Construction of highly nonlinear resilient S-boxes with given degree

Abstract

We provide two new construction methods for nonlinear resilient S-boxes with given degree. The first method is based on the use of linear error correcting codes together with highly nonlinear S-boxes. Given a [u, m, t +1] linear code where u = n −d −1, d > m, we show that it is possible to construct (n, m, t, d) resilient S-boxes which have currently best known nonlinearity. Our second construction provides highly nonlinear (n, m, t, d) resilient S-boxes which do not have linear structure, then an improved version of this construction is given.

On cryptographic properties of (n + 1)-bit S-boxes constructed by known n-bit S-boxes

“…In 2016, a construction of resilient S-boxes with higher-dimensional vectorial outputs and strictly almost optimal non-linearity was presented in [15]. A construction of highly nonlinear (n, m, t, d) resilient S-boxes with given algebraic degree was gave in [6]. 2.…”

Secondary Constructions of Bent Functions and Highly Nonlinear Resilient Functions

“…Resilient functions have important applications in the nonlinear combiner model of stream cipher [1,39,42]. Over the last decades, much attention was paid to the construction of highly nonlinear Boolean functions in the cryptographic literature [7,22,34,37,43,46,44,45]. In terms of constructions of resilient functions, there are also two kinds of constructions which are primary constructions and secondary constructions.…”