Caesar cipher decoder with automatic shift detection

A Caesar cipher shifts every letter by a fixed amount. There are only 25 useful keys, so it is trivially breakable by trying all of them - the only real question is which of the 25 candidates is the right one, and that is a question you should never answer by reading them yourself.

Why chi-squared beats eyeballing

English letter frequencies are stable: E around 12.7%, T around 9.1%, Z under 0.1%. Score each of the 26 rotations against those expected frequencies with a chi-squared statistic and the correct shift usually wins by a wide margin. The advantage over scanning by eye grows with the length of the text and, crucially, it does not degrade when the plaintext is unusual - a shifted flag full of digits and underscores still scores correctly on its letters alone.

EXPECTED = {'a': 0.0817, 'b': 0.0150, ...}  # English unigram frequencies

def chi_squared(text):
    letters = [c for c in text.lower() if c.isalpha()]
    n = len(letters)
    score = 0.0
    for ch, expected_freq in EXPECTED.items():
        expected = expected_freq * n
        observed = letters.count(ch)
        score += (observed - expected) ** 2 / expected
    return score          # lower is more English-like

best = min(range(26), key=lambda k: chi_squared(rotate(ct, k)))

When the shift is not 13

Short ciphertexts - under about 30 letters - are where statistics get unreliable, because a single unusual word skews the distribution. ctfpal still ranks all 26 and shows them, so a short text becomes a list to skim rather than a set of 26 separate round trips to a website.