A deterministic algorithm finds a normal element in F_{q^n} in O_ε((n² log q)^{1+ε}) bit operations by bounding bad parameters t via the non-vanishing of a cleared Moore circulant determinant and computing it fast.
Proceedings of the 2025 ACM-SIAM Symposium on Discrete Algorithms (SODA) , year =
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Fast Deterministic Normal Bases and Circulant Polynomial Determinants
A deterministic algorithm finds a normal element in F_{q^n} in O_ε((n² log q)^{1+ε}) bit operations by bounding bad parameters t via the non-vanishing of a cleared Moore circulant determinant and computing it fast.