Vernam Cipher in Cryptography

Vernam Cipher is a method of encrypting alphabetic text. It is one of the Substitution techniques for converting plain text into cipher text. In this mechanism, we assign a number to each character of the Plain-Text, like (a = 0, b = 1, c = 2, … z = 25). 
Method to take key: In the Vernam cipher algorithm, we take a key to encrypt the plain text whose length should be equal to the length of the plain text. 

Encryption Algorithm

• Assign a number to each character of the plain text and the key according to alphabetical order. 
• Bitwise XOR both the number (Corresponding plain-text character number and Key character number). 
• Subtract the number from 26 if the resulting number is greater than or equal to 26, if it isn’t then leave it.

Example 1:

Plain-Text: O A K
Key: S O N

O ==> 14 = 0 1 1 1 0
S ==> 18 = 1 0 0 1 0
Bitwise XOR Result: 1 1 1 0 0 = 28

Since the resulting number is greater than 26, subtract 26 from it.  Then convert the Cipher-Text character number to the Cipher-Text character.

28 - 26 = 2 ==> C
CIPHER-TEXT: C

Similarly, do the same for the other corresponding characters,

PT: O  A  K
NO: 14 00 10
KEY: S  O  N
NO:  18 14 13

New Cipher-Text is after getting the corresponding character from the resulting number. 

CT-NO: 02 14 07
CT:    C  O  H

Example 2:

Plain-Text: RAMSWARUPK
Key: RANCHOBABA 

Now according to our encryption algorithm, we assign a number to each character of our plain text and key.

PT:   R  A  M   S   W   A  R   U   P   K
NO:   17 0  12  18  22  0  17  20  15  10
KEY:  R   A  N   C  H  O   B  A  B  A  
NO:   17  0  13  2  7  14  1  0  1  0 

Now Bitwise XOR the number of Plain-Text and Key and after doing the XOR operation and subtraction operation (if required), we will get the corresponding Cipher-Text character number. 

CT-NO: 0  0  1  16  17  14  16  20  14  10 

Since there are no numbers that are greater than or equal to 26 we do not have to subtract 26 from any of them.

New Cipher-Text is after getting the corresponding character from the number. 

CIPHER-TEXT: A  A  B  Q  R  O  Q  U  O  K 

Note: For the Decryption apply the just reverse process of encryption.

Example

let’s implement the Vernam Cipher in Python:

Python

import random

def generate_key(plaintext_length):
    key = ''.join(random.choice('ABCDEFGHIJKLMNOPQRSTUVWXYZ') for _ in range(plaintext_length))
    return key

def encrypt(plaintext, key):
    ciphertext = ''.join(chr(ord(p) ^ ord(k)) for p, k in zip(plaintext, key))
    return ciphertext

def decrypt(ciphertext, key):
    decrypted_text = ''.join(chr(ord(c) ^ ord(k)) for c, k in zip(ciphertext, key))
    return decrypted_text

# Example usage
if __name__ == "__main__":
    plaintext = "HELLO"
    key = generate_key(len(plaintext))

    print("Plaintext:", plaintext)
    print("Key:", key)

    ciphertext = encrypt(plaintext, key)
    print("Ciphertext:", ciphertext)

    decrypted_text = decrypt(ciphertext, key)
    print("Decrypted Text:", decrypted_text)

Explanation

• The ‘generate_key()' function creates a random key of the same length as the plaintext. For this example, we are using uppercase letters from ‘A’ to ‘Z’ for simplicity, but in practice, any binary data or random characters should be used.
• The ‘encrypt()' function takes the plaintext and the key as input and performs the encryption using bitwise XOR (^) operation. Each character in the plaintext is combined with the corresponding character in the key using XOR, producing the ciphertext.
• The ‘decrypt()' function performs the decryption in the same way as the encryption. By XORing the ciphertext with the key, it retrieves the original plaintext.
• In the example usage section, we define a sample plaintext (“HELLO”) and generate a random key using ‘generate_key()'.
• We then encrypt the plaintext using the Vernam Cipher and the generated key and print the resulting ciphertext.
• Finally, we decrypt the ciphertext back to the original plaintext using the same key and print the decrypted text.

Output:

Plaintext: HELLO
Key: OCVHW
Ciphertext: iRTZP
Decrypted Text: HELLO

In this example, the Vernam Cipher successfully encrypts and decrypts the plaintext, demonstrating the correctness of the algorithm. However, it is essential to note that the one-time pad requires a truly random and secret key, which must be exchanged securely between the sender and receiver. Additionally, the key should never be reused, or else the security of the cipher is compromised.

Advantages of the Vernam Cipher

• Perfect Secrecy: With a truly random and unpredictable key of the same length as the message, the charnum cipher provides perfect confidentiality. This means that, in theory, an encrypted message provides no information about the original message.

• Unbreakable with a Truly Random Key: In theory, if the key stream were truly random and used only once (hence the name “one-time pad”), the Vernam cipher would be unbreakable. The key stream is the same length as the message, and the likelihood of any decryption of the ciphertext is equal.

• No Pattern Recognition: Unlike other encryption algorithms, the Vernam cipher does not produce a pattern of ciphertext that can be used to break the code. Each character of the ciphertext is encrypted independently.

• Simple Algorithm: Both the encryption and decryption algorithms are simple and involve a bitwise XOR operation. This simplicity can be an advantage in some situations.

Disadvantages of the Vernam Cipher

• Key Management: The main practical challenge of Vernam ciphers is the management of truly random private keys. The key must be the same length as the message, and a new key must be generated for each message. Distributing keys securely is not a trivial problem.

• Key Reuse Compromises Security: If keys are reused, the security of the Vernum cipher is compromised. If an attacker intercepts two ciphertexts encrypted with the same key, he can use XOR to cancel the key stream and reveal the XOR of the two plaintexts. This could potentially leak information about the original message.

• Key Storage and Transmission: Transmitting and storing keys securely is a major challenge. Once an adversary has access to the key, he or she can decrypt the ciphertext.

• Practicality and Efficiency: Vernam ciphers are often impractical for large-scale use due to the challenges of generating and securely distributing one-time pads. It is typically used only in scenarios where complete confidentiality is most important.

• Key Length Equal to Message Length: The key must be at least as long as the message, which can be inefficient for long messages. This is especially true when compared to modern symmetric key cryptography, which uses shorter keys.

For the implementation please refer to this article: Implementation of Vernam Cipher or One Time Pad Algorithm