Publication detail
On the Detection of Permutation Polynomials
GHARIBAH, M.
Czech title
Na detekci permutace polynomy
English title
On the Detection of Permutation Polynomials
Type
conference paper
Language
en
Original abstract
Multivariate Public keyPublic key cryptosystems are widely spread and ever evolving domain. This study aims to find new techniques to characterize and detect permutation polynomialsPermutation polynomial over finite fieldsFinite field, which enable us to find trapdoor, one way, functions that are essential to build robust cryptosystems. Let f be a polynomial over Fq, a finite fieldFinite field of order q, where q=pm, p is a prime number. If f induces a bijective mapping, one-to-one mapping, of Fq, we call f a permutation polynomialPermutation polynomial over Fq. In order to detect these polynomials, we constructed a program implementing multiple algorithmsAlgorithm based on Galois fieldGalois field arithmetic. As a result, we have the number of all possible permutation polynomialsPermutation polynomial in the fields F4, F8 and F16
Czech abstract
Vícerozměrné Veřejné keyPublic klíčové kryptografické systémy jsou velmi rozšířené a stále se vyvíjející oblast. Tato studie si klade za cíl najít nové techniky pro charakterizaci a zjištění permutace polynomialsPermutation polynomu nad konečným fieldsFinite oblasti, které nám umožní najít poklop, na jednu stranu, funkce, které jsou nezbytné pro vybudování silného kryptosystémů. Nechť f je polynom nad Fq, konečné fieldFinite pole řádu q, kde q = pm, p je prvočíslo. Pokud f indukuje bijective mapování, one-to-one mapování, o Fq, říkáme fa permutace polynomialPermutation polynom nad Fq. Za účelem zjištění těchto polynomů, vyrobeno jsme program, kterým se provádí více algorithmsAlgorithm na základě Konečná fieldGalois poli aritmetiky. V důsledku toho máme počet všech možných permutací polynomialsPermutation polynomu v oblastech, F4, F8 a F16
English abstract
Multivariate Public keyPublic key cryptosystems are widely spread and ever evolving domain. This study aims to find new techniques to characterize and detect permutation polynomialsPermutation polynomial over finite fieldsFinite field, which enable us to find trapdoor, one way, functions that are essential to build robust cryptosystems. Let f be a polynomial over Fq, a finite fieldFinite field of order q, where q=pm, p is a prime number. If f induces a bijective mapping, one-to-one mapping, of Fq, we call f a permutation polynomialPermutation polynomial over Fq. In order to detect these polynomials, we constructed a program implementing multiple algorithmsAlgorithm based on Galois fieldGalois field arithmetic. As a result, we have the number of all possible permutation polynomialsPermutation polynomial in the fields F4, F8 and F16
Keywords in English
Algebra;finite fields;rings;polynomials;permutation;cryptography;quantum;physics
RIV year
2014
Released
15.04.2014
Publisher
Springer Berlin Heidelberg
Location
France
ISBN
978-3-642-55360-8
ISSN
2194-1009
Book
Algebra, Geometry and Mathematical Physics
Volume
85
Edition number
85
Pages from–to
651–660
Pages count
9
BIBTEX
@inproceedings{BUT109063,
author="Mazen {Gharibah},
title="On the Detection of Permutation Polynomials",
booktitle="Algebra, Geometry and Mathematical Physics",
year="2014",
volume="85",
month="April",
pages="651--660",
publisher="Springer Berlin Heidelberg",
address="France",
isbn="978-3-642-55360-8",
issn="2194-1009"
}