A new family of semifields with 2 parameters
Yue Zhou, Alexander Pott
TL;DR
This paper introduces a new two-parameter family of commutative semifields, analyzes their nuclei, proves non-isotopy for different parameters, and explores their applications in constructing inequivalent planar and APN functions.
Contribution
It presents a novel family of semifields with detailed structural properties and demonstrates their use in generating new cryptographic functions.
Findings
Semifields are non-isotopic for different parameter pairs.
Some semifields produce two inequivalent planar functions.
New APN functions are constructed using this family.
Abstract
A new family of commutative semifields with two parameters is presented. Its left and middle nucleus are both determined. Furthermore, we prove that for any different pairs of parameters, these semifields are not isotopic. It is also shown that, for some special parameters, one semifield in this family can lead to two inequivalent planar functions. Finally, using similar construction, new APN functions are given.
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