Trace Expression of r-th Root over Finite Field

Gook Hwa Cho; Namhun Koo; Eunhye Ha; Soonhak Kwon

Paper 2013/041

Trace Expression of r-th Root over Finite Field

Gook Hwa Cho, Namhun Koo, Eunhye Ha, and Soonhak Kwon

Abstract

Efficient computation of $r$ -th root in $F_{q}$ has many applications in computational number theory and many other related areas. We present a new $r$ -th root formula which generalizes Müller's result on square root, and which provides a possible improvement of the Cipolla-Lehmer algorithm for general case. More precisely, for given -th power , we show that there exists such that where and is a root of certain irreducible polynomial of degree over .

Metadata

Available format(s): PDF
Category: Applications
Publication info: Published elsewhere. Unknown where it was published
Keywords: finite field r-th root linear recurrence relation Tonelli-Shanks algorithm Adleman-Manders-Miller algorithm Cipolla-Lehmer algorithm
Contact author(s): shkwon7 @ gmail com
History: 2013-01-30: revised; 2013-01-29: received; See all versions
Short URL: https://ia.cr/2013/041
License: CC BY

BibTeX

@misc{cryptoeprint:2013/041,
      author = {Gook Hwa Cho and Namhun Koo and Eunhye Ha and Soonhak Kwon},
      title = {Trace Expression of r-th Root over Finite Field},
      howpublished = {Cryptology {ePrint} Archive, Paper 2013/041},
      year = {2013},
      url = {https://eprint.iacr.org/2013/041}
}