On Resilient Boolean and Vectorial Boolean Functions with High Nonlinearity
نویسندگان
چکیده
Boolean functions and vectorial are the most important nonlinear components of stream ciphers. They should satisfy several criteria such as high nonlinearity, proper resiliency so on to guarantee security whole system. However, there some constraints among criteria, how achieve a trade-off between them is an issue. In this paper, possessing simple algebraic normal form with special Walsh spectrum proposed. By using these functions, we provide two construction methods balanced resilient nonlinearity. addition, based disjoint linear codes vector matrices properties, currently best-known nonlinearity have also been given.
منابع مشابه
A New Construction of Resilient Boolean Functions with High Nonlinearity
In this paper we develop a technique that allows us to obtain new effective construction of 1-resilient Boolean functions with very good nonlinearity and autocorrelation. Our strategy to construct a 1-resilient function is based on modifying a bent function, by toggling some of its output bits. Two natural questions that arise in this context are “at least how many bits and which bits in the ou...
متن کاملOn Resilient Boolean Functions with Maximal Possible Nonlinearity
It is proved that the maximal possible nonlinearity of n-variable m-resilient Boolean
متن کاملNew Constructions of Resilient Boolean Functions with Maximal Nonlinearity
In this paper we develop a technique that allows to obtain new effective constructions of highly resilient Boolean functions with high nonlinearity. In particular, we prove that the upper bound 2n−1 − 2 on nonlinearity of m-resilient n-variable Boolean functions is achieved for 0.6n− 1 ≤ m ≤ n− 2.
متن کاملConstruction of 1-Resilient Boolean Functions with Very Good Nonlinearity
In this paper we present a strategy to construct 1-resilient Boolean functions with very good nonlinearity and autocorrelation. Our strategy to construct a 1-resilient function is based on modifying a bent function, by toggling some of its output bits. Two natural questions that arise in this context are “at least how many bits and which bits in the output of a bent function need to be changed ...
متن کاملNonlinearity Bounds and Constructions of Resilient Boolean Functions
In this paper we investigate the relationship between the nonlinearity and the order of resiliency of a Boolean function. We first prove a sharper version of McEliece theorem for Reed-Muller codes as applied to resilient functions, which also generalizes the well known XiaoMassey characterization. As a consequence, a nontrivial upper bound on the nonlinearity of resilient functions is obtained....
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematics
سال: 2022
ISSN: ['2227-7390']
DOI: https://doi.org/10.3390/math10244822