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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...
High Dimensional Stochastic Regression with Latent Factors, Endogeneity and Nonlinearity
α-mixing dimension reduction instrument variables nonstationarity time series
2016/1/26
We consider a multivariate time series model which represents a high dimensional vector process as a sum of three terms: a linear regression of some observed regressors, a linear com-bination of some ...
High dimensional stochastic regression with latent factors, endogeneity and nonlinearity
α-mixing dimension reduction instrument variables nonstationarity time series
2016/1/25
We consider a multivariate time series model which represents a high dimensional vector process as a sum of three terms: a linear regression of some observed regressors,a linear combination of some la...
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...
High dimensional stochastic regression with latent factors, endogeneity and nonlinearity
α-mixing, dimension reduction instrument variables nonstationarity time series
2016/1/20
We consider a multivariate time series model which represents a high dimensional vector process as a sum of three terms: a linear regression of some observed regressors,a linear combination of some la...
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...
Uniqueness of circuits and systems containing one nonlinearity
The nonlinear circuits nonlinear nonlinear elements
2015/8/13
We study systems containing one memoryless nonlinearity. We show that two such systems have the same I/O operator only when they are related by simple scaling, delay, and loop transformations. The the...
Extending a biologically inspired model of choice:multi-alternatives,nonlinearity,and value-based multidimensional choice
biologically inspired model of choice multi-alternatives nonlinearity multidimensional choice
2015/6/23
The Leaky Competing Accumulator (LCA) is a biologically inspired model of choice. It describes the processes of leaky accumulation and competition observed in neuronal populations during choice tasks ...
Solitons in triangular and honeycomb dynamical lattices with the cubic nonlinearity
Stability in two-dimensional discrete nonlinear schrodinger equation lattice discrete soliton
2014/12/29
We study the existence and stability of localized states in the discrete nonlinear Schrödinger equation on two-dimensional nonsquare lattices. The model includes both the nearest-neighbor and lon...
Averaging for Solitons with Nonlinearity Management
Average method of nonlinear schrodinger equation the soliton periodic variation nonlinear coefficient and condensate
2014/12/29
We develop an averaging method for solitons of the nonlinear Schrödinger equation with a periodically varying nonlinearity coefficient, which is used to effectively describe solitons in Bose-Eins...
Rich example of geometrically induced nonlinearity: From rotobreathers and kinks to moving localized modes and resonant energy transfer
Mechanical systems linear geometric properties nonlinear dynamic equations nonlinear wave resonance energy transfer
2014/12/29
We present an experimentally realizable, simple mechanical system with linear interactions whose geometric nature leads to nontrivial, nonlinear dynamical equations. The equations of motion are derive...