Journal of the
Korean Mathematical Society
JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

Article

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J. Korean Math. Soc. 2015; 52(1): 209-224

Printed January 1, 2015

https://doi.org/10.4134/JKMS.2015.52.1.209

Copyright © The Korean Mathematical Society.

Polynomial representations for $n$-th roots in finite fields

Seunghwan Chang, Bihtnara Kim, and Hyang-Sook Lee

Ewha Womans University, Ewha Womans University, Ewha Womans University

Abstract

Computing square, cube and $n$-th roots in general, in finite fields, are important computational problems with significant applications to cryptography. One interesting approach to computational problems is by using polynomial representations. Agou, Del\'eglise and Nicolas proved results concerning the lower bounds for the length of polynomials representing square roots modulo a prime $p$. We generalize the results by considering $n$-th roots over finite fields for arbitrary $n >2$.

Keywords: cube roots, $n$-th roots, finite fields

MSC numbers: Primary 12E20, 68W40