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A further study on the construction methods of bent functions and self-dual bent functions based on Rothaus’s bent function
Bent functions are maximally nonlinear Boolean functions. They are important functions introduced by Rothaus and studied firstly by Dillon and next...
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Derivatives of bent functions in connection with the bent sum decomposition problem
In this paper, we investigate when a balanced function can be a derivative of a bent function. We prove that every nonconstant affine function in an...
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Decomposing self-dual bent functions
Bent functions are Boolean functions in even number of variables that have maximal nonlinearity. They have flat Walsh–Hadamard spectrum and are of...
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Look into the Mirror: Evolving Self-dual Bent Boolean Functions
Bent Boolean functions are important objects in cryptography and coding theory, and there are several general approaches for constructing such...
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Semantic mutation operator for a fast and efficient design of bent Boolean functions
Boolean functions are important cryptographic primitives with extensive use in symmetric cryptography. These functions need to possess various...
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Several secondary methods for constructing bent–negabent functions
In this paper, we present three secondary methods for constructing bent–negabent functions under the frameworks of the indirect sum construction...
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Explicit infinite families of bent functions outside the completed Maiorana–McFarland class
During the last five decades, many different secondary constructions of bent functions were proposed in the literature. Nevertheless, apart from a...
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Vectorial bent functions and linear codes from quadratic forms
In this paper, we study the vectorial bentness of an arbitrary quadratic form and construct two classes of linear codes of few weights from the...
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On the higher-order nonlinearity of a new class of biquadratic Maiorana–McFarland type bent functions
In 1974, Dillon introduced two significant classes of bent functions, namely the Maiorana–McFarland class and the Partial Spread class. In this...
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Heuristic search of (semi-)bent functions based on cellular automata
An interesting thread in the research of Boolean functions for cryptography and coding theory is the study of secondary constructions : given a known...
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Quadratic bent functions and their duals
We obtain geometric characterizations of the dual functions for quadratic bent and vectorial bent functions in terms of quadrics. Additionally, using...
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Bent functions in the partial spread class generated by linear recurring sequences
We present a construction of partial spread bent functions using subspaces generated by linear recurring sequences (LRS). We first show that the...
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On the higher-order nonlinearity of a Boolean bent function class (Constructed via Niho power functions)
The r th-order nonlinearity of a Boolean function plays a vital role in analyzing the security of stream and block ciphers. In this paper, we present...
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Constructing new superclasses of bent functions from known ones
Some recent research articles (Zhang et al. in Lecture Notes in Computer Science, 10194, 298-313. (
2017 ), Zhang et al. in Discret. Appl. Math.... -
Some general properties of modified bent functions through addition of indicator functions
Properties of a secondary bent function construction that adds the indicator of an affine subspace of arbitrary dimension to a given bent function in n ...
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Vectorial Boolean functions with the maximum number of bent components beyond the Nyberg’s bound
Recently, several interesting constructions of vectorial Boolean functions with the maximum number of bent components (MNBC functions, for short)...
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Results on the nonexistence of bent-negabent rotation symmetric Boolean functions
In this paper, we study the conjecture that there doesn’t exist bent-negabent rotation symmetric Boolean functions. We prove that the conjecture is...
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Two secondary constructions of bent functions without initial conditions
In this article, we propose two secondary constructions of bent functions without any conditions on initial bent functions employed by these methods....