#ifndef BIGINT_H_INCLUDED
#define BIGINT_H_INCLUDED
#include <iostream>
#include <string>
#include <cstdlib>
#include <algorithm>//reverse函数所需添加的头文件
using namespace std;
/*
大整数类
*/
class BigInt
{
private:inline int compare(string s1, string s2){if(s1.size() < s2.size())return -1;else if(s1.size() > s2.size())return 1;elsereturn s1.compare(s2);}
public:bool flag;//true表示正数，false表示负数，0默认为正数string values;//保存所有位上的数字BigInt():values("0"),flag(true){};//构造函数BigInt(string str)//类型转换构造函数(默认为正整数){values = str;flag = true;}
public:friend ostream& operator << (ostream& os, const BigInt& bigInt);//重载输出操作符friend istream& operator>>(istream& is, BigInt& bigInt);//输入操作符重载BigInt operator+(const BigInt& rhs);//加法操作重载BigInt operator-(const BigInt& rhs);//减法操作重载BigInt operator*(const BigInt& rhs);//乘法操作重载BigInt operator/(const BigInt& rhs);//除法操作重载BigInt operator%(const BigInt& rhs);//求余操作重载
};
/*
重载流提取运算符'>>'，输出一个整数
*/
ostream& operator << (ostream& os, const BigInt& bigInt)
{if (!bigInt.flag){os << '-';}os << bigInt.values;return os;
}
/*
重载流插入运算符'>>'，输入一个正整数
*/
istream& operator >> (istream& is, BigInt& bigInt)
{string str;is >> str;bigInt.values = str;bigInt.flag = true;return is;
}
/*
两个正整数相加
*/
BigInt BigInt::operator+(const BigInt& rhs)
{BigInt ret;ret.flag = true;//正整数相加恒为正数string lvalues(values), rvalues(rhs.values);//处理特殊情况if (lvalues == "0"){ret.values = rvalues;return ret;}if (rvalues == "0"){ret.values = lvalues;return ret;}//调整s1与s2的长度unsigned int i, lsize, rsize;lsize = lvalues.size();rsize = rvalues.size();if (lsize < rsize){for (i = 0; i < rsize - lsize; i++)//在lvalues左边补零{lvalues = "0" + lvalues;}}else{for (i = 0; i < lsize - rsize; i++)//在rvalues左边补零{rvalues = "0" + rvalues;}}//处理本质情况int n1, n2;n2 = 0;lsize = lvalues.size();string res = "";reverse(lvalues.begin(), lvalues.end());//颠倒字符串，以方便从低位算起计算reverse(rvalues.begin(), rvalues.end());for (i = 0; i < lsize; i++){n1 = (lvalues[i] - '0' + rvalues[i] - '0' + n2) % 10;//n1代表当前位的值n2 = (lvalues[i] - '0' + rvalues[i] - '0' + n2) / 10;//n2代表进位res = res + char(n1 + '0');}if (n2 == 1){res = res + "1";}reverse(res.begin(), res.end());ret.values = res;return ret;
}
/*
两个整数相减
*/
BigInt BigInt::operator-(const BigInt& rhs)
{BigInt ret;string lvalues(values), rvalues(rhs.values);//负数减负数if(flag==false&&rhs.flag==false){string tmp = lvalues;lvalues = rvalues;rvalues = tmp;}//负数减正数if(flag==false&&rhs.flag==true){BigInt res(lvalues);ret=res+rhs;ret.flag = false;return ret;}if(flag==true&&rhs.flag==false){BigInt rel(lvalues),res(rhs.values);ret=rel+res;ret.flag = true;return ret;}//处理特殊情况if (rvalues == "0"){ret.values = lvalues;ret.flag = true;return ret;}if (lvalues == "0"){ret.values = rvalues;ret.flag = false;return ret;}//调整s1与s2的长度unsigned int i, lsize, rsize;lsize = lvalues.size();rsize = rvalues.size();if (lsize < rsize){for (i = 0; i < rsize - lsize; i++)//在lvalues左边补零{lvalues = "0" + lvalues;}}else{for (i = 0; i < lsize - rsize; i++)//在rvalues左边补零{rvalues = "0" + rvalues;}}//调整使‘-’号前边的数大于后边的数int t = lvalues.compare(rvalues);//相等返回0，str1<str2返回负数，str1>str2返回正数if (t < 0){ret.flag = false;string tmp = lvalues;lvalues = rvalues;rvalues = tmp;}else if (t == 0){ret.values = "0";ret.flag = true;return ret;}else{ret.flag = true;}//处理本质情况unsigned int j;lsize = lvalues.size();string res = "";reverse(lvalues.begin(), lvalues.end());//颠倒字符串，以方便从低位算起计算reverse(rvalues.begin(), rvalues.end());for (i = 0; i < lsize; i++){if (lvalues[i] < rvalues[i])//不足，向前借一维{j = 1;while(lvalues[i+j] == '0'){lvalues[i+j] = '9';j++;}lvalues[i+j] -= 1;res = res + char(lvalues[i] + ':' - rvalues[i]);}else{res = res + char(lvalues[i] - rvalues[i] + '0');}}reverse(res.begin(), res.end());res.erase(0, res.find_first_not_of('0'));//去掉前导零ret.values = res;return ret;
}/*
两个整数相乘
*/
BigInt BigInt::operator*(const BigInt& rhs)
{BigInt ret;string lvalues(values), rvalues(rhs.values);//处理0或结果正负if (lvalues == "0" || rvalues == "0"){ret.values = "0";ret.flag = true;return ret;}if(flag==false||rhs.flag==false){ret.flag=false;}//处理特殊情况unsigned int lsize, rsize;lsize = lvalues.size();rsize = rvalues.size();string temp;BigInt res, itemp;//让lvalues的长度最长if (lvalues < rvalues){temp = lvalues;lvalues = rvalues;rvalues = temp;lsize = lvalues.size();rsize = rvalues.size();}//处理本质情况int i, j, n1, n2, n3, t;reverse(lvalues.begin(), lvalues.end());//颠倒字符串reverse(rvalues.begin(), rvalues.end());for (i = 0; i < rsize; i++){temp = "";n1 = n2 = n3 = 0;for (j = 0; j < i; j++){temp = temp + "0";}n3 = rvalues[i] - '0';for (j = 0; j < lsize; j++){t = (n3*(lvalues[j] - '0') + n2);n1 = t % 10;//n1记录当前位置的值n2 = t / 10;//n2记录进位的值temp = temp + char(n1 + '0');}if (n2){temp = temp + char(n2 + '0');}reverse(temp.begin(), temp.end());itemp.values = temp;res = res + itemp;}ret.values = res.values;return ret;
}
/*
两个正整数相除
*/
BigInt BigInt::operator/(const BigInt& rhs)
{BigInt ret;string lvalues(values), rvalues(rhs.values);string quotient;string temp;//处理特殊情况if(rvalues == "0"){ret.values = "error";//输出错误ret.flag = true;return ret;}if(lvalues == "0"){ret.values = "0";ret.flag = true;return ret;}if(compare(lvalues, rvalues) < 0){ret.values = "0";ret.flag = true;return ret;}else if(compare(lvalues, rvalues) == 0){ret.values = "1";ret.flag = true;return ret;}else{//处理本质情况unsigned int lsize, rsize;lsize = lvalues.size();rsize = rvalues.size();int i;if(rsize > 1) temp.append(lvalues, 0, rsize-1);for(i = rsize - 1; i < lsize; i++){temp = temp + lvalues[i];//试商for(char c = '9'; c >= '0'; c--){BigInt t = (BigInt)rvalues * (BigInt)string(1, c);BigInt s = (BigInt)temp - t;if(s.flag == true){temp = s.values;quotient = quotient + c;break;}}}}//去除前导零quotient.erase(0, quotient.find_first_not_of('0'));ret.values = quotient;ret.flag = true;return ret;
}
/*
两个正整数取余
*/
BigInt BigInt::operator%(const BigInt& rhs)
{BigInt ret,kj(values),ki(rhs.values);string lvalues(values), rvalues(rhs.values);string quotient;string temp;//处理特殊情况if(rvalues == "0"){ret.values = "error";//输出错误ret.flag = true;return ret;}if(lvalues == "0"){ret.values = "0";ret.flag = true;return ret;}if(compare(lvalues, rvalues) < 0){if(flag==false){ret.values=(ki-kj).values;ret.flag = true;return ret;}else{ret.values = lvalues;ret.flag = true;return ret;}}else if(compare(lvalues, rvalues) == 0){ret.values = "0";ret.flag = true;return ret;}else{//处理本质情况unsigned int lsize, rsize;lsize = lvalues.size();rsize = rvalues.size();int i;if(rsize > 1) temp.append(lvalues, 0, rsize-1);for(i = rsize - 1; i < lsize; i++){if(temp=="0"){temp=lvalues[i];}else{temp = temp + lvalues[i];}//试商for(char c = '9'; c >= '0'; c--){BigInt t = (BigInt)rvalues * (BigInt)string(1, c);BigInt s = (BigInt)temp - t;if(s.flag == true){//cout<<s.values<<endl;temp = s.values;quotient = quotient + c;break;}}}}//去除前导零quotient.erase(0, quotient.find_first_not_of('0'));ret.values = temp;ret.flag = true;return ret;
}
/*
一个大整数和一个小整数的取余int divMod(string ch,int num)
{int s=0;for(int i=0;ch[i]!='\0';i++)s=(s*10+ch[i]-'0')%num;return s;
}*//*
欧几里德求GCD
*/
BigInt gcd(BigInt a,BigInt b)
{BigInt stemp;//cout<<a<<endl;//cout<<b<<endl;if((a-b).flag==false)//判断大小{stemp.values=a.values;a.values=b.values;b.values=stemp.values;}if(b.values=="0") return a;else return gcd(b,a%b);
}
/*
快速幂
*/
BigInt fast(BigInt a,BigInt b)
{BigInt aa=a,t("1"),k("2");//   int b2=atoi(b1[lsize-1].c_str());while(b.values!="0"){if((b%k).values!="0"){t=t*aa;}aa=aa*aa;b=b/k;}return t;
}
/*
快速幂模
*/
BigInt mod_fast(BigInt a,BigInt b,BigInt p)
{BigInt aa=a,t("1"),k("2");//   int b2=atoi(b1[lsize-1].c_str());while(b.values!="0"){if((b%k).values!="0"){t=(t%p)*(aa%p)%p;}aa=(aa%p)*(aa%p)%p;b=b/k;}return t%p;
}/*
扩展欧几里德实现乘法逆
*/
BigInt extgcd(BigInt a, BigInt b, BigInt& x, BigInt& y)
{BigInt d(a.values);if(b.values != "0"){d = extgcd(b, a % b, y, x);y = y-(a / b) * x;//   cout<<"a:"<<a<<endl;//  cout<<"b:"<<b<<endl;//  cout<<"x:"<<x<<endl;//  cout<<"y:"<<y<<endl<<endl<<endl;}else {x.values = "1";y.values = "0";}return d;
}
BigInt mod_inverse(BigInt a, BigInt m)
{BigInt x, y;extgcd(a, m, x, y);if(x.flag==false){x.flag=true;x=m-x;}return (m + x % m) % m;
}#endif // BIGINT_H_INCLUDED

main.cpp

#include"BigInt.h"
int main()
{BigInt p("965020263285415169225506842409"),q("415924872698612520126277439911"),N,n,a("1"),b("2");BigInt d,e;BigInt m,s;N=p*q;s=gcd(p-a,q-a);n=s*((p-a)/s)*((q-a)/s);//cout<<s<<endl;//cout<<(p-a)*(q-a)<<endl;cout<<"n: "<<n<<endl;cout<<"N: "<<N<<endl;while(1){cout<<"请输入整数e："<<endl;cin>>e;cout<<"gcd(e,n): "<<gcd(e,n)<<endl;if(gcd(e,n).values=="1"&&(n-e).flag==true){d=mod_inverse(e,n);cout<<"d："<<d<<endl;cout<<"请输入需要加密的字符："<<endl;cin>>m;BigInt t;cout<<"加密："<<mod_fast(m,e,N)<<endl;cout<<"解密："<<mod_fast(mod_fast(m,e,N),d,N)<<endl;}else{cout<<"d和N非互素或者非1<e<n！"<<endl;}}return 0;
}

三、运行结果