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Characterizations of the Degraded Boolean Function and Cryptanalysis of the SAFER Family
Cryptography Block cipher Degradation property Zero- correlation linear cryptanalysis
2016/1/27
This paper investigates the degradation properties of Boolean functions from the aspects of the distributions of di erences and linear masks, and shows two characterizations of the degraded Boolean fu...
When a Boolean Function can be Expressed as the Sum of two Bent Functions
Bent functions Sum of bent functions Maiorana-MacFarland bent function
2016/1/26
In this paper we study the problem that when a Boolean function can
be represented as the sum of two bent functions. This problem was recently
presented by N. Tokareva in studying the number of bent...
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...
Quantum algorithm to check Resiliency of a Boolean function
check Resiliency a Boolean function
2014/3/13
In this paper, for the first time, we present quantum algorithms to check the order of resiliency of a Boolean function. We first show that the Deutsch-Jozsa algorithm can be directly used for this pu...
1-Resilient Boolean Function with Optimal Algebraic Immunity
Boolean function Algebraic immunity 1-Resilient Balancedness Nonlinearity Algebraic degree
2012/3/23
In this paper, We propose a class of 2k-variable Boolean functions, which have optimal algebraic degree, high nonlinearity, and are 1-resilient. These functions have optimal algebraic immunity when k ...
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...
Efficient Approximation of Higher Order Boolean function in a Low Order Function
Efficient Approximation Higher Order Boolean function Low Order Function
2009/7/14
A few of non-linear approximation methods for Boolean functions
have been developed but they are not of practical application. However,
if a low order Boolean function can be found that can nearly a...
A First Order Recursive Construction of Boolean Function with Optimum Algebraic Immunity
stream cipher algebraic attacks Boolean function
2009/6/12
This paper proposed a first order recursive construction of
Boolean function with optimum algebraic immunity. We also show that
the Boolean functions are balanced and have good algebraic degrees.
Constructions of Even-variable Boolean Function with Optimum Algebraic Immunity
stream cipher algebraic attacks Boolean function
2009/6/12
This paper proposed an improved construction of even-variable
Boolean function with optimum algebraic degree. Compared with those
in [1], our Boolean functions are more balance. Specially, for k=2t+...
New construction of Boolean function with optimum algebraic immunity
Boolean functions Algebraic attack Algebraic immunity
2009/6/4
Information research department , Information engineering university, zhengzhou, 450002
Abstract: Because of the algebraic attacks, a high algebraic immunity is
now an important criteria for Boolean...
Finding Low Degree Annihilators for a Boolean Function Using Polynomial Algorithms
Boolean function low degree annihilator polynomial algorithm recursive algorithm
2008/10/23
Low degree annihilators for Boolean functions are of great interest in
cryptology because of algebraic attacks on LFSR-based stream ciphers. Several
polynomial algorithms for construction of low deg...
Balanced Boolean Function on 13-variables having Nonlinearity strictly greater than the Bent Concatenation Bound
Keywords: Balancedness Boolean Function Nonlinearity
2008/5/30
Very recently, Kavut and Yucel identified 9-variable Boolean functions having
nonlinearity 242, which is currently the best known. However, any of these functions
do not contain any zero in the Wals...