Do the Untwist

 

Do the Untwist

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others) Total Submission(s): 982    Accepted Submission(s): 638

Problem Description

Cryptography deals with methods of secret communication that transform a message (the plaintext) into a disguised form (the ciphertext) so that no one seeing the ciphertext will be able to figure out the plaintext except the intended recipient. Transforming the plaintext to the ciphertext is encryption; transforming the ciphertext to the plaintext is decryption. Twisting is a simple encryption method that requires that the sender and recipient both agree on a secret key k, which is a positive integer. The twisting method uses four arrays: plaintext and ciphertext are arrays of characters, and plaincode and ciphercode are arrays of integers. All arrays are of length n, where n is the length of the message to be encrypted. Arrays are origin zero, so the elements are numbered from 0 to n - 1. For this problem all messages will contain only lowercase letters, the period, and the underscore (representing a space). The message to be encrypted is stored in plaintext. Given a key k, the encryption method works as follows. First convert the letters in plaintext to integer codes in plaincode according to the following rule: '_' = 0, 'a' = 1, 'b' = 2, ..., 'z' = 26, and '.' = 27. Next, convert each code in plaincode to an encrypted code in ciphercode according to the following formula: for all i from 0 to n - 1, ciphercode[i] = (plaincode[ki mod n] - i) mod 28.

(Here x mod y is the positive remainder when x is divided by y. For example, 3 mod 7 = 3, 22 mod 8 = 6, and -1 mod 28 = 27. You can use the C '%' operator or Pascal 'mod' operator to compute this as long as you add y if the result is negative.) Finally, convert the codes in ciphercode back to letters in ciphertext according to the rule listed above. The final twisted message is in ciphertext. Twisting the message cat using the key 5 yields the following:

 

Array	0	1	2
plaintext	'c'	'a'	't'
plaincode	3	1	20
ciphercode	3	19	27
ciphertext	'c'	's'	'.'

  Your task is to write a program that can untwist messages, i.e., convert the ciphertext back to the original plaintext given the key k. For example, given the key 5 and ciphertext 'cs.', your program must output the plaintext 'cat'. The input file contains one or more test cases, followed by a line containing only the number 0 that signals the end of the file. Each test case is on a line by itself and consists of the key k, a space, and then a twisted message containing at least one and at most 70 characters. The key k will be a positive integer not greater than 300. For each test case, output the untwisted message on a line by itself. Note: you can assume that untwisting a message always yields a unique result. (For those of you with some knowledge of basic number theory or abstract algebra, this will be the case provided that the greatest common divisor of the key k and length n is 1, which it will be for all test cases.)

Sample Input

5 cs.
101 thqqxw.lui.qswer
3 b_ylxmhzjsys.virpbkr
0

Sample Output

cat
this_is_a_secret
beware._dogs_barking

题目链接：http://acm.hdu.edu.cn/showproblem.php?pid=1129

题目意思很简单，倒推明文；题目给出的例子是：【cat --> cs.】  
第一步：把cat转化成对应数字 plaincode，文中有提到，_=0,  .=27,  a=1 ...【cat --> 3,1,20】  
第二步：利用公式将 plaincode转化成密文对应的数字 ciphercode【3,1,20 --> 3,19,27】  
第三步：将 ciphercode转化成密文 【3,19,27 --> cs.】  
题目给出密匙k和密文，要求求出明文;   此题最关键的是公式的转化! 
公式如下：  
明文-->密文：ciphercode[i] = (plaincode[ki mod n] - i) mod 28.   
密文-->明文：plaincode[ki mod n] = (ciphercode[i] + i) mod 28. 

 

#include<stdio.h>
#include<string.h>
int main()
{
    char s[100],b[100];
    int i,j,n,k;
    while(scanf("%d",&k),k)
    {
        scanf("%s",s);
        n=strlen(s);
        for(i=0;i<n;i++)
        {
            if(s[i]=='_')
                s[i]=0;
            else if(s[i]=='.')
                s[i]=27;
            else
                s[i]=s[i]-'a'+1;                
        } 
        for(i=0;i<n;i++)
        {
            b[k*i%n]=(s[i]+i)%28;
        }
        for(i=0;i<n;i++)
        {
            if(b[i]==27)
                printf(".");
            else if(b[i]==0)
                printf("_");
            else
                printf("%c",b[i]+'a'-1);
        }
        printf("
");    
    }
    return 0;
}