Asymptotic enumeration of correlation-immune boolean functions

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 ...

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...

Asymptotic Nonlinearity of Boolean Functions

Boolean functions on the space F2 are not only important in the theory of error-correcting codes, but also in cryptography. In these two cases, the nonlinearity of these functions is a main concept. Carlet, Olejár and Stanek gave an asymptotic lower bound for the nonlinearity of most of them, and I gave an asymptotic upper bound which was strictly larger. In this article, I improve the bounds a...

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...