**On r-th Root Extraction Algorithm in F_q For q=lr^s+1 (mod r^(s+1)) with 0 < l < r and Small s**

*Namhun Koo and Gook Hwa Cho and Soonhak Kwon*

**Abstract: **We present an r-th root extraction algorithm over a finite field
F_q. Our algorithm precomputes a primitive r^s-th root of unity where s is the largest positive integer satisfying r^s| q-1, and is applicable for the cases when s is small. The proposed algorithm requires one exponentiation for the r-th root computation and is favorably compared to the existing algorithms.

**Category / Keywords: **applications / r-th root algorithm, finite field, Adleman-Manders-Miller algorithm, Cipolla-Lehmer algorithm

**Date: **received 25 Feb 2013

**Contact author: **shkwon7 at gmail com

**Available format(s): **PDF | BibTeX Citation

**Version: **20130227:180513 (All versions of this report)

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