SUBGROUP REFINEMENT ALGORITHMS FOR ROOT FINDING IN GF(Q)

This paper presents a generalization of Moenck's root finding algorith m over GF(q), for q a prime or prime power. The generalized algorithm, like its predecessor, is deterministic, given a primitive element-ome ga for GF(q). If q-1 is b-smooth, where b = (log q)O(1), then the algo rithm runs in polynomial time. An analogue of this generalization whic h applies to extension fields GF(q(m)) is also considered. The analogu e is a deterministic algorithm based on the recently introduced affine method for root finding in GF(q(m)), where m > 1; it is, however, les s efficient that the affine method itself.