🚀 go-pugleaf

(C)hris <chris@staubli.ch> wrote:
> (A XOR B) XOR C ist nicht gleich A XOR (B XOR C).

a b c a X b  b X c  (a X b) X c  a X (b X c)
0 0 0   0      0         0           0
0 0 1   0      1         1           1
0 1 0   1      1         1           1
0 1 1   1      0         0           0
1 0 0   1      0         1           1
1 0 1   1      1         0           0
1 1 0   0      1         0           0
1 1 1   0      0         1           1

maybe I am missing something, but it looks commutative (b.) and
associative (a.), thus
   a. (a X b) x c == a X (b X c)
   b. (a X b) == (b X a)

But not distributive (unlike AND, for example)
   (a X b) X c != (a X c) X (b X c)
counter example:
   a = 0, b = 0, c = 1

   (0 X 0) X 1  !=  (0 X 1) X (0 X 1)
       1        !=          0


`AND' is distributive:
    (a AND b) AND c == (a AND c) AND (b AND c)
                    == a AND c AND b AND c
                    == a AND b AND c == (a AND b) AND c

Another interesting property of XOR:
   if
      a X b == c 
   then
      a == c X b == (a X b) X b == a X (b X b) == a

This is because:   c X b == (a X b) X b == a X (b X b) == a
                                        ^ associativity (cf above)

Some ciphers probably also are based on the property that
   (text X key) X key == text

RAID systems are interested in p = a X B; a == p X B for example.