**Correlation Immune Boolean Functions with Very High Nonlinearity**

*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.

**Category / Keywords: **secret-key cryptography / Boolean Function, Stream Cipher

**Date: **received 27 Oct 2000

**Contact author: **subho at isical ac in

**Available format(s): **Postscript (PS) | Compressed Postscript (PS.GZ) | BibTeX Citation

**Version: **20001027:173601 (All versions of this report)

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