Paper 2026/2451 Original: eprint.iacr.org/2026/2451 ↗
Extended biprojective APN functions
Abstract
Almost perfect nonlinear (APN) functions provide optimal resistance to differential cryptanalysis in characteristic two, and constructing new infinite families inequivalent to the known ones remains an important problem in the study of cryptographic functions. We introduce extended biprojective functions, obtained by augmenting biprojective polynomials with truncated trace terms, and establish a new infinite family of quadratic APN functions. To investigate these constructions, we develop an efficient APN test based on the ranks of binary matrices and employ it in exhaustive searches in dimensions up to 28. Using ortho-derivative differential spectra to distinguish CCZ-equivalence classes, we identify APN functions inequivalent to known families and uncover a systematic pattern across dimensions, leading to conjectures on further infinite families of quadratic APN functions.
Metadata
- Available format(s)
PDF- Category
- Secret-key cryptography
- Publication info
- Preprint.
- History
- 2026-10-14: last updated
- 2026-10-12: published
- Short URL
- https://ia.cr/2026/2451
- License
- https://creativecommons.org/licenses/by-nc-nd/4.0/
BibTeX
@misc{cryptoeprint:2026/2451,
author = {Nadiia Ichanska and Nikolay Kaleyski},
title = {Extended biprojective APN functions},
howpublished = {Cryptology {ePrint} Archive, Paper 2026/2451},
year = {2026},
url = {https://eprint.iacr.org/2026/2451}
}