Paper 2026/1799

Two Constructions of Rotation-Symmetric Bent Functions Outside the Completed Maiorana--McFarland Class with Any Possible Algebraic Degree

Abstract

Rotation-symmetric Boolean functions form an important class of cryptographically significant Boolean functions. In 2017, Su and Tang proposed in [IEEE TIT 63(7): 4658–4667, 2017] an infinite class of rotation-symmetric bent functions of every possible algebraic degree. In this paper, we present two constructions of rotation-symmetric bent functions outside the completed Maiorana--McFarland class on $n=30\cdot 7^j$ variables with $j\geq0$ and $n=70t$ variables with $t\geq1$, respectively. Each of the two constructions generates bent functions of every possible algebraic degree ranging from $3$ to $n/2$. Since the algebraic degree of an $n$-variable bent function is at most $n/2$ and every quadratic bent function belongs to the completed Maiorana--McFarland class, the interval from $3$ to $n/2$ is the full possible degree range for bent functions outside this class. To the best of our knowledge, these are the first infinite constructions of rotation-symmetric bent functions in which functions have algebraic degrees ranging from $3$ to $n/2$ while remaining entirely outside the completed Maiorana--McFarland class.