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Fix sphinx/build_docs warnings for ciphers (#12485)
* Fix sphinx/build_docs warnings for ciphers * Fix
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Maxim Smolskiy
@ -11,33 +11,31 @@ def decrypt_caesar_with_chi_squared(
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"""
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Basic Usage
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===========
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Arguments:
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* ciphertext (str): the text to decode (encoded with the caesar cipher)
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* `ciphertext` (str): the text to decode (encoded with the caesar cipher)
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Optional Arguments:
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* cipher_alphabet (list): the alphabet used for the cipher (each letter is
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a string separated by commas)
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* frequencies_dict (dict): a dictionary of word frequencies where keys are
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the letters and values are a percentage representation of the frequency as
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a decimal/float
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* case_sensitive (bool): a boolean value: True if the case matters during
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decryption, False if it doesn't
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* `cipher_alphabet` (list): the alphabet used for the cipher (each letter is
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a string separated by commas)
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* `frequencies_dict` (dict): a dictionary of word frequencies where keys are
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the letters and values are a percentage representation of the frequency as
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a decimal/float
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* `case_sensitive` (bool): a boolean value: ``True`` if the case matters during
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decryption, ``False`` if it doesn't
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Returns:
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* A tuple in the form of:
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(
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most_likely_cipher,
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most_likely_cipher_chi_squared_value,
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decoded_most_likely_cipher
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)
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* A tuple in the form of:
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(`most_likely_cipher`, `most_likely_cipher_chi_squared_value`,
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`decoded_most_likely_cipher`)
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where...
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- most_likely_cipher is an integer representing the shift of the smallest
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chi-squared statistic (most likely key)
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- most_likely_cipher_chi_squared_value is a float representing the
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chi-squared statistic of the most likely shift
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- decoded_most_likely_cipher is a string with the decoded cipher
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(decoded by the most_likely_cipher key)
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where...
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- `most_likely_cipher` is an integer representing the shift of the smallest
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chi-squared statistic (most likely key)
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- `most_likely_cipher_chi_squared_value` is a float representing the
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chi-squared statistic of the most likely shift
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- `decoded_most_likely_cipher` is a string with the decoded cipher
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(decoded by the most_likely_cipher key)
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The Chi-squared test
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@ -45,52 +43,57 @@ def decrypt_caesar_with_chi_squared(
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The caesar cipher
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-----------------
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The caesar cipher is a very insecure encryption algorithm, however it has
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been used since Julius Caesar. The cipher is a simple substitution cipher
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where each character in the plain text is replaced by a character in the
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alphabet a certain number of characters after the original character. The
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number of characters away is called the shift or key. For example:
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Plain text: hello
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Key: 1
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Cipher text: ifmmp
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(each letter in hello has been shifted one to the right in the eng. alphabet)
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| Plain text: ``hello``
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| Key: ``1``
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| Cipher text: ``ifmmp``
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| (each letter in ``hello`` has been shifted one to the right in the eng. alphabet)
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As you can imagine, this doesn't provide lots of security. In fact
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decrypting ciphertext by brute-force is extremely easy even by hand. However
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one way to do that is the chi-squared test.
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one way to do that is the chi-squared test.
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The chi-squared test
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-------------------
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--------------------
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Each letter in the english alphabet has a frequency, or the amount of times
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it shows up compared to other letters (usually expressed as a decimal
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representing the percentage likelihood). The most common letter in the
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english language is "e" with a frequency of 0.11162 or 11.162%. The test is
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completed in the following fashion.
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english language is ``e`` with a frequency of ``0.11162`` or ``11.162%``.
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The test is completed in the following fashion.
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1. The ciphertext is decoded in a brute force way (every combination of the
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26 possible combinations)
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``26`` possible combinations)
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2. For every combination, for each letter in the combination, the average
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amount of times the letter should appear the message is calculated by
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multiplying the total number of characters by the frequency of the letter
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multiplying the total number of characters by the frequency of the letter.
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For example:
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In a message of 100 characters, e should appear around 11.162 times.
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| For example:
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| In a message of ``100`` characters, ``e`` should appear around ``11.162``
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times.
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3. Then, to calculate the margin of error (the amount of times the letter
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SHOULD appear with the amount of times the letter DOES appear), we use
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the chi-squared test. The following formula is used:
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3. Then, to calculate the margin of error (the amount of times the letter
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SHOULD appear with the amount of times the letter DOES appear), we use
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the chi-squared test. The following formula is used:
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Let:
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- n be the number of times the letter actually appears
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- p be the predicted value of the number of times the letter should
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appear (see #2)
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- let v be the chi-squared test result (referred to here as chi-squared
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value/statistic)
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Let:
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- n be the number of times the letter actually appears
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- p be the predicted value of the number of times the letter should
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appear (see item ``2``)
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- let v be the chi-squared test result (referred to here as chi-squared
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value/statistic)
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(n - p)^2
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--------- = v
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p
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::
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(n - p)^2
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--------- = v
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p
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4. Each chi squared value for each letter is then added up to the total.
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The total is the chi-squared statistic for that encryption key.
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@ -98,16 +101,16 @@ def decrypt_caesar_with_chi_squared(
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to be the decoded answer.
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Further Reading
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================
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===============
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* http://practicalcryptography.com/cryptanalysis/text-characterisation/chi-squared-
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statistic/
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* http://practicalcryptography.com/cryptanalysis/text-characterisation/chi-squared-statistic/
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* https://en.wikipedia.org/wiki/Letter_frequency
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* https://en.wikipedia.org/wiki/Chi-squared_test
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* https://en.m.wikipedia.org/wiki/Caesar_cipher
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Doctests
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========
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>>> decrypt_caesar_with_chi_squared(
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... 'dof pz aol jhlzhy jpwoly zv wvwbshy? pa pz avv lhzf av jyhjr!'
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... ) # doctest: +NORMALIZE_WHITESPACE
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