The affine cipher is a substitution cipher, where a plaintext letter x is enciphered into a ciphertext letter y as follows: x y = x + (mod 26) The key for this encryption function is (, ), where 0 , 25. There are 12 possible choices for with gcd(, 26) = 1, where gcd stands for the greatest common divisor, and 26 choices for (i.e., 0, 1, 2, , 25). Thus, there are 12 26 = 312 choices for the key. The decryption is accomplished by an affine function as follows: y x = 1(y ) (mod 26), where 1 = 1 (mod 26). 1. Write an algorithm for an affine cipher. 2. Show that your proposed algorithm is correct using an informal proof (i.e., discussion). 3. Give a program corresponding to your proposed algorithm, using your favorite programming language. Your program should simulate this cipher and display the ciphertext along with the corresponding plaintext and key. The implementation of this affine cipher software should be as structured as possible. You should have a user-friendly interface showing all the steps of this cipher, including encryption and decryption.

Project 2 (Affine Cipher): The affine cipher is a substitution cipher, where a plaintext letter x is enciphered into a ciphertext letter y as follows: x y= ax + B (mod 26) The key for this encryption function is (a, b), where 0 sa, s25. There are 12 possible choices for a with ged(a, 26) = 1, where god stands for the greatest common divisor, and 26 choices for B (i.e., 0, 1, 2, ..., 25). Thus, there are 12 x 26 = 312 choices for the key. The decryption is accomplished by an affine function as follows: y x= a'(y B) (mod 26), where aa' = 1 (mod 26). 1. Write an algorithm for an affine cipher. 2. Show that your proposed algorithm is correct using an informal proof (i.e., discussion). 3. Give a program corresponding to your proposed algorithm, using your favorite programming language. Your program should simulate this cipher and display the ciphertext along with the corresponding plaintext and key. The implementation of this affine cipher software should be as structured as possible. You should have a user-friendly interface showing all the steps of this cipher, including encryption and decryption Project 2 (Affine Cipher): The affine cipher is a substitution cipher, where a plaintext letter x is enciphered into a ciphertext letter y as follows: x y= ax + B (mod 26) The key for this encryption function is (a, b), where 0 sa, s25. There are 12 possible choices for a with ged(a, 26) = 1, where god stands for the greatest common divisor, and 26 choices for B (i.e., 0, 1, 2, ..., 25). Thus, there are 12 x 26 = 312 choices for the key. The decryption is accomplished by an affine function as follows: y x= a'(y B) (mod 26), where aa' = 1 (mod 26). 1. Write an algorithm for an affine cipher. 2. Show that your proposed algorithm is correct using an informal proof (i.e., discussion). 3. Give a program corresponding to your proposed algorithm, using your favorite programming language. Your program should simulate this cipher and display the ciphertext along with the corresponding plaintext and key. The implementation of this affine cipher software should be as structured as possible. You should have a user-friendly interface showing all the steps of this cipher, including encryption and decryption