Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Taking Roots over High Extensions of Finite Fields   We present a new algorithm for computing $m$-th roots over the finite field
$\F_q$, where $q = p^n$, with $p$ a prime, and $m$ any positive integer. In the
particular case $m=2$, the cost of the new algorithm is an expected
$O(\M(n)\log (p) + \CC(n)\log(n))$ operations in $\F_p$, where $\M(n)$ and
$\CC(n)$ are bounds for the cost of polynomial multiplication and modular
polynomial composition. Known results give $\M(n) = O(n\log (n) \log\log (n))$
and $\CC(n) = O(n^{1.67})$, so our algorithm is subquadratic in $n$.

22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
15
The categories of this paper are: nucl-ex
19
The categories of this paper are: eess
0
The categories of this paper are: hep-ph
13
The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc
14
The categories of this paper are: math-ph
16
The categories of this paper are: stat
20
The categories of this paper are: acc-phys
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The categories of this paper are: dg-ga
17
The categories of this paper are: q-fin
25
The categories of this paper are: patt-sol
28
The categories of this paper are: alg-geom
9
The categories of this paper are: nlin
3
The categories of this paper are: physics