Bent Boolean functions play a very significant role in the design of strong symmetric cryptosystems. In this paper, we present an analysis of Bent functions in the Haar domain. We first present a brief overview of Bent Boolean functions and then derive expressions for the Haar spectrum of Bent functions. The Haar spectral coefficients of Bent functions are given in two ways namely; in terms of ...

Introduced by Rothaus in 1976 as interesting combinatorial objects, bent functions are maximally nonlinear Boolean functions with even numbers of variables whose Hamming distance to the set of all affine functions equals 2n−1 ± 2 n 2 −1. Not only bent functions are applied in cryptography, such as applications in components of S-box, block cipher and stream cipher, but also they have relations ...

Almost bent functions oppose an optimum resistance to linear and differential cryptanalysis. We present basic properties of almost bent functions; particularly we give an upper bound on the degree. We develop the “coding theory” point of view for studying the existence of almost bent functions, showing explicitly the links with cyclic codes. We also give new characterizations of almost bent fun...

We have studied the phase sequence and physical properties of an asymmetric bent-core material with a chiral rigid cholesteryl moiety, and a flexible achiral alkyl side chain at the other end. The combination of the achiral bent core with the chiral cholesteryl unit results in properties different from those of both the usual calamitic and bent-core materials. We find that the presence of the b...

It has been an active research issue for many years to construct new bent functions. For k odd with gcd(n, k) = 1, and a ∈ F3n , the function f(x) = Tr(ax 3k+1 2 ) is weakly regular bent over F3n , where Tr(·) : F3n → F3 is the trace function. This is the well-known Coulter-Matthews bent function. In this paper, we determine the dual function of f(x) completely. As a consequence, we find many c...

In this paper, we describe a different approach to the proof of the nonexistence of homogeneous rotation symmetric bent functions. As a result, we obtain some new results which support the conjecture made in this journal, i.e., there are no homogeneous rotation symmetric bent functions of degree > 2. Also we characterize homogeneous degree 2 rotation symmetric bent functions by using GCD of pol...

Bent functions shows some vital properties among all combinatorial objects. Its links in combinatorics, cryptography and coding theory attract the scientific community to construct new class of bent functions. Since the entire characterisation of bent functions is still unexplored but several construction on different algebraic structure is in progress. In this paper we proposed a generalized M...

Recently discovered chiral properties of several bent-core smectic liquid crystal phases are summarized and discussed in detail under the assumption that typical bent-core molecules may exist in chiral conformational states and are achiral only on average. Results of atomistic computer simulations are presented which indicate the existence of strongly chiral conformational states for typical be...