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# The Value $4$ of Binary Kloosterman Sums

Abstract : Kloosterman sums have recently become the focus of much research, most notably due to their applications in cryptography and their relations to coding theory. Very recently Mesnager has showed that the value $4$ of binary Kloosterman sums gives rise to several infinite classes of bent functions, hyper-bent functions and semi-bent functions in even dimension. In this paper we analyze the different strategies used to find zeros of binary Kloosterman sums to develop and implement an algorithm to find the value $4$ of such sums. We then present experimental results showing that the value $4$ of binary Kloosterman sums gives rise to bent functions for small dimensions, a case with no mathematical solution so far.
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Cited literature [39 references]

https://hal.archives-ouvertes.fr/hal-00642290
Contributor : Jean-Pierre Flori Connect in order to contact the contributor
Submitted on : Thursday, November 17, 2011 - 5:15:56 PM
Last modification on : Monday, January 24, 2022 - 11:43:20 AM
Long-term archiving on: : Friday, November 16, 2012 - 11:21:30 AM

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• HAL Id : hal-00642290, version 1

### Citation

Jean-Pierre Flori, Sihem Mesnager, Gérard Cohen. The Value $4$ of Binary Kloosterman Sums. 2011. ⟨hal-00642290⟩

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