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Isogenies and the Discrete Logarithm Problem in Jacobians of Genus 3 Hyperelliptic Curves
[article]
2009
arXiv
pre-print
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 (/2)^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
arXiv:0806.2995v2
fatcat:xpkzor6lcbdadekeo4fvwgwil4