Paper 2019/767 Original: eprint.iacr.org/2019/767 ↗
On cryptographic parameters of permutation polynomials of the form $x^rh(x^{(q-1)/d})$
Abstract
The differential uniformity, the boomerang uniformity, and the extended Walsh spectrum etc are important parameters to evaluate the security of S(substitution)-box. In this paper, we introduce efficient formulas to compute these cryptographic parameters of permutation polynomials of the form $x^rh(x^{(q-1)/d})$ over a finite field of $q=2^n$ elements, where $r$ is a positive integer and $d$ is a positive divisor of $q-1$. The computational cost of those formulas is proportional to $d$. We investigate differentially 4-uniform permutation polynomials of the form $x^rh(x^{(q-1)/3})$ and compute the boomerang spectrum and the extended Walsh spectrum of them using the suggested formulas when $4\le n\le 10$ is even, where $d=3$ is the smallest nontrivial $d$ for even $n$. We also investigate the differential uniformity of some permutation polynomials introduced in some recent papers for the case $d=2^{n/2}+1$
Metadata
- Available format(s)
PDF- Category
- Secret-key cryptography
- Publication info
- Preprint.
- History
- 2022-02-25: last updated
- 2019-07-02: published
- Short URL
- https://ia.cr/2019/767
- License
- https://creativecommons.org/licenses/by/4.0/
BibTeX
@misc{cryptoeprint:2019/767,
author = {Jaeseong Jeong and Chang Heon Kim and Namhun Koo and Soonhak Kwon and Sumin Lee},
title = {On cryptographic parameters of permutation polynomials of the form $x^rh(x^{(q-1)/d})$},
howpublished = {Cryptology {ePrint} Archive, Paper 2019/767},
year = {2019},
url = {https://eprint.iacr.org/2019/767}
}