A general conjecture similar to T-D conjecture and its applications in constructing Boolean functions with optimal algebraic immunity.
Qingfang Jin, Zhuojun Liu, Baofeng Wu, Xiaoming Zhang · IACR Cryptology ePrint Archive · 2011
In this paper, we propose two classes of 2k-variable Boolean functions, which have optimal algebraic immunity under the assumption that a general combinatorial conjecture is correct. These functions also have high algebraic degree and high nonlinearity. One class contain more bent functions, and the other class are balanced.