Introduction to Cryptography Lab 3

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Experiment 3: Affine Cipher

Aim: To study and implement the Affine Cipher.

Learning Outcomes:

1. Understand steps of the Affine Cipher.
2. Implement the Affine Cipher.
3. Understand variations of the Affine Cipher and its effectiveness.

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Theory:

The Affine Cipher is a type of monoalphabetic substitution cipher. Each letter in an alphabet is mapped to its numeric equivalent, encrypted using a mathematical function, and then converted back to a letter.

The formula used is:

• Encryption:

$E(x)=(ax+b)modmE(x)=(ax+b)\mathrm{mod}m$

• Decryption:

$D(x)=a-1(x-b)modmD(x)=a^{-1}(x-b)\mathrm{mod}m$

Where:

• m = size of the alphabet (typically 26 for the English alphabet)
• a and b are the keys.
• a^{-1} is the modular inverse of a modulo m.

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Encryption Example:

Given a = 17 and b = 20:

• Plaintext: “TWENTYFIFTEEN” → Corresponding numbers: 19, 22, 4, 13, 19, 24, 5, 8, 5, 4, 19, 5, 4, 4, 13
• Encrypted Text: Using the formula (ax+b)mod  26(ax + b) \mod 26, the encrypted text will be: “FFKHFMBABFKKH”.

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Code Explanation:

The code provides functions to:

• Encrypt: Convert plaintext to its numeric equivalent, apply the affine formula, and convert it back to letters.
• Decrypt: Reverse the encryption by using the modular inverse of a.

from sympy import isprime
 
# Function to find modular inverse of 'a' modulo 26
def mod_inverse(a, m):
    for i in range(1, m):
        if (a * i) % m == 1:
            return i
    return 0  # Return None if no inverse exists
 
# Encrypt function
def encrypt(plaintext, a, b):
    encrypted_text = ""
    for char in plaintext:
        if char.isalpha():
            is_upper = char.isupper()
            x = ord(char.upper()) - ord('A')
            encrypted_char = (a * x + b) % 26
            encrypted_text += chr(encrypted_char + (ord('A') if is_upper else ord('a')))
        else:
            encrypted_text += char
    return encrypted_text
 
# Decrypt function
def decrypt(ciphertext, a, b):
    decrypted_text = ""
    a_inv = mod_inverse(a, 26)
    if a_inv == 0:
        return "Inverse does not exist, decryption impossible."
    for char in ciphertext:
        if char.isalpha():
            is_upper = char.isupper()
            y = ord(char.upper()) - ord('A')
            decrypted_char = (a_inv * (y - b)) % 26
            decrypted_text += chr(decrypted_char + (ord('A') if is_upper else ord('a')))
        else:
            decrypted_text += char
    return decrypted_text
 
# Sample input
plaintext = input("Enter the plaintext: ")
while True:
    a = int(input("Enter a value for 'a' (make sure it's prime): "))
    if isprime(a):
        break
    else:
        print("Invalid input. 'a' must be a prime number.")
b = int(input("Enter a value for 'b': "))
encrypted = encrypt(plaintext, a, b)
print("Encrypted Text: " + encrypted)
decrypted = decrypt(encrypted, a, b)
print("Decrypted Text: " + decrypted)

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Output:

• Input:

  Enter the plaintext: TWENTYFIFTEEN
  Enter a value for 'a' (make sure it's prime): 17
  Enter a value for 'b': 20
  

• Encrypted Text:

  Encrypted Text: FFKHFMBABFKKH
  

• Decrypted Text:

  Decrypted Text: TWENTYFIFTEEN
  

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Questions:

1. If the plaintext “HELLO” encrypts to “AXEEH”, determine the keys a and b?

   • To solve this, you would need to set up a system of linear equations based on the encryption formula and solve for a and b using the known ciphertext and plaintext.

2. What are the common types of attacks on the Affine Cipher?

   • Frequency Analysis: Since it’s a substitution cipher, frequency analysis can help deduce the keys.
   • Brute Force: Trying all possible values for a and b since a must be coprime with 26.

3. What is a Three Pass Protocol? How does it help in the Affine Cipher?

   • A Three Pass Protocol involves the encryption and decryption of a message in three stages, ensuring that even if an attacker intercepts the message, they cannot easily decrypt it. It adds an extra layer of security.

4. Compare Vigenere Cipher and Affine Cipher w.r.t the following paper:

   • Vigenère Cipher is polyalphabetic (uses multiple cipher alphabets), whereas Affine Cipher is monoalphabetic (uses a single alphabet).
   • Vigenère Cipher is considered more secure than Affine Cipher because of the use of a key phrase that changes the cipher alphabet for each letter in the plaintext.

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