ciphers.decrypt_caesar_with_chi_squared

Functions

decrypt_caesar_with_chi_squared(→ tuple[int, float, str])

Basic Usage

Module Contents

ciphers.decrypt_caesar_with_chi_squared.decrypt_caesar_with_chi_squared(ciphertext: str, cipher_alphabet: list[str] | None = None, frequencies_dict: dict[str, float] | None = None, case_sensitive: bool = False) → tuple[int, float, str]

Basic Usage

Arguments:

  • ciphertext (str): the text to decode (encoded with the caesar cipher)

Optional Arguments:

  • cipher_alphabet (list): the alphabet used for the cipher (each letter is a string separated by commas)

  • frequencies_dict (dict): a dictionary of word frequencies where keys are the letters and values are a percentage representation of the frequency as a decimal/float

  • case_sensitive (bool): a boolean value: True if the case matters during decryption, False if it doesn’t

Returns:

  • A tuple in the form of: (most_likely_cipher, most_likely_cipher_chi_squared_value, decoded_most_likely_cipher)

    where…

    • most_likely_cipher is an integer representing the shift of the smallest chi-squared statistic (most likely key)

    • most_likely_cipher_chi_squared_value is a float representing the chi-squared statistic of the most likely shift

    • decoded_most_likely_cipher is a string with the decoded cipher (decoded by the most_likely_cipher key)

The Chi-squared test

The caesar cipher

The caesar cipher is a very insecure encryption algorithm, however it has been used since Julius Caesar. The cipher is a simple substitution cipher where each character in the plain text is replaced by a character in the alphabet a certain number of characters after the original character. The number of characters away is called the shift or key. For example:

Plain text: hello
Key: 1
Cipher text: ifmmp
(each letter in hello has been shifted one to the right in the eng. alphabet)

As you can imagine, this doesn’t provide lots of security. In fact decrypting ciphertext by brute-force is extremely easy even by hand. However one way to do that is the chi-squared test.

The chi-squared test

Each letter in the english alphabet has a frequency, or the amount of times it shows up compared to other letters (usually expressed as a decimal representing the percentage likelihood). The most common letter in the english language is e with a frequency of 0.11162 or 11.162%. The test is completed in the following fashion.

  1. The ciphertext is decoded in a brute force way (every combination of the 26 possible combinations)

  2. For every combination, for each letter in the combination, the average amount of times the letter should appear the message is calculated by multiplying the total number of characters by the frequency of the letter.

    For example:
    In a message of 100 characters, e should appear around 11.162 times.

  3. Then, to calculate the margin of error (the amount of times the letter SHOULD appear with the amount of times the letter DOES appear), we use the chi-squared test. The following formula is used:

    Let:

    • n be the number of times the letter actually appears

    • p be the predicted value of the number of times the letter should appear (see item 2)

    • let v be the chi-squared test result (referred to here as chi-squared value/statistic)

    (n - p)^2
--------- = v
   p

  4. Each chi squared value for each letter is then added up to the total. The total is the chi-squared statistic for that encryption key.

  5. The encryption key with the lowest chi-squared value is the most likely to be the decoded answer.

Further Reading

Doctests

>>> decrypt_caesar_with_chi_squared(
...    'dof pz aol jhlzhy jpwoly zv wvwbshy? pa pz avv lhzf av jyhjr!'
... )  
(7, 3129.228005747531,
 'why is the caesar cipher so popular? it is too easy to crack!')

>>> decrypt_caesar_with_chi_squared('crybd cdbsxq')
(10, 233.35343938980898, 'short string')

>>> decrypt_caesar_with_chi_squared('Crybd Cdbsxq', case_sensitive=True)
(10, 233.35343938980898, 'Short String')

>>> decrypt_caesar_with_chi_squared(12)
Traceback (most recent call last):
AttributeError: 'int' object has no attribute 'lower'