Xor

The argument leads to the conclusion that an omnipotent being could rationally be able to do one xor the other and still be omnipotent.

The XOR of (0,0) is 0; (0,1) is 1; (1,0) is 1; and (1,1) is 0.

The XOR gate can take only two inputs at a time and give an output. The output of the XOR gate is high (1) only when its two inputs are dissimilar i.e., if one of them is low (0) then other one will be high (1).

XOR can be used to add bits without carrying.

The XORed sequence has the same period as the sequence that is not XORed.

XORing different constants into the four s-boxes in such a cipher has exactly the same effect as XORing a single constant into each round function output.

There are weak keys in the sense that their use by foisting chosen plaintexts can be proved, which could be interesting for chip cards with a ‘burnt-in key’. First of all, however, these keys can be easily avoided—one only needs to XOR all subkeys with the hexadecimal number 0x0dae—and second, the probability that such a key can be caught is 2⁻⁹⁶; that is about one out of 10²⁹ randomly selected keys (this number even has a name: 100 quadrilliards).