## Cryptology ePrint Archive: Report 2000/054

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

Short URL: ia.cr/2000/054

[ Cryptology ePrint archive ]