Results 181 to 190 of about 1,481 (204)

Exact relation between nonlinearity and algebraic immunity

Discrete Mathematics and Applications, 2006
We sharpen some lower bounds on the higher order nonlinearity of a Boolean function in terms of the value of its algebraic immunity and obtain new tight bounds. We prove a universal tight lower bound, which enables us to reduce the problem of estimating higher order nonlinearity to finding the dimension of certain linear subspaces in the space of ...
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Construction of Boolean Functions with Optimal Algebraic Immunity

2016
Boolean functions with good cryptographic properties act as important nonlinear components in symmetric cryptography which is often used to encrypt stored data for cloud computing. In this paper, we develop a new class of Boolean functions with optimal algebraic immunity by utilizing the Reed-Muller code. In addition, our new functions are balanced and
Hang Liu, Dong Zheng 0001, Qinglan Zhao
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Using Wiedemann’s Algorithm to Compute the Immunity Against Algebraic and Fast Algebraic Attacks

2006
We show in this paper how to apply well known methods from sparse linear algebra to the problem of computing the immunity of a Boolean function against algebraic or fast algebraic attacks. For an n-variable Boolean function, this approach gives an algorithm that works for both attacks in O(n2nD) complexity and O(n2n) memory. Here and d corresponds to
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Algebraic immune functions

2020
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On Symmetric Boolean Functions With High Algebraic Immunity on Even Number of Variables

IEEE Transactions on Information Theory, 2011
Quanshui Wu, Haibin Kan
exaly  

On the 2m-variable symmetric Boolean functions with maximum algebraic immunity

Science in China Series F: Information Sciences, 2008
Longjiang Qu, Qu Longjiang
exaly  

A note on the fast algebraic immunity and its consequences on modified majority functions

Advances in Mathematics of Communications, 2020
Deng Tang
exaly  

The Exact Fast Algebraic Immunity of Two Subclasses of the Majority Function

IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, 2016
Deng Tang, Rong Luo, Xiaoni Du
exaly  

Constructing odd-variable RSBFs with optimal algebraic immunity, good nonlinearity and good behavior against fast algebraic attacks

Discrete Applied Mathematics, 2019
Yindong Chen
exaly  

Two Classes of Symmetric Boolean Functions With Optimum Algebraic Immunity: Construction and Analysis

IEEE Transactions on Information Theory, 2011
Yindong Chen, Peizhong Lu
exaly