Taking roots over high extensions of finite fields

We present a new algorithm for computing m \mathbb{F}_q, with p any positive integer. In the particular case m=2 O(\mathsf {M}(n)\log (p) + \mathsf {C}(n)\log (n)) \mathbb{F}_p \mathsf {M}(n) \mathsf {C}(n) \mathsf {M}(n) = O(n\log (n) \log \log (n)) \mathsf {C}(n) = O(n^{1.67}).

Saved in:

Bibliographic Details
Published in:	Mathematics of computation Vol. 83; no. 285; pp. 435 - 446
Main Authors:	DOLISKANI, JAVAD, SCHOST, ÉRIC
Format:	Journal Article
Language:	English
Published:	American Mathematical Society 01-01-2014
Subjects:	Algebra Algorithms Computer science Cryptography Cubes Exponentiation Factorization Integers Logarithms Polynomials square roots Root extraction finite field arithmetic
Online Access:	Get full text
Tags:	Add Tag No Tags, Be the first to tag this record!

Description
Summary:	We present a new algorithm for computing m \mathbb{F}_q, with p any positive integer. In the particular case m=2 O(\mathsf {M}(n)\log (p) + \mathsf {C}(n)\log (n)) \mathbb{F}_p \mathsf {M}(n) \mathsf {C}(n) \mathsf {M}(n) = O(n\log (n) \log \log (n)) \mathsf {C}(n) = O(n^{1.67}).
ISSN:	0025-5718 1088-6842
DOI:	10.1090/S0025-5718-2013-02715-9