AffineCipher

AffineCipher#

The AffineCipher class implements the Affine cipher, a type of monoalphabetic substitution cipher. The Affine cipher is a combination of the Additive and Multiplicative ciphers, having two keys: one for addition and one for multiplication.

class AffineCipher(a: int, b: int)#

Creates a new AffineCipher instance with the specified keys.

Parameters:

  • a (int) – The multiplicative key. Must be coprime with 26.

  • b (int) – The additive key.

Attention

AffineCipher is a basic symmetric cipher, which should be used ONLY for educational purposes, and NOT in production. Proceed accordingly.

Introduction#

The Affine cipher is a type of monoalphabetic substitution cipher. It is a combination of the Additive and Multiplicative ciphers, having two keys: one for addition and one for multiplication. Each character in the plaintext is shifted by a fixed number of positions based on the given keys, first by multiplication and then by addition. This creates a more complex encryption than either multiplicative or additive ciphers alone.

Mathematical Details#

In the Affine cipher:

  • Each letter in the alphabet is mapped to a numeric value.

  • The encryption formula is:
    \[c = (a \times p + b) \mod 26\]
    where:

    • \(c\) is the ciphertext letter value

    • \(p\) is the plaintext letter value

    • \(a\) is the multiplicative key (must be coprime with 26)

    • \(b\) is the additive key

  • The decryption formula is:
    \[p = a^{-1}(c - b) \bmod 26\]
    where

    • \(a^{-1}\) is the modular multiplicative inverse of \(a\) modulo 26.

Note

The keys \(a\) and \(b\) must be coprime with 26 for the Affine cipher to work correctly. If the keys are not coprime, the decryption process may not be possible.

Usage#

# Example usage of Affine Cipher to encrypt and decrypt a message
from cryptosystems import AffineCipher
cipher = AffineCipher(5, 8)
ciphertext = cipher.encrypt("Hello World")
print(ciphertext) # 'Rclla Oaplx'
plaintext = cipher.decrypt(ciphertext)
print(plaintext) # 'Hello World'

Methods#

encrypt(plaintext: str) → str#

Encrypts the given plaintext using the Affine cipher.

Parameters:

plaintext (str) – The plaintext message to be encrypted.

Returns:

The encrypted ciphertext.

Return type:

str

decrypt(ciphertext: str) → str#

Decrypts the given ciphertext using the Affine cipher.

Parameters:

ciphertext (str) – The ciphertext message to be decrypted.

Returns:

The decrypted plaintext.

Return type:

str

Notes#

  • Multiplicative Inverse: The multiplicative key \(a\) must have a multiplicative inverse modulo 26 for decryption to work correctly (ie, \(a\) should be coprime with 26). This is because the decryption formula involves multiplying by the inverse of the key modulo 26. If the key does not have a multiplicative inverse, decryption will not be possible.

  • Limitations: The Affine cipher can only encrypt and decrypt letters of the alphabet. It does not handle spaces, punctuation, or other characters. The keys \(a\) and \(b\) must be integers between 0 and 25.

  • Security: The Affine cipher is relatively weak compared to modern encryption methods and can be easily broken using frequency analysis or brute force methods.

  • Application: Suitable for educational purposes, but not secure for practical use in modern cryptography.