PLEASE ANSWER IN C PROGRAMMING

1 Affine Cipher (70 points)

The Affine cipher is a cryptographic method for encrypting text such that it becomes unreadable to a party without access to the cryptographic key. The encryption and decryption operations are simple shifts of the alphabet letters in a cyclic fashion. Mathematically, for a key k = (, ), the encryption and decryption are defined as:

Encryption: c=(x+) mod26,126and126 Decryption:x=1(c) mod26.

Here, 1 is a multiplicative inverse of in the group of integers modulo 26. To find the multiplicative inverse of one needs to find x such that

x=1 mod26. (1) A simple way of finding the inverse of is to consider all numbers from 1 to 25 and see which one satisfies equation

(1).

To illustrate the use of the Affine cipher, consider the encryption of defend the east wall of the castle with keyk = (,) = (5,7). The first letter d is mapped to number 3 (alphabet letters are numbered from 0 to 25). Inserting 3 to the encryption functions yields

c=53+7 mod26=22 mod26=22

which corresponds to letter w. Applying the same process for ever letter, the plaintext sentence is translated to wbgbuw yqb bhty nhkk zg yqb rhtykb . Now to decode, we first need to find the inverse of 5 modulo 26. Scanning every number from 1 to 25, we observe that

521 mod26=1, so the inverse of 5 is 21. Using 21 for decrypting the first letter w (or 22) becomes

21(227) mod26=3,

which reverses back to letter d. NOTE: The modulo operation for negative numbers is different from the % arithmetic operator in C.

Write a C program that decrypts a file named encrypted.txt and places the decryption output to a file called de- crypted.txt. A file encrypted with k = (5, 7) is provided with the assignment. You can use it to test your decryption function. You will know when you have succeeded because the text becomes readable. In your program

1

Ask the user to enter the decryption key. Repeat the request until the right key is entered. Display a message when file decryption is over. Ask the user to enter a key to re-encrypt the file. Re-encrypt file decrypted.txt and store it at encrypted.txt Display a message when file encryption is over.

Only alphabet letters (uppercase/lowercase) must be encrypted. The remaining characters (question marks, periods, etc. must remain intact).

Your code must be modular. Use the following function prototypes for encryption and decryption:

char encryptFun(int a, int b, char letter); // This function receives as input the key components (,) and the plaintext letter and returns the encrypted letter.

char decryptFun(int a, int b, char letter); // This function receives as input the key components (,) and an encrypted letter and returns the decrypted letter.

int inverse(int x); // This function as input receives an int x and returns the multiplicative inverse of x modulo 26.

You are also given the following function that correctly implements the modulo operation for both positive and negative numbers

int mod (int x, int y){while(x < 0){

x+ = y;}

return x%y;}