On Negabent Functions and Nega-Hadamard Transform

The Boolean function which has equal absolute spectral values under the nega-Hadamard transform is called negabent function. In this paper, the special Boolean functions by concatenation are presented. We investigate their nega-Hadamard transforms, nega-autocorrelation coefficients, sum-of-squares indicators, and so on. We establish a new equivalent statement on f1∥f2 which is negabent function. Based on them, the construction for generating the negabent functions by concatenation is given. Finally, the function expressed as f(Ax⊕a)⊕b·x⊕c is discussed. The nega-Hadamard transform and nega-autocorrelation coefficient of this function are derived. By applying these results, some properties are obtained

Further research results on confusion coefficient of Boolean functions

The notion of confusion coefficient (CC) is a property that attempts to characterize the confusion property of cryptographic algorithms against differential power analysis. In this article, we establish a relationship between CC and the transparency order (TO) for any Boolean function and deduce some relationships between the sum-of-squares of CC, signal-to-noise ratio, and TO. We also give a tight upper bound and a tight lower bound on the sum-of-squares of CC for balanced s-plateaued functions. Finally, the results generalized a lower bound on the sum-of-squares of CC of Boolean functions with the Hamming weight k

The Walsh Transform of a Class of Boolean Functions

The Walsh transform is an important tool to investigate cryptographic properties of Boolean functions. This paper is devoted to study the Walsh transform of a class of Boolean functions defined as g(x)=f(x)Tr1n(x)+h(x)Tr1n(δx), by making use of the known conclusions of Walsh transform and the properties of trace function, and the conclusion is obtained by generalizing an existing result