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

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

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