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
2 ITI - Département Image et Traitement Information
3 FSR - Faculté des sciences de Rabat

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.

Mots clés: Tu-Deng conjecture; Combinatorics; Algebraic immunity; Boolean functions

Domaines: Cryptographie et sécurité [cs.CR]; Mathématique discrète [cs.DM]; Combinatoire [math.CO]

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⟩