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New results about Tu-Deng's conjecture

Soukayna Qarboua 1, 2, 3 Julien Schrek 1, 2 Caroline Fontaine 1, 2
1 Lab-STICC_TB_CID_SFIIS
Lab-STICC - Laboratoire des sciences et techniques de l'information, de la communication et de la connaissance
Abstract : To design robust symmetric encryption schemes, we need to use Boolean functions with suitable properties. Among the security criteria these functions need to fulfill, we can mention algebraic immunity. A lot of papers study how to construct suitable functions, but some of them assume the validity of Tu- Deng's combinatorial conjecture [2] to estimate the algebraic immunity of the Boolean functions they design. In this paper we prove two new results about this conjecture and point out a new family of integers that satisfy it.
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https://hal.archives-ouvertes.fr/hal-01635350
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Submitted on : Wednesday, November 15, 2017 - 9:51:53 AM
Last modification on : Wednesday, November 3, 2021 - 5:44:58 AM

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Soukayna Qarboua, Julien Schrek, Caroline Fontaine. New results about Tu-Deng's conjecture. ISIT 2016 : IEEE International Symposium on Information Theory, Jul 2016, Barcelona, Spain. pp.485 - 489, ⟨10.1109/ISIT.2016.7541346⟩. ⟨hal-01635350⟩

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