Description
An isogeny graph is a graph whose vertices are abelian varieties (typically elliptic curves, or Jacobians of genus 2 hyperelliptic curves) and whose edges are isogenies between them. Such a graph is "horizontal" if all the abelian varieties have the same endomorphism ring. We study the connectivity and the expander properties of these graphs. We use these results, together with a recent algorithm for computing explicit isogenies in genus 2, to prove random self-reducibility of the discrete logarithm problem for Jacobians of genus 2 hyperelliptic curves with fixed endomorphism ring. In addition, we remove the heuristics in the complexity analysis of an algorithm of Galbraith for explicitly computing isogenies between two elliptic curves in the same isogeny class, and extend it to a more general setting including genus 2.
Next sessions
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Oblivious Transfer from Zero-Knowledge Proofs (or how to achieve round-optimal quantum Oblivious Transfer without structure)
Speaker : Léo Colisson - Université Grenoble Alpes
We provide a generic construction to turn any classical Zero-Knowledge (ZK) protocol into a composable oblivious transfer (OT) protocol (the protocol itself involving quantum interactions), mostly lifting the round-complexity properties and security guarantees (plain-model/statistical security/unstructured functions…) of the ZK protocol to the resulting OT protocol. Such a construction is unlikely[…]-
Cryptography
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