream oss;
		for(std::size_t i=0;i<n-1;++i)
			oss<<hex_table[rand()%16];
		oss<<hex_table[1];
		string str(oss.str());
		return BigInt(str);
	}
	else
		return BigInt::Zero;
}

bool Rsa::isPrime(const BigInt& n,const unsigned int k)
{//判断素数
	assert(n!=BigInt::Zero);
	if(n==BigInt::Two)
		return true;

	BigInt n_1=n-1;
	BigInt::bit b(n_1);//二进制位
	if(b.at(0)==1)
		return false;

	for(std::size_t t=0;t<k;++t)
	{
		BigInt a=createRandomSmallThan(n_1);//随机数
		BigInt d(BigInt::One);
		for(int i=b.size()-1;i>=0;--i)
		{
			BigInt x=d;
			d=(d*d)%n;
			if(d==BigInt::One && x!=BigInt::One && x!=n_1)
				return false;

			if(b.at(i))
			{
				assert(d!=BigInt::Zero);
				d=(a*d)%n;
			}
		}
		if(d!=BigInt::One)
			return false;
	}
	return true;
}

BigInt Rsa::createRandomSmallThan(const BigInt& a)
{
	unsigned long t=0;
	do
	{
		t=rand();
	}while(t==0);

	BigInt mod(t);
	BigInt r=mod%a;
	if(r==BigInt::Zero)
		r=a-BigInt::One;	
	return r;
}

BigInt Rsa::createPrime(unsigned int n,int it_count)
{//生成长度为n的素数
	assert(it_count>0);
	BigInt res=createOddNum(n);
	while(!isPrime(res,it_count))
	{
		res.add(BigInt::Two);
	}
	return res;
}

void Rsa::createExp(const BigInt& ou)
{//从一个欧拉数中生成公钥、私钥指数
	//e=5;
	e=65537;
	_d=e.extendEuclid(ou);
}

BigInt Rsa::encryptByPu(const BigInt& m)
{//公钥加密
	return m.moden(e,N);
}

BigInt Rsa::decodeByPr(const BigInt& c)
{//私钥解密
	return c.moden(_d,N);
}

BigInt Rsa::encryptByPr(const BigInt& m)
{//私钥加密
	return decodeByPr(m);
}

BigInt Rsa::decodeByPu(const BigInt& c)
{//公钥解密
	return encryptByPu(c);
}