Paper 2018/103 Original: eprint.iacr.org/2018/103 ↗
Decomposition of Permutations in a Finite Field
Abstract
We describe a method to decompose any power permutation, as a sequence of power permutations of lower algebraic degree. As a result we obtain decompositions of the inversion in $\mathrm{GF}(2^n)$ for small $n$ from $3$ up to $16$, as well as for the APN functions, when $n=5$. More precisely, we find decompositions into quadratic power permutations for any $n$ not multiple of $4$ and decompositions into cubic power permutations for $n$ multiple of $4$. Finally, we use the Theorem of Carlitz to prove that for $3 \leq n \leq 16$ any $n$-bit permutation can be decomposed in quadratic and cubic permutations.
Metadata
- Available format(s)
PDF- Category
- Secret-key cryptography
- Publication info
- Preprint.
- History
- 2020-11-02: last updated
- 2018-01-29: published
- Short URL
- https://ia.cr/2018/103
- License
- https://creativecommons.org/licenses/by/4.0/
BibTeX
@misc{cryptoeprint:2018/103,
author = {Svetla Nikova and Ventzislav Nikov and Vincent Rijmen},
title = {Decomposition of Permutations in a Finite Field},
howpublished = {Cryptology {ePrint} Archive, Paper 2018/103},
year = {2018},
url = {https://eprint.iacr.org/2018/103}
}