RSA 公钥密码实验1

RSA 公钥密码实验1

// RSA公钥密码.cpp : 定义控制台应用程序的入口点。//#include "stdafx.h"#include<windows.h>#include <iostream>#include <vector>#include <string.h>using namespace std;//n大于aint Euclid(int a, int n){    int x, y, r;    x = n; y = a;    for (int i = 0;;){        if (y == 0)            return x;        if (y == 1)            return y;        r = x%y;        x = y;        y = r;    }}//利用扩展的EUCLID计算a mod n的乘法逆元double extenEuclid(double a, double n){    double x1 = 1, x2 = 0, x3 = n, y1 = 0, y2 = 1, y3 = a, Q;    double t1, t2, t3;    for (int i = 0;;){        if (y3 == 0){            return x3;            cout << "no reverse" << endl;        }        if (y3 == 1)            return y2;        Q = int(x3 / y3);        t1 = x1 - Q*y1;        t2 = x2 - Q*y2;        t3 = x3 - Q*y3;        x1 = y1; x2 = y2; x3 = y3;        y1 = t1; y2 = t2; y3 = t3;    }}//Miller-Rabin素性测试算法对一个给定的大数进行测试bool Rabin(int a, int n){    vector<int> b;    unsigned int N = n - 1;    for (int i = 0, j = 1;; i++){//将n-1表示成二进制形式        if (j>N)            break;        if ((N >> i) & (unsigned int)1){            b.push_back(1);            return true;        }        else{            b.push_back(0);            return false;        }        j *= 2;    }}void transfer(char cypher[], double c[]){    int m[100] = { 0 };    for (int i = 0, j = 0; cypher[j] != '\0'; i += 2){        if (cypher[j] == ' '){            m[i] = 0; m[i + 1] = 0;        }        else{            m[i] = cypher[j] - 64;            if (m[i]<10){                m[i + 1] = m[i];                m[i] = 0;            }            else{                m[i + 1] = m[i] % 10;                m[i] = m[i] / 10;            }        }        j++;    }    for (int k2 = 0; k2<2 * strlen(cypher); k2++)        cout << m[k2];    cout << endl;    //int c[100]={0};    int n, k;    for (k = 0, n = 0; k<2 * strlen(cypher); k += 4){        c[n] = m[k] * 1000 + m[k + 1] * 100 + m[k + 2] * 10 + m[k + 3];        n++;    }    for (; c[n - 1]<1000;)//最后一个数填充零,不过此例可要可不要        c[n - 1] *= 10;}double quickindex1(double a, double m, double n){//实现a^m mod n 的运算 {    vector<int>b;    unsigned int N = m;    for (int ii = 0, j = 1;; ii++){        if (j>N)            break;        if ((N >> ii)& (unsigned int)1)            b.push_back(1);        else            b.push_back(0);        j *= 2;    }    double c = 0, d = 1;    for (int i = b.size() - 1; i >= 0; i--){        c *= 2;        d = (d*d) - int((d*d) / n)*n;        if (b[i] == 1){            c += 1;            d = (d*a) - int((d*a) / n)*n;        }    }    return d;}//主函数int main(){    double c[100] = { 0 };    double a[100] = { 0 };    double b[100] = { 0 };    char cypher[] = "I LOVE THE PEOPLE'S REPUBLIC OF CHINA";//对“我爱中华人民共和国”加解密    transfer(cypher, c);//字母变数字的过程    for (int k1 = 0; c[k1] != '\0'; k1++)        cout << c[k1] << " ";//选取两个素数p=563，q=823    double n = 0, fn = 0, p = 563, q = 823, d = 0;    n = p*q; fn = (q - 1)*(p - 1);//选e与fn互素    double e;    for (e = 2; e<fn; e += 3){        if (Euclid(e, fn) == 1)            break;    }    d = extenEuclid(e, fn);    cout << endl << "密码和密钥e d and n:";    cout << e << " " << d << " " << n << endl;    //加密过程    cout << endl << "加密：";    for (int i = 0; c[i] != '\0'; i++){        a[i] = quickindex1(c[i], e, n);        cout << a[i] << " ";    }    //解密过程    cout << endl << "解密：";    for (int j = 0; a[j] != '\0'; j++){        b[j] = quickindex1(a[j], d, n);        cout << b[j] << " ";    }    cout << endl;    printf("\n");    system("pause");    return 0;}