Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Subexponential Algorithm for Evaluating Large Degree Isogenies   An isogeny between elliptic curves is an algebraic morphism which is a group
homomorphism. Many applications in cryptography require evaluating large degree
isogenies between elliptic curves efficiently. For ordinary curves of the same
endomorphism ring, the previous best known algorithm has a worst case running
time which is exponential in the length of the input. In this paper we show
this problem can be solved in subexponential time under reasonable heuristics.
Our approach is based on factoring the ideal corresponding to the kernel of the
isogeny, modulo principal ideals, into a product of smaller prime ideals for
which the isogenies can be computed directly. Combined with previous work of
Bostan et al., our algorithm yields equations for large degree isogenies in
quasi-optimal time given only the starting curve and the kernel.

21
The categories of this paper are: adap-org
27
The categories of this paper are: comp-gas
7
The categories of this paper are: hep-th
11
The categories of this paper are: hep-lat
37
The categories of this paper are: supr-con
15
The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg
25
The categories of this paper are: patt-sol
9
The categories of this paper are: nlin
1
The categories of this paper are: cs
5
The categories of this paper are: gr-qc
4
The categories of this paper are: cond-mat
30
The categories of this paper are: q-alg
24
The categories of this paper are: dg-ga
31
The categories of this paper are: ao-sci
16
The categories of this paper are: stat