RSA算法介绍与C实现算法

#include <stdio.h>
#include <math.h>
#include <stdlib.h> 
int length = 0 ;
bool JudgeP (int prime)             //判断是不是素数
{
    int i=0;
    long double temp=0 ;
    if (prime == 0||prime == 2)
        return false;
    else
    {
    temp =sqrt((float)prime);
    for (i=2;i<=temp;i++)
    {
        if (prime%i == 0)
                return false;       //输入的不是素数        
    }
    return true ;                    //输入的数是素数
    }
 
}
long int InputP ( )        //直到输入素数
{
    int num;
        scanf_s("%d",&num);
    while (!JudgeP(num))
    {
        printf("您输入的的不是素数，请重新输入!\n");
        scanf_s("%d",&num);
    }
    return num ;
}
int gcd(int a , int b){
    return b==0?a:gcd(b,a%b);
}
long int  CheckE (long int f_n )        //判断e是否符合要求  1<e <f_n且e 与f_n互素
{
    long int e ;
    int k ;
    printf("please enter e(1<e<f_n) :");
    scanf_s("%d",&e );
    while (e > f_n || e<= 1)                        //确定e的范围
    {
        printf("e is‘t fit ,enter again!(1<e<f_n)");
        scanf_s("%d",&e );
    }
    k =gcd(f_n,e) ;
    while (k != 1)
    {        
        printf("e with f_n relatively prime，enter again!");
        scanf_s("%d",&e);
        k =gcd(f_n,e) ;
    }
    return e ;
}
long int  CalculateD(long int  f_n ,long  int e)     //辗转相除
{
    int i , j = 1 , t1 , t2= 1 , k = 0  , m ;

    int arry_1[30] = {f_n,e} ,arry_2[30] ={0} ;
    printf(" the Calculation:\n") ;
    for (i=1 ; (arry_1[i] != 0 )&&( arry_1[i] != 1); i ++)
    {
        arry_1[i+1] =arry_1[i-1]%arry_1[i] ;
        arry_2 [i-1] = arry_1[i-1]/arry_1[i] ;
        printf(" %d = %d*%d+%d\n",arry_1[i-1],arry_1[i],arry_2[i-1],arry_1[i+1] ) ; 
    }
    t1 = 1 ;
    t2 = -arry_2[i-2] ;
    while((i -2)!= k )
    {
        m = t1 ;
        t1 = t2  ;
        if (j%2 != 0)
            t2 = (abs(m)+arry_2[i-3]*abs(t2) );
        else
            t2 = -(abs(m)+arry_2[i-3]*abs(t2) );
        
        i -- ;   
        j++ ;
    }
    
    while(t2 < 0)
    {
        t2 = f_n + t2 ;
    }
    k = t2 ;
    while(t2 = t2/f_n)
    {
        k = t2%f_n      ; 
    }
    printf("k = %d\n",k);
    
    return k ;
}
int * Dec2Bin(int e ) //转换为二进制
 {
  int i = 0 ;
 int str1[20] ,str2[20] ;

 while(e)
 {
  str1[i] = e%2 ;
  e = e/2 ;
   i++ ;
 }
 i -- ;
 printf("The binary is :");
 for (length = 0 ; i>=0 ; length ++)
 {
 str2[length] = str1[i] ;
 printf("%d",str2[length]);
 i -- ;
 }
 return str2 ;
 
 }
 int  Encrypt(int m , int e , int n)  //平方乘法
 {
     int  c =1  , i ;
    int *p =  Dec2Bin(e) ;
    
     for (i = 0  ; i < length;i ++)
     {
         c = c %n;
         c =c*c%n ;
          if (*(p+i) == 1)
         { c =c%n;
          c =c*m%n;
          }
     }
     return c ;
 }
int main(void)
{
    long int p,q ,n,f_n ,e ,d,m,c,l;
    printf("please enter p:");  //p,q输入
    p = InputP();   
    printf("please enter q ");
    q = InputP();

    n = p*q ;                    //计算n,f_n
    f_n =(p-1)*(q-1);

    e = CheckE(f_n );            //计算e
    d=CalculateD(f_n,e);        //计算d

    printf("please enter m ");
    scanf_s("%d",&m) ;
    c =Encrypt(m,e,n);
    printf("c is %d\n",c );
    l=Encrypt(c,d,n);
    printf("l is %d\n",l );
system("pause");
return 0 ;
}