Paper 2019/1491 Original: eprint.iacr.org/2019/1491 ↗
Classification of quadratic APN functions with coefficients in GF(2) for dimensions up to 9
Abstract
Almost perfect nonlinear (APN) and almost bent (AB) functions are integral components of modern block ciphers and play a fundamental role in symmetric cryptography. In this paper, we describe a procedure for searching for quadratic APN functions with coefficients in GF(2) over the finite fields GF(2^n) and apply this procedure to classify all such functions over GF(2^n) with n up to 9. We discover two new APN functions (which are also AB) over GF(2^9) that are CCZ-inequivalent to any known APN function over this field. We also verify that there are no quadratic APN functions with coefficients in GF(2) over GF(2^n) with n between 6 and 8 other than the currently known ones.
Metadata
- Available format(s)
PDF- Category
- Foundations
- Publication info
- Preprint.
- History
- 2019-12-30: last updated
- 2019-12-30: published
- Short URL
- https://ia.cr/2019/1491
- License
- https://creativecommons.org/licenses/by/4.0/
BibTeX
@misc{cryptoeprint:2019/1491,
author = {Yuyin Yu and Nikolay Kaleyski and Lilya Budaghyan and Yongqiang Li},
title = {Classification of quadratic APN functions with coefficients in GF(2) for dimensions up to 9},
howpublished = {Cryptology {ePrint} Archive, Paper 2019/1491},
year = {2019},
url = {https://eprint.iacr.org/2019/1491}
}