Resilient Boolean functions with high nonlinearity and good algebraic properties play an important role in designing certain stream cipher schemes. In this paper, two construction methods are proposed to obtain such functions. It is shown that a class of resilient functions with high algebraic degree and currently best known nonlinearity can be constructed by using our technique. The algebraic immunity of the constructed functions is also analyzed.Maitra and Pasalic provided a generalized construction method for m-resilient functions in [8]. We first recall this construction that will play an important role in our paper.Security Comm. Networks (2015)
Resilient substitution boxes (S-boxes) with high nonlinearity are important cryptographic primitives in the design of certain encryption algorithms. There are several trade-offs between the most important cryptographic parameters and their simultaneous optimization is regarded as a difficult task. In this paper we provide a construction technique to obtain resilient S-boxes with so-called strictly almost optimal (SAO) nonlinearity for a larger number of output bits m than previously known. This is the first time that the nonlinearity bound 2 n−1 − 2 n/2 of resilient (n, m) S-boxes, where n and m denote the number of the input and output bits respectively, has been exceeded for m > n 4. Thus, resilient S-boxes with extremely high nonlinearity and a larger output space compared to other design methods have been obtained.
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