Paper 2013/007
A Matrix Approach for Constructing Quadratic APN Functions
Yuyin Yu, Mingsheng Wang, and Yongqiang Li
Abstract
We find a one to one correspondence between quadratic APN functions without linear or constant terms and a special kind of matrices (We call such matrices as QAMs). Based on the nice mathematical structures of the QAMs, we have developed efficient algorithms to construct quadratic APN functions. On $\mathbb{F}_{2^7}$, we have found more than 470 classes of new CCZ-inequivalent quadratic APN functions, which is 20 times more than the known ones. Before this paper, there are only 23 classes of CCZ-inequivalent APN functions on $\mathbb{F}_{2^{8}}$ have been found. With our method, we have found more than 2000 classes of new CCZ-inequivalent quadratic APN functions, and this number is still increasing quickly.
Note: We give more APN Functions on GF(256) in Appendix 2.
Metadata
- Available format(s)
-
PDF
- Publication info
- Published elsewhere. Unknown status
- Keywords
- APNquadratic functionsEA-equivalenceCCZ-equivalence.
- Contact author(s)
- yuyuyin @ 163 com
- History
- 2015-04-27: last of 2 revisions
- 2013-01-11: received
- See all versions
- Short URL
- https://ia.cr/2013/007
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2013/007,
author = {Yuyin Yu and Mingsheng Wang and Yongqiang Li},
title = {A Matrix Approach for Constructing Quadratic {APN} Functions},
howpublished = {Cryptology {ePrint} Archive, Paper 2013/007},
year = {2013},
url = {https://eprint.iacr.org/2013/007}
}
