Abstract Algebra chapter 7

7.7:Encrypt each of the following RSA messages x so that x is divided into blocks of integers of length 2; that is, if x = 142528,encode 14,25,and 28 separately.

RSA加密方法：y=x^E mod n

计算时可采用重复乘方法（repeated squares）

 1 #include<iostream>
 2 #include<algorithm>
 3 #include<cstring>
 4 #include<string>
 5 #include<cmath>
 6 #include<cstdio>
 7 using namespace std;
 8 
 9 int binary[20];
10 double mod[20];
11 
12 int main()
13 {
14     int n,E,x;
15     while ((cin>>n>>E>>x)&&n&&E&&x)
16     {
17         memset(binary,0,sizeof(binary));
18         memset(mod,0,sizeof(mod));
19         for (int i=19;i>=0;i--)
20         {
21             if (1<<i <= E) 
22             {
23                 binary[i]=1;
24                 E-= (1<<i);
25             }
26             if (E<=0.001) break;
27         }
28         mod[0]=x%n;
29         for (int i=1;i<sizeof(binary);i++)
30         {
31             mod[i]=fmod(pow(mod[i-1],2),n);
32         }
33         double temp = 1;
34         for (int i=0;i<sizeof(binary);i++)
35         {
36             if (binary[i]==1) 
37             {
38                 temp = fmod(fmod(temp,n)*fmod(mod[i],n),n);
39             }
40         }
41         cout<<temp<<endl;
42     }
43     return 0;
44 }
45

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