Paper 2013/117

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.