XOR cipher decoder and key recovery

XOR is the workhorse of CTF crypto because it is symmetric, byte-oriented, and trivial to implement badly. Every XOR challenge is one of three shapes: a single-byte key, a short repeating key, or a key as long as the message that got reused.

Single-byte XOR: 256 candidates

Try all 256 bytes and score each result for English-likeness. This is the same chi-squared machinery the Caesar solver uses, extended to bytes rather than letters, with a bonus for printable characters and for flag-shaped substrings. It is exhaustive and instant.

Repeating-key XOR: find the keysize first

For a repeating key, the trick is the normalised Hamming distance. Take two adjacent blocks of length K, count the differing bits, divide by K. When K is the true keysize, both blocks were XORed with the same key bytes, so the distance reflects only the plaintext difference and drops sharply. Test K from 2 to 40, take the lowest few, then split the ciphertext into K columns - each column is single-byte XOR, solved by the previous step.

def normalised_distance(data, k):
    blocks = [data[i * k:(i + 1) * k] for i in range(4)]
    pairs = [(a, b) for i, a in enumerate(blocks) for b in blocks[i + 1:]]
    total = sum(hamming(a, b) for a, b in pairs) / len(pairs)
    return total / k          # normalise so keysizes are comparable

best = sorted(range(2, 41), key=lambda k: normalised_distance(ct, k))[:3]