为什么这个微小的RSA实现会产生错误的结果？

Question

我正在尝试实现一个简单的RSA加密/解密过程,我很确定我已经以正确的方式获得了方程式.虽然加密后似乎没有打印出正确的解密值.有任何想法吗？.

//test program
#include <iostream>
#include <string.h>
#include <math.h>
using namespace std;
int gcd(int a, int b);

int main(){
    char character = 'A'; //character that is to be encrypted


    int p = 7;
    int q = 5;
    int e = 0; // just initializing to 0, assigning actual e value in the 1st for loop 


    int n = p*q;
    int phi = (p-1)*(q-1);
    int d = 0; // " " 2nd for loop

    //---------------------------finding 'e' with phi. where "1 < e < phi(n)"
    for (int i=2; i < phi; i++){
        if (gcd(i,phi) == 1){ //if gcd is 1
            e = i;
            break;
        }
    }
    //----------------------------

    //---------------------------finding 'd' 

    for (int i = 2; i < phi; i++){
        int temp = (e*i)%phi;
        if (temp == 1){
            d = i;
            break;
        }
    }

    printf("n:%d , e:%d , phi:%d , d:%d \n",n,e,phi,d);
    printf("\npublic key is:[%d,%d]\n",e,n);
    printf("private key is:[%d,%d]\n",d,n);

    int m = static_cast<int>(character); //converting to a number
    printf("\nconverted character num:%d\n",m);


    //Encryption part  ie. c = m^e MOD n
    int power = pow(m,e); // m^e
    int c = power%n;      // c = m^e MOD n. ie. encrypted character
    printf("\n\nEncrypted character number:%d\n",c);

    //decryption part,  ie. m = c^d MOD n
    power = pow(c,d);
    int m2 = power%n; 
    printf("\n\ndecrypted character number:%d\n",m2);


    return 0;
}

int gcd(int a, int b){
    int r;
    if (a < 0) a = -a;
    if (b < 0) b = -b;
    if (b > a) { 
        r = b; b = a; a = r;
    }
    while (b > 0) {
        r = a % b;
        a = b;
        b = r;
    }
    return a;
}

(正在使用的素数是5和7,用于测试)

在这里,我将字符'A'转换为其数值,当然是65.当我使用c = m^e MOD n(其中m是转换值,即65)加密此值时,它给出c为25.

现在,为了扭转这个过程,我这样做了 m = c^d MOD n,这给了我m30个......这真的不正确,因为它应该是65,不是吗？

哪里出错我？

[编辑]

我的计算d是否正确？

Answer 1

加密的消息m必须小于n.您不能使用大于n的值,因为计算是以模n完成的.你的情况m=65和n=35.所以你实际上得到了正确的答案模数n,因为65 % 35 == 30.