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Improved upper bound on root number of linearized polynomials and its application to nonlinearity estimation of Boolean functions
Boolean Functions Nonlinearity Linearized Polynomial Root Number
2018/12/3
To determine the dimension of null space of any given linearized polynomial is one of vital problems in finite field theory, with concern to design of modern symmetric cryptosystems. But, the known ge...
Differentially 4-Uniform Permutations with the Best Known Nonlinearity from Butterflies
S-boxes APN butterfly structure
2017/5/25
Many block ciphers use permutations defined over the finite field F22kF22k with low differential uniformity, high nonlinearity, and high algebraic degree to provide confusion. Due to the lack of knowl...
Improving the lower bound on the maximum nonlinearity of 1-resilient Boolean functions and designing functions satisfying all cryptographic criteria
Boolean functions nonlinearity resiliency algebraic immunity
2016/12/8
In this paper, we improve the lower bound on the maximum nonlinearity of 1-
resilient Boolean functions, for n even, by proposing a method of constructing this
class of functions attaining the best ...
A GMM type construction for resilient S-boxes with higher-dimensional vectorial outputs and strictly almost optimal nonlinearity
secret-key cryptography Boolean functions
2016/7/4
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 impor...
On the nonlinearity of monotone Boolean functions
Boolean functions monotone functions Walsh–Hadamard spectrum
2016/2/23
We first prove the truthfulness of a conjecture on the nonlinearity of
monotone Boolean functions in even dimension, proposed in the recent paper “Cryptographic
properties of monotone Boolean functi...
Generalized proper matrices and constructing of $m$-resilient Boolean functions with maximal nonlinearity for expanded range of parameters
Boolean functions symmetric-key cryptography nonlinearity
2016/1/25
Nonlinearity and resiliency are well known as some of the most important cryptographic parameters of Boolean functions, it is actual the problem of the constructing of functions that have high nonline...
Patterson-Wiedemann type functions on 21 variables with Nonlinearity greater than Bent Concatenation bound
Covering Radius First Order Reed-Muller Code Nonlinearity
2015/12/22
Nonlinearity is one of the most challenging combinatorial property in the domain of Boolean function research.
Obtaining nonlinearity greater than the bent concatenation bound for odd number of varia...
Cryptographic applications, such as hashing, block ciphers and stream ciphers, make use of functions which are simple by some criteria (such as circuit implementations), yet hard to invert almost ever...
A method for obtaining lower bounds on the higher order nonlinearity of Boolean function
Boolean function algebraic immunity
2014/3/12
Obtainment of exact value or high lower bound on the $r$-th order nonlinearity of Boolean function is a very complicated problem (especial if $r > 1$). In a number of papers lower bounds on the $r$-th...
Evolving balanced Boolean functions with optimal resistance to algebraic and fast algebraic attacks, maximal algebraic degree, and very high nonlinearity
Algebraic immunity nonlinearity metaheuristics simulated annealing
2013/2/21
Using simulated annealing, we derive several equivalence classes of balanced Boolean functions with optimum algebraic immunity, fast algebraic resistance, and maximum possible algebraic degree. For nu...
The Good lower bound of Second-order nonlinearity of a class of Boolean function
Boolean function Higher-order derivatives Second-order nonlinearit Walsh-spectrum
2012/3/26
this paper we find the lower bound of second-order nonlinearity of Boolean function $f_{\lambda}(x) = Tr_{1}^{n}(\lambda x^{p})$ with $p = 2^{2r} + 2^{r} + 1$, $\lambda \in \mathbb{F}_{2^{r}}^{*}$ and...
Maiorana-McFarland Functions with High Second-Order Nonlinearity
secret-key cryptography / boolean functions
2012/3/28
The second-order nonlinearity, and the best quadratic approximations, of Boolean functions are studied in this paper. We prove that cubic functions within the Maiorana-McFarland class achieve very hig...
On the Affine Equivalence and Nonlinearity Preserving Bijective Mappings
Boolean functions nonlinearity affine equivalence automorphism groups Sylvester Hadamard matrices
2011/1/5
It is well-known that affine equivalence relations keep nonlineaerity invariant for all Boolean functions. The set of all Boolean functions, $\mathcal{F}_n$, over $\bbbf_2^n$, is naturally regarded as...
Balanced Boolean Functions with Optimum Algebraic Immunity and High Nonlinearity
Boolean function stream cipher balancedness algebraic degree algebraic immunity nonlinearity fast algebraic attack
2010/10/20
In this paper, three constructions of balanced Boolean functions with optimum algebraic immunity are proposed. The cryptographical properties such as algebraic degree and nonlinearity of the construct...
Balanced Boolean Functions with (Almost) Optimal Algebraic Immunity and Very High Nonlinearity
Boolean functions balancedness algebraic immunity nonlinearity algebraic degree
2010/8/24
In this paper, we present a class of $2k$-variable balanced Boolean functions and a class of $2k$-variable $1$-resilient Boolean functions for an integer $k\ge 2$, which both have the maximal algebrai...