Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Faster computation of isogenies of large prime degree   Let $\mathcal{E}/\mathbb{F}_q$ be an elliptic curve, and $P$ a point in
$\mathcal{E}(\mathbb{F}_q)$ of prime order $\ell$. V\'elu's formulae let us
compute a quotient curve $\mathcal{E}' = \mathcal{E}/\langle{P}\rangle$ and
rational maps defining a quotient isogeny $\phi: \mathcal{E} \to \mathcal{E}'$
in $\tilde{O}(\ell)$ $\mathbb{F}_q$-operations, where the $\tilde{O}$ is
uniform in $q$.This article shows how to compute $\mathcal{E}'$, and $\phi(Q)$
for $Q$ in $\mathcal{E}(\mathbb{F}_q)$, using only $\tilde{O}(\sqrt{\ell})$
$\mathbb{F}_q$-operations, where the $\tilde{O}$ is again uniform in $q$.As an
application, this article speeds up some computations used in the isogeny-based
cryptosystems CSIDH and CSURF.

4
The categories of this paper are: cond-mat
0
The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg
23
The categories of this paper are: solv-int
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The categories of this paper are: eess
20
The categories of this paper are: acc-phys
25
The categories of this paper are: patt-sol
8
The categories of this paper are: hep-ex
36
The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th
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The categories of this paper are: gr-qc
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The categories of this paper are: adap-org
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The categories of this paper are: nlin
17
The categories of this paper are: q-fin