Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Easy decision-Diffie-Hellman groups   The decision-Diffie-Hellman problem (DDH) is a central computational problem
in cryptography. It is known that the Weil and Tate pairings can be used to
solve many DDH problems on elliptic curves. Distortion maps are an important
tool for solving DDH problems using pairings and it is known that distortion
maps exist for all supersingular elliptic curves. We present an algorithm to
construct suitable distortion maps. The algorithm is efficient on the curves
usable in practice, and hence all DDH problems on these curves are easy. We
also discuss the issue of which DDH problems on ordinary curves are easy.

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The categories of this paper are: atom-ph
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The categories of this paper are: supr-con
26
The categories of this paper are: bayes-an
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The categories of this paper are: eess
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The categories of this paper are: alg-geom
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The categories of this paper are: ao-sci
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The categories of this paper are: adap-org
3
The categories of this paper are: physics
1
The categories of this paper are: cs
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The categories of this paper are: mtrl-th
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-ex
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The categories of this paper are: q-alg
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The categories of this paper are: q-fin
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The categories of this paper are: chem-ph
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The categories of this paper are: plasm-ph