Generalized bent functions enhance p-ary cryptography constructions
Generalized $p$-ary $\cPS$ Bent Functions
Information TheoryDiscrete Mathematics
Summary
In cryptography, bent functions help create secure communication methods. This paper builds on previous work by introducing new classes of bent functions based on mathematical structures called partial spreads. These new constructions work over a range of values that are powers of an odd prime number. The authors extend known designs, potentially offering more options for cryptographic function design.
What this means in practice
- •For cryptographic engineers: Build cryptographic schemes using generalized bent functions for improved nonlinear properties over odd prime fields.
- •For coding theory developers: Design error-correcting codes leveraging new p-ary bent function classes constructed from partial spreads.
Authors
Alexander Kholosha, Mohit Pal
Abstract
We use $m$-dimensional partial spreads of $\fp^{2n}$, where $p$ is an odd prime, $n$ is a positive integer and $m$ divides $n$, to construct two classes of bent functions from $\fp^{2n}$ to $\fp$. Our construction generalizes the classes of $p$-ary $\cPS^{-}$ and $\cPS^{+}$ bent functions proposed by P. Lison\v ek and H. Y. Lu (Des. Codes Cryptogr. 73 (2014), 209--216).