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?

November 3, 2014 at 5:58 am

Presuming this can be expanded to cover some polynomial-trapdoor reduction…

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November 4, 2014 at 3:29 am

No bites…

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March 1, 2015 at 2:57 am

Phill,

Is this an involution?

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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?

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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.

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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

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March 1, 2015 at 6:57 am

Ok, thanks Alex! Give me some time to absorb all of that.

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