Enumerative encoding of correlation-immune Boolean functions

Construction of correlation immune Boolean functions

It is shown in this paper that every correlation immune Boolean function of n variables can be written as f(x) = g(xG ), where 9 is an algebraic non-degenerate Boolean function of k (k :::; n) variables and G is a generating matrix of an tn, k, d] linear code. In this expression the correlation immunity of f(x) must be at least d 1. In this paper we further prove when the correlation immunity e...

Spectral Domain Analysis of Correlation Immune and Resilient Boolean Functions

On Nonlinearity and Autocorrelation Properties of Correlation Immune Boolean Functions

+ 2 2 2 2 2 2 n n and a maximum possible algebraic degree of n − 1. Moreover, we present a detailed study on the Walsh spectra of these functions. Next we study the autocorrelation values of correlation immune and resilient Boolean functions. We provide new lower bounds and related results on the absolute indicator and sum of square indicator of autocorrelation values for low orders of correlat...

Improved Asymptotic Formulas for Counting Correlation Immune Boolean Functions

A Boolean function is called correlation immune if every input is independent of the output, when the inputs are chosen from a uniform distribution. Such functions are of interest in machine learning and stream cipher design. We show how an asymptotic formula of Denisov, which approximately counts the n-variable correlation immune functions, can be improved so as to be accurate even for fairly ...

Results on Rotation Symmetric Bent and Correlation Immune Boolean Functions

Recent research shows that the class of Rotation Symmetric Boolean Functions (RSBFs), i.e., the class of Boolean functions that are invariant under circular translation of indices, are potentially rich in functions of cryptographic significance. Here we present new results regarding the Rotation Symmetric (rots) correlation immune (CI) and bent functions. We present important data structures fo...