A method for constructing permutations, involutions and orthomorphisms with strong cryptographic properties

de la Cruz Jiménez, R. A.

A method for constructing permutations, involutions and orthomorphisms with strong cryptographic properties

Дата публикации: 2019

Дата публикации в реестре: 2020-03-03T18:42:26Z

Аннотация:

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 = 2к, к 2. The main cores of our constructions are: the inversion in GF(2k), an arbitrary к-bit non-bijective function (which has no pre-image for 0) and any к-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.

Ключевые слова:
s-боксы, булевы функции

Тип: статьи в журналах

Источник: Прикладная дискретная математика. Приложение. 2019. № 12. С. 145-151