[Resource Topic] 2000/054: Correlation Immune Boolean Functions with Very High Nonlinearity

Welcome to the resource topic for 2000/054

Title:
Correlation Immune Boolean Functions with Very High Nonlinearity

Authors: Subhamoy Maitra

Abstract:

Here we provide a construction method for unbalanced, first order
correlation immune Boolean functions on even number of variables
n \geq 6. These functions achieve the currently best known
nonlinearity 2^{n-1} - 2^{\frac{n}{2}} + 2^{\frac{n}{2} - 2} .
Then we provide a simple modification of these functions to get
unbalanced correlation immune Boolean functions on even number of
variables n, with nonlinearity
2^{n-1} - 2^{\frac{n}{2}} + 2^{\frac{n}{2} - 2} - 2 and maximum
possible algebraic degree n-1. Moreover, we present a detailed
study on the Walsh spectra of these functions.

ePrint: https://eprint.iacr.org/2000/054

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