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.
Seunghwan Chang, Bihtnara Kim, and Hyang-Sook Lee
Ewha Womans University, Ewha Womans University, Ewha Womans University
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
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