2020
DOI: 10.1049/cje.2019.12.008
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The GAC Property of a Class of 1‐Resilient Functions with High Nonlinearity

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Cited by 1 publication
(7 citation statements)
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“…Secondly, we obtain two new classes of 1-resilient functions having very high nonlinearity and very low absolute indicator, from bent functions and from plateaued functions, respectively. Moreover, we prove that our 1-resilient functions from bent functions possess the currently highest known nonlinearity 2 n−1 − 2 n/2−1 − 2 n/4 and possess the currently known lowest absolute indicator 2 n/2 + 2 n/4+1 simultaneously, which breaks the previously best upper bound of the minimum absolute indicator of 1-resilient functions given by Ge et al in [10], and allows us to give another new smaller upper bound for the minimum absolute indicator of 1-resilient functions.…”
Section: Conjecturesupporting
confidence: 74%
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“…Secondly, we obtain two new classes of 1-resilient functions having very high nonlinearity and very low absolute indicator, from bent functions and from plateaued functions, respectively. Moreover, we prove that our 1-resilient functions from bent functions possess the currently highest known nonlinearity 2 n−1 − 2 n/2−1 − 2 n/4 and possess the currently known lowest absolute indicator 2 n/2 + 2 n/4+1 simultaneously, which breaks the previously best upper bound of the minimum absolute indicator of 1-resilient functions given by Ge et al in [10], and allows us to give another new smaller upper bound for the minimum absolute indicator of 1-resilient functions.…”
Section: Conjecturesupporting
confidence: 74%
“…Remark 4. Note that the currently known highest nonlinearity of 1-resilient functions is 2 n−1 − 2 n/2−1 − 2 n/4 [30] and the previously best known upper bound of the minimum absolute indicator of 1-resilient functions is 5 • 2 n/2 − 2 n/4+2 + 4 [10]. Theorem 2 provides a class of 1-resilient functions with the currently highest nonlinearity and the currently lowest absolute indicator simultaneously.…”
Section: A Sao 1-resilient Functions From Bent Functionsmentioning
confidence: 90%
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