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A Maiorana–McFarland type construction for resilient Boolean functions on n variables (n even) with nonlinearity >2n-1-2n/2+2n/2-2

2006
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Discrete Applied Mathematics
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In this paper, we present a construction method of m-resilient Boolean functions with very high nonlinearity for low values of m. The construction only considers functions in even number of variables n. So far the maximum nonlinearity attainable by resilient functions was 2 n−1 − 2 n/2 + 2 n/2−2 . Here, we show that given any m, one can construct n-variable, m-resilient functions with nonlinearity 2 n−1 − 11 · 2 n/2−4 for all n 8m + 6 which is strictly greater than 2 n−1 − 2 n/2 + 2 n/2−2 . We

doi:10.1016/j.dam.2005.03.014
fatcat:5aijo4u4qje2rkbcv24h3uczu4