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Characterization of Exact One-Query Quantum Algorithms for Partial Boolean Functions
The query model (or black-box model) has attracted much attention from the communities of both classical and quantum computing. Usually, quantum...
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New characterizations of generalized Boolean functions
This paper focuses on providing the characteristics of generalized Boolean functions from a new perspective. We first generalize the classical...
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Distribution of the autocorrelation of random Boolean functions
The nonlinearity of Boolean functions is well known and the behaviour of the nonlinearity of random Boolean functions has been studied, showing that...
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The Application of Majority Voting Functions to Estimate the Number of Monotone Self-Dual Boolean Functions
AbstractOne of the problems of modern discrete mathematics is Dedekind’s problem on the number of monotone Boolean functions. For other precomplete...
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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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A survey of metaheuristic algorithms for the design of cryptographic Boolean functions
Boolean functions are mathematical objects used in diverse domains and have been actively researched for several decades already. One domain where...
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Improved cryptographic properties of Boolean functions obtained from the neighbourhood of Patterson-Wiedemann functions
More than a decade ago, the balanced and 1-resilient Boolean functions on 15 variables with the best known nonlinearities 16272 and 16264,...
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A New Angle: On Evolving Rotation Symmetric Boolean Functions
Rotation symmetric Boolean functions represent an interesting class of Boolean functions as they are relatively rare compared to general Boolean...
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On those Boolean functions that are coset leaders of first order Reed-Muller codes
In this paper, we study the class of those Boolean functions that are coset leaders of first order Reed-Muller codes. We study their properties and...
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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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On cryptographic properties of cubic and splitting Boolean functions
The weight, balancedness and nonlinearity are important properties of Boolean functions, but they can be difficult to determine in general. In this...
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Analysis of boolean functions related to binary input binary output two-party nonlocal games
The famous CHSH game can be interpreted with Boolean functions while understanding the success probability in the classical scenario. In this paper,...
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Partially Defined Boolean Functions in TRIZ
The most recognized area where Boolean functions are used in TRIZ is, presumably, the cause-effect analysis, with logical operators indicating how...
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Probabilistic estimation of the algebraic degree of Boolean functions
The algebraic degree is an important parameter of Boolean functions used in cryptography. When a function in a large number of variables is not given...
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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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Symbolic dynamics and rotation symmetric Boolean functions
We identify the weights w t ( f n ) of a family { f n } of rotation symmetric Boolean functions with the cardinalities of the sets of n -periodic points of a...
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Synchronous Boolean Finite Dynamical Systems on Directed Graphs over XOR Functions
In this paper, we investigate the complexity of a number of computational problems defined on a synchronous boolean finite dynamical system, where...
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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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The linear structures and fast points of rotation symmetric Boolean functions
The existence of nonzero fast points and linear structures reflects the properties of Boolean function’s higher order derivatives, which is closely...