Cracking XOR Ciphers Without Knowing the Key but Knowing the Key Length

Cracking an XOR cipher when the key length is known but the actual key is not, can be achieved through a series of steps that involve understanding the cipher, analyzing frequency patterns, and employing a systematic approach. This guide will walk you through each step in detail, ensuring you can successfully decrypt your ciphertext.

Understanding the XOR Cipher

An XOR cipher encrypts data by applying the XOR operation between the plaintext and a key. If the key is shorter than the plaintext, it is repeated until it matches the length of the plaintext. Since the XOR operation is its own inverse (i.e., A ^ B ^ B A), knowing the key length is crucial in decrypting the message.

Extracting Key Length

Since you already know the key length, we will denote it as n. Treat the ciphertext as consisting of n separate streams to crack the cipher effectively.

Splitting the Ciphertext

Divide the ciphertext into n separate byte streams. For example, if your ciphertext is C and the key length is n, you would create n streams as follows:

For the first byte of the key: C[0] C[n] C[2n] ... For the second byte of the key: C[1] C[n 1] C[2n 1] ... And so on...

This splitting allows you to focus on each stream individually, making the frequency analysis more effective.

Frequency Analysis

Analyze each stream individually. Since XORing with a single byte can be considered a substitution cipher, you can use frequency analysis on each stream to determine the most likely byte used in the XOR operation. A common approach is to XOR each byte in the stream with every possible byte value (0-255) and look for the result that produces a high frequency of common letters like e, t, a, etc. in English text.

Brute Force Each Stream

For each stream, try all possible values (0-255) for the key byte and check the resulting plaintext for intelligibility. You can automate this process by scoring the output of each possible plaintext based on letter frequency or using a dictionary of common words to find the most coherent output.

Combine Key Bytes

Once you have determined the likely byte for each position in the key, combine these bytes to form the complete key. This will allow you to decrypt the entire ciphertext accurately.

Example Pseudocode

def xor_decrypt_ciphertext(ciphertext, key):    return bytes([c ^ key[i % len(key)] for i, c in enumerate(ciphertext)])def score_plaintext(plaintext):    # Implement a scoring function based on letter frequency    score  0    # Add scoring logic here    return scoredef crack_xor_cipher(ciphertext, key_length):    key  bytearray(len(key_length))    for i in range(key_length):        best_byte  None        best_score  float('-inf')        for possible_key in range(256):            # Extract the ith byte stream            stream  ciphertext[i::key_length]            decrypted_stream  xor_decrypt_ciphertext(stream, [possible_key])            score  score_plaintext(decrypted_stream)            if score  best_score:                best_score  score                best_byte  possible_key        key[i]  best_byte    return bytes(key)

Example Usage

Ciphertext b... Your XOR encrypted ciphertext

Key Length n (Known key length)

key crack_xor_cipher(ciphertext, key_length)

decrypted_text xor_decrypt_ciphertext(ciphertext, key)

Important Considerations

Language: The effectiveness of frequency analysis depends on the language of the plaintext. The above method assumes English.

Key Length: If the key length is too short compared to the plaintext, it may lead to more significant patterns, making it easier to break.

Complexity: This method is computationally feasible for reasonably sized ciphertexts and key lengths.

By following these steps, you should be able to crack an XOR cipher given the key length without knowing the actual key.