XOR cipher

In cryptography, the simple XOR cipher is a type of additive cipher,^[1] an encryption algorithm that operates according to the principles:

A ${\displaystyle \oplus }$ 0 = A,

A ${\displaystyle \oplus }$ A = 0,

A ${\displaystyle \oplus }$ B = B ${\displaystyle \oplus }$ A,

(A ${\displaystyle \oplus }$ B) ${\displaystyle \oplus }$ C = A ${\displaystyle \oplus }$ (B ${\displaystyle \oplus }$ C),

(B ${\displaystyle \oplus }$ A) ${\displaystyle \oplus }$ A = B ${\displaystyle \oplus }$ 0 = B,

For example where ${\displaystyle \oplus }$ denotes the exclusive disjunction (XOR) operation.^[2] This operation is sometimes called modulus 2 addition (or subtraction, which is identical).^[3] 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.