On Some Invertible S-boxes Associated with Calm Filtrons
Paweł Siwak, Izabela Janicka-Lipska, Daniel M. Dubois · AIP conference proceedings · 2008
Rijndael S‐boxes, applied in symmetric cryptographic systems, are based on particular finite field algebra of 8‐bit strings B with addition “+” and multiplication “•”. These are permutations B→B, and imply cyclic processing. We present a new family F of S‐boxes. They are implied by so called filtrons that emerge during iterated string processing performed by a class of automata. They can be described by a single switching function (SF), called the creating function. The S‐boxes from F operate over finite strings of any length and imply cyclic processing. We show some properties of the proposed S‐boxes. Especially, it has been found that there are two classes of S‐boxes from F; one is self‐inverse, the second consists of dual boxes. We show the relations between creating functions and implied SFs of S‐boxes. Also, some properties of SFs associated with blocks from F have been verified. Certain SFs, when used in cryptographic systems, have to be discarded in the S‐boxes because of bad nonlinearity values. We also formulate an algorithm that resolves inverse state assignment problem. It allows one to determine whether each SF implied by binary coding Q↔{0,1}k of given permutation Q→Q is dependent on all input variables in the resulting S‐box {0,1}k→{0,1}k.