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Highly Nonlinear Resilient Functions without Linear Structures
Jian LIU Lusheng CHEN Xuan GUANG
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Publication Date: 2014/06/01
Online ISSN: 1745-1337
Type of Manuscript: PAPER
Category: Cryptography and Information Security
Boolean function, resiliency, linear structure, nonlinearity,
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In this paper, we provide several methods to construct nonlinear resilient functions with multiple good cryptographic properties, including high nonlinearity, high algebraic degree, and non-existence of linear structures. Firstly, we present an improvement on a known construction of resilient S-boxes such that the nonlinearity and the algebraic degree will become higher in some cases. Then a construction of highly nonlinear t-resilient Boolean functions without linear structures is given, whose algebraic degree achieves n-t-1, which is optimal for n-variable t-resilient Boolean functions. Furthermore, we construct a class of resilient S-boxes without linear structures, which possesses the highest nonlinearity and algebraic degree among all currently known constructions.