RSA加密的简单实现【C++ Code】

原理不再细述, 下面是简单的实现,没有使用比较大的质数, 主要是用C++不想写大数…
支持对中文的加密

#include 
using namespace std;
typedef long long LL;
const int MAX_N = 1000;
wifstream wfin;
wofstream wfout;

//locale loc("zh_CN.UTF-8"); //Linux 下需要

//拓展欧几里得  已知a,b 求满足ax + by = gcd(a, b) 的一组解
int exgcd(int a, int b, int &x, int &y)
{
    if (b == 0){
        x = 1;
        y = 0;
        return a;
    }
    int ans = exgcd(b, a % b, x, y);

    int tmp = x;
    x = y;
    y = tmp - a / b * y;
    return ans;
}
// 暴力找出200 ~ MAX_N 的所有质数
void get_Prime_Number(int *Prime, int &cnt)
{
    cnt = 0;
    for (int i = 201;i < MAX_N; i+=2){
        bool flag = false;
        for (int j = 2;(j * j) <= i; j++){
            if (i % j == 0){
                flag = true;
                break;
            }
        }
        if (!flag) Prime[cnt++] = i;
    }
}
//RSA初始化
void RSA_Initialize(int &n, int &e, int &d)
{
    int Prime[MAX_N], cnt = 0;
    get_Prime_Number(Prime, cnt);
    srand((unsigned)time(NULL));
    int r1 = rand() % cnt;
    int r2 = rand() % cnt;
    int p1 = Prime[r1], p2 = Prime[r2]; // 随机取两个质数.
    n = p1 * p2; // 计算n

    int  m = (p1 - 1) * (p2 - 1);

    int y;
    // 选择一个与n互质的元素,记为e,求得模反元素d
    for (int i = 3; i < m; i += 1331){
        int gcd = exgcd(i, m, d, y);
        if (gcd == 1 && d > 0){
            e = i;
            break;
        }
    }
}
// 快速幂求 a^b % c
int Quick_Pow(int a, int b, int c)
{
    int tot = 1;
    while (b){
        if (b & 1) tot = (1LL * tot * a) % c; //可能会溢出
        a = (1LL * a * a) % c;
        b >>= 1;
    }
    return tot;
}

//RSA 加密
void RSA_Encrypt(int e, int n, wstring wstr)
{
    int len = wstr.size();
    for (int i = 0; i < len; i++){
        wfout << Quick_Pow(wstr[i], e, n) << " "; //输出密文
    }
    wfout << endl;
}

//RSA 解密
void RSA_Decrypt(int d, int n, wstring wstr)
{
    wstringstream wss(wstr);
    int x;
    while (wss >> x){
        wfout << (wchar_t)Quick_Pow(x, d, n); //输出解密后的原文对应字符
    }
    wfout << endl;
}


int main()
{
    wstring wstr;
    wfin.open("Plain_text.txt");
    wfout.open("Cipher_text.txt");
    //wfin.imbue(loc); //Linux 下需要
    int n, e, d;
    RSA_Initialize(n, e, d);
    printf("Public  Key (e, n) : (%d, %d).\n",e, n);
    printf("Private Key (d, n) : (%d, %d).\n\n",d, n);

    int Case = 0;
    while (getline(wfin, wstr)){
        printf("Line %d data is being encrypted.\n",++Case);
        RSA_Encrypt(e, n, wstr);
    }

    wfin.close();
    wfout.close();

    wfin.open("Cipher_text.txt");
    wfout.open("Decrypt_text.txt");
    //wfout.imbue(loc); //Linux 下需要

    Case = 0;
    while (getline(wfin, wstr)){
        printf("Line %d data is being decrypted.\n",++Case);
        RSA_Decrypt(d, n, wstr);
    }
    wfin.close();
    wfout.close();
}