New general methods create advanced bent partitions for cryptography
General constructions of normal bent partitions related to vectorial dual-bent functions
Discrete Mathematics
Summary
Bent functions are special mathematical tools used to make secure communication better. The paper shows new general ways to build bent partitions, which help create these special functions. The authors’ methods include many known examples but also create many new ones. This helps improve the study and design of bent functions for practical use.
What this means in practice
- •For cryptographic engineers: Design stronger cryptographic algorithms by using new bent partitions to improve security properties of Boolean functions.
- •For error correction developers: Develop codes with better error detection and correction by applying bent function partitions from these constructions.
Authors
Alexander Kholosha, Mohit Pal
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.