Description
Given two l-isogenous elliptic curves, a well-known algorithm of Elkies uses modular polynomials to compute this isogeny explicitly. In this work, we generalize his ideas to Jacobians of genus 2 curves. Our algorithms works for both l-isogenies and (in the RM case) cyclic isogenies, and uses Siegel or Hilbert type modular equations respectively. This has applications for point counting in genus 2: SEA-style methods are now available.<br/> lien: http://desktop.visio.renater.fr/scopia?ID=726145***4969&autojoin
Next sessions
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Algorithms for post-quantum commutative group actions
Speaker : Marc Houben - Inria Bordeaux
At the historical foundation of isogeny-based cryptography lies a scheme known as CRS; a key exchange protocol based on class group actions on elliptic curves. Along with more efficient variants, such as CSIDH, this framework has emerged as a powerful building block for the construction of advanced post-quantum cryptographic primitives. Unfortunately, all protocols in this line of work are[…] -
Endomorphisms via Splittings
Speaker : Min-Yi Shen - No Affiliation
One of the fundamental hardness assumptions underlying isogeny-based cryptography is the problem of finding a non-trivial endomorphism of a given supersingular elliptic curve. In this talk, we show that the problem is related to the problem of finding a splitting of a principally polarised superspecial abelian surface. In particular, we provide formal security reductions and a proof-of-concept[…]-
Cryptography
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