Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A quantum circuit to find discrete logarithms on ordinary binary
  elliptic curves in depth O(log^2 n)   Improving over an earlier construction by Kaye and Zalka, Maslov et al.
describe an implementation of Shor's algorithm which can solve the discrete
logarithm problem on binary elliptic curves in quadratic depth O(n^2). In this
paper we show that discrete logarithms on such curves can be found with a
quantum circuit of depth O(log^2 n). As technical tools we introduce quantum
circuits for GF(2^n) multiplication in depth O(log n) and for GF(2^n) inversion
in depth O(log^2 n).

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The categories of this paper are: acc-phys
19
The categories of this paper are: eess
35
The categories of this paper are: mtrl-th
11
The categories of this paper are: hep-lat
37
The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom
18
The categories of this paper are: econ
26
The categories of this paper are: bayes-an
34
The categories of this paper are: chem-ph
12
The categories of this paper are: nucl-th
22
The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
7
The categories of this paper are: hep-th
24
The categories of this paper are: dg-ga
8
The categories of this paper are: hep-ex
14
The categories of this paper are: math-ph