The function itself, as opposed to the representation above?
The above was meant to show the (reduction between) fn & its inverse…
In terms of the fn itself;
If a permutation, a point reflection, affine transform are involutions, then yes?
I see where you’re headed with this I think… an XOR is an involution?
Tambo University 
November 3, 2014 at 5:58 am
Presuming this can be expanded to cover some polynomial-trapdoor reduction…
LikeLike
November 4, 2014 at 3:29 am
No bites…
LikeLike
March 1, 2015 at 2:57 am
Phill,
Is this an involution?
LikeLike
March 1, 2015 at 4:54 am
The function itself, as opposed to the representation above?
The above was meant to show the (reduction between) fn & its inverse…
In terms of the fn itself;
If a permutation, a point reflection, affine transform are involutions, then yes?
I see where you’re headed with this I think… an XOR is an involution?
LikeLike
March 1, 2015 at 6:36 am
yes, reflection is an involution.
If the product between the transpose of f and f is equato to identity matrix, f is a permutation; and If f²=Id, this permutations is an involution.
f(control=0,1, target=0,1) = (control, control XOR target) is an involution, because f²=Id.
LikeLike
March 1, 2015 at 6:45 am
if (control XOR target) is irreducible, then this XOR provides a hidden bit for inverting the function f
LikeLiked by 1 person
March 1, 2015 at 6:57 am
Ok, thanks Alex! Give me some time to absorb all of that.
LikeLike