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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.
small characteristic. It works especially well when the characteristic
is fixed. Indeed, in this case, we obtain a total complexity of $L(1/4+o(1)).$