We study the relations between boolean functions and symmetric groups. We consider elements of a symmetric group as variable transformation operators for boolean functions. Boolean function may be xed or permuted by these operators. We give some properties relating the symmetric group Sn and boolean functions on Vn.

The rotation symmetric Boolean functions which are invariant under the action of cyclic group have been used as components of different cryptosystems. In order to resist algebraic attacks, Boolean functions should have high algebraic immunity. This paper studies the construction of even-variable rotation symmetric Boolean functions with optimum algebraic immunity. We construct ( / 4 3) n    ...

Highly nonlinear Boolean functions play a central role in the design and security analysis of high speed stream cyphers and block cyphers. We focus on analyzing the structure of Boolean functions that exhibit high second order nonlinearity. We commence with a theoretical overview of Boolean functions and ReedMuller codes. We then introduce a new equivalence relation, 2-equivalence, for which we...

Boolean functions are important primitives in cryptography. Accordingly, there exist numerous works on the methods of constructions of Boolean functions. However, the property specifying the resistance of Boolean functions against Differential Power Analysis (DPA) attacks was until now scarcely investigated and only for S-boxes. Here, we evolve Boolean functions that have higher resistance to D...

This paper presents algorithms for disjunctive and nondisjunctive decomposition of Boolean functions and Boolean methods for identifying common subfunctions from multiple Boolean functions. Ordered Binary Decision Diagrams are used to represent and manipulate Boolean functions so that the proposed methods can be implemented concisely. These techniques are applied to the synthesis of look-up tab...

Boolean functions have important applications in cryptography and coding theory. Two famous classes of binary codes derived from Boolean functions are the Reed-Muller codes and Kerdock codes. In the past two decades, a lot of progress on the study of applications of Boolean functions in coding theory has been made. Two generic constructions of binary linear codes with Boolean functions have bee...

Traditionally Sum-Of-Products (SOPs) have been studied as expressions of Boolean functions. It has been shown by Sasao in [7] that Exclusive-or-Sum-Of-Products (ESOPs) are more compact representations of Boolean functions than SOPs. The problem to identify an exact minimal ESOP of a Boolean function is despite of some partial results still unsolved. Our new results rely on recently detected pro...

Recently, 9-variable Boolean functions having nonlinearity 241, which is strictly greater than the bent concatenation bound of 240, have been discovered in the class of Rotation Symmetric Boolean Functions (RSBFs) by Kavut, Maitra and Yücel. In this paper, we present several 9-variable Boolean functions having nonlinearity of 242, which we obtain by suitably generalizing the classes of RSBFs an...

In this article, a relationship between the Walsh-Hadamard spectrum and σ f , the sum-of-squares-modulus indicator (SSMI) of the generalized Boolean function is presented. It is demonstrated for every s-plateaued generalized Boolean function in n variables that σ f = 22n+s. Two constructions on generalized semi-bent Boolean functions are presented. A class of generalized semi-bent functions in ...