Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Isogenies and the Discrete Logarithm Problem in Jacobians of Genus 3
  Hyperelliptic Curves   We describe the use of explicit isogenies to translate instances of the
Discrete Logarithm Problem (DLP) from Jacobians of hyperelliptic genus 3 curves
to Jacobians of non-hyperelliptic genus 3 curves, where they are vulnerable to
faster index calculus attacks. We provide explicit formulae for isogenies with
kernel isomorphic to $(\ZZ/2\ZZ)^3$ (over an algebraic closure of the base
field) for any hyperelliptic genus 3 curve over a field of characteristic not 2
or 3. These isogenies are rational for a positive fraction of all hyperelliptic
genus 3 curves defined over a finite field of characteristic $p > 3$. Subject
to reasonable assumptions, our constructions give an explicit and efficient
reduction of instances of the DLP from hyperelliptic to non-hyperelliptic
Jacobians for around 18.57% of all hyperelliptic genus 3 curves over a given
finite field. We conclude with a discussion on extending these ideas to
isogenies with more general kernels. A condensed version of this work appeared
in the proceedings of the EUROCRYPT 2008 conference.

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The categories of this paper are: nucl-ex
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The categories of this paper are: bayes-an
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The categories of this paper are: dg-ga
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The categories of this paper are: funct-an
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The categories of this paper are: alg-geom
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The categories of this paper are: stat
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The categories of this paper are: q-alg
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The categories of this paper are: hep-th
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The categories of this paper are: patt-sol
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The categories of this paper are: atom-ph
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The categories of this paper are: eess
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The categories of this paper are: plasm-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: chem-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: solv-int