Paper 2015/434 Original: eprint.iacr.org/2015/434 ↗
Dickson Polynomials that are Involutions
Abstract
Dickson polynomials which are permutations are interesting combinatorial objects and well studied. In this paper, we describe Dickson polynomials of the first kind in $\mathbb{F}_2[x]$ that are involutions over finite fields of characteristic $2$. Such description is obtained using modular arithmetic's tools. We give results related to the cardinality and the number of fixed points (in the context of cryptographic application) of this corpus. We also present a class of Dickson involutions with high degree.
Metadata
- Available format(s)
PDF- Category
- Secret-key cryptography
- Publication info
- Preprint.
- History
- 2015-05-06: last updated
- 2015-05-06: published
- Short URL
- https://ia.cr/2015/434
- License
- https://creativecommons.org/licenses/by/4.0/
BibTeX
@misc{cryptoeprint:2015/434,
author = {Pascale Charpin and Sihem Mesnager and Sumanta Sarkar},
title = {Dickson Polynomials that are Involutions},
howpublished = {Cryptology {ePrint} Archive, Paper 2015/434},
year = {2015},
url = {https://eprint.iacr.org/2015/434}
}