Subgroup Refinement Algorithms for Root Finding in
AJ Menezes, PC van Oorschot, SA Vanstone�- SIAM Journal on Computing, 1992 - SIAM
AJ Menezes, PC van Oorschot, SA Vanstone
SIAM Journal on Computing, 1992•SIAMThis paper presents a generalization of Moenck's root finding algorithm over GF(q), for qa
prime or prime power. The generalized algorithm, like its predecessor, is deterministic, given
a primitive element ω for GF(q). If q-1 is b-smooth, where b=(\logq)^O(1), then the algorithm
runs in polynomial time. An analogue of this generalization which applies to extension fields
GF(q^m) is also considered. The analogue is a deterministic algorithm based on the recently
introduced affine method for root finding in GF(q^m), where m>1; it is, however, less efficient�…
prime or prime power. The generalized algorithm, like its predecessor, is deterministic, given
a primitive element ω for GF(q). If q-1 is b-smooth, where b=(\logq)^O(1), then the algorithm
runs in polynomial time. An analogue of this generalization which applies to extension fields
GF(q^m) is also considered. The analogue is a deterministic algorithm based on the recently
introduced affine method for root finding in GF(q^m), where m>1; it is, however, less efficient�…
This paper presents a generalization of Moenck’s root finding algorithm over , for q a prime or prime power. The generalized algorithm, like its predecessor, is deterministic, given a primitive element for . If is b-smooth, where , then the algorithm runs in polynomial time. An analogue of this generalization which applies to extension fields is also considered. The analogue is a deterministic algorithm based on the recently introduced affine method for root finding in , where ; it is, however, less efficient that the affine method itself.
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