Nikolay Kaleyski, Ph.D.

On APN functions

Oh, how I love those wondrous functions
that are defined over a finite field,
and all of whose non-zero differentials
no more than two solutions yield.

Are they not infinitely graceful,
so far from linearity's misdeeds
as is the breeze at sunset graceful
when it whispers in the evening reeds.

So beautiful, yet so mysterious,
the rules to which these maps conform;
oh, how I long to know their nature
and their algebraic normal form!

Now, I have praised them all but little,
yet I swear to God, my words are true:
for I do not know more perfect functions
when the field is of characteristic two!