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Concept
XOR cipher
Summary
In cryptography, the simple XOR cipher is a type of additive cipher, an encryption algorithm that operates according to the principles:
A 0 = A,
A A = 0,
A B = B A,
(A B) C = A (B C),
(B A) A = B 0 = B,
For example where denotes the exclusive disjunction (XOR) operation. This operation is sometimes called modulus 2 addition (or subtraction, which is identical). With this logic, a string of text can be encrypted by applying the bitwise XOR operator to every character using a given key. To decrypt the output, merely reapplying the XOR function with the key will remove the cipher.
The string "Wiki" ( in 8-bit ASCII) can be encrypted with the repeating key as follows:
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| = || style="border-top: 1px solid black" |
|}
And conversely, for decryption:
{|
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| = || style="border-top: 1px solid black" |
|}
The XOR operator is extremely common as a component in more complex ciphers. By itself, using a constant repeating key, a simple XOR cipher can trivially be broken using frequency analysis. If the content of any message can be guessed or otherwise known then the key can be revealed. Its primary merit is that it is simple to implement, and that the XOR operation is computationally inexpensive. A simple repeating XOR (i.e. using the same key for xor operation on the whole data) cipher is therefore sometimes used for hiding information in cases where no particular security is required. The XOR cipher is often used in computer malware to make reverse engineering more difficult.
If the key is random and is at least as long as the message, the XOR cipher is much more secure than when there is key repetition within a message. When the keystream is generated by a pseudo-random number generator, the result is a stream cipher. With a key that is truly random, the result is a one-time pad, which is unbreakable in theory.
The XOR operator in any of these ciphers is vulnerable to a known-plaintext attack, since plaintext ciphertext = key.
It is also trivial to flip arbitrary bits in the decrypted plaintext by manipulating the ciphertext.
Official source
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