A method for constructing permutations, involutions and orthomorphisms with strong cryptographic properties
Reynier Antonio de la Cruz Jiménez · Prikladnaya diskretnaya matematika Prilozhenie · 2019
S-Boxes are crucial components in the design of many symmetric ciphers.To construct permutations having strong cryptographic properties is not a trivial task.In this work, we propose a new scheme based on the well-known Lai-Massey structure for generating permutations of dimension n = 2k, k 2. The main cores of our constructions are: the inversion in GF(2 k ), an arbitrary k-bit non-bijective function (which has no pre-image for 0) and any k-bit permutation.Combining these components with the finite field multiplication, we provide new 8-bit permutations without fixed points possessing a very good combination for nonlinearity, differential uniformity and minimum degree (104; 6; 7) which can be described by a system of polynomial equations with degree 3. Also, we show that our approach can be used for constructing involutions and orthomorphisms with strong cryptographic properties.