CryptoDB
Correlation Immune Boolean Functions with Very High Nonlinearity
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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. |
BibTeX
@misc{eprint-2000-11398, title={Correlation Immune Boolean Functions with Very High Nonlinearity}, booktitle={IACR Eprint archive}, keywords={secret-key cryptography / Boolean Function, Stream Cipher}, url={http://eprint.iacr.org/2000/054}, note={ subho@isical.ac.in 11257 received 27 Oct 2000}, author={Subhamoy Maitra}, year=2000 }