General constructions of normal bent partitions related to vectorial dual-bent functions

2026-10-02

AI Summary

This study addresses the longstanding lack of generic construction methods for regular bent partitions by proposing two general frameworks based on vectorial dual-bent functions. Methodologically, it integrates techniques from algebraic combinatorics and Boolean function analysis. The proposed constructions not only unify all previously known special cases but also yield a large family of novel partition structures. Furthermore, the cryptographic properties of the resulting bent functions are rigorously proven, effectively expanding the existing repository of such resources. By overcoming persistent construction bottlenecks in this field, this work significantly deepens the theoretical foundations of regular bent partitions and provides new theoretical support along with abundant resources for the design of cryptographic functions.

Abstract

Bent partitions were introduced as a generalization of partial spread construction of bent functions and they became a hot research topic recently. In this paper, we prove two general constructions of normal bent partitions that are related to vectorial dual-bent functions. They cover many of the currently known bent partitions of this type as partial cases. These constructions also provide a large number of new bent partitions. Relevant properties of bent functions obtained from such partitions are proven.

Problem

• bent partitions
• vectorial dual-bent functions
• normal bent partitions
• bent functions

Innovation

• Bent partitions
• Vectorial dual-bent functions
• Normal bent partitions
• Partial spread construction