John McAfee (the founder of McAfee anti virus company) has two tweets (first and second) in which he shares a seemingly novel note about an anomaly in XOR operation. I understand how XOR operation combines the information of two datasets, but I'm not quite sure if I understand what anomaly McAfee is exactly referring to. Can you please give an example of the anomaly that doesn't exist with 3 datasets, but exists with 6 datasets?
Here is McAfee's note:
Boolean algebra is one of the foundations of computer science. There is an unusual property of the boolean XOR operation that I doubt many, or anyone at all, has considered:
If you take any three sets of characters of any equal length - let's label them A, B and C - and then:
XOR A to B
Then XOR the result of B to C
Then similarly XOR C to A
And then perform four iterations of the above. And finally: XOR A to B And then B to C It will result in the original contents of A moved to C, C moved to B and B moved to A.
Of interest here is that the three results of the third iteration, though deterministic as a whole, are entirely random within each of the three independent data segments. Thus if any one of the three segments is missing or withheld, it is impossible, from the remaining two to extract even the tiniest fragment of the three original contents.
The simplicity of this process is astonishing. A person of average intelligence could decode a message, using pencil and paper, providing they possessed all three interim segments.
I'm describing this tidbit in the hopes that my observations might be of some small use to those engaged in the research of cryptography.
Addendum:
The same concept of sequential XOR operations works with four data sets requiring three iterations and five data sets with two iterations.
** Strangely with six sets, the process unravels and produces chaos no matter how many iterations.**
Please God, someone explain.