As an extra comment: main cost of factorization is modular
exponentiotion. For field of cardinality p^k, that is
algebraic extentions of prime field our current method
has cost proportional to length of p^k, that is k*length(p).
This can be lowered to length(p) + other term which is smaller
by using modular composition. But for large p and moderate
k possible speedup is limited.
--
Waldek Hebisch
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