New results about Tu-Deng's conjecture

International audienceTo 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