Square Root Algorithm in F q for q ≡ 2 s + 1 ( mod 2 s + 1 ) Namhun Koo ,

We present a square root algorithm in Fq which generalizes Atkins’s square root algorithm [6] for q ≡ 5 (mod 8) and Kong et al.’s algorithm [8] for q ≡ 9 (mod 16). Our algorithm precomputes a primitive 2-th root of unity ξ where s is the largest positive integer satisfying 2|q − 1, and is applicable for the cases when s is small. The proposed algorithm requires one exponentiation for square root computation and is favorably compared with the algorithms of Atkin, Müller and Kong et al.