[Resource Topic] 2019/1202: Rational isogenies from irrational endomorphisms

Welcome to the resource topic for 2019/1202

Rational isogenies from irrational endomorphisms

Authors: Wouter Castryck, Lorenz Panny, Frederik Vercauteren


In this paper, we introduce a polynomial-time algorithm to compute a connecting \mathcal{O}-ideal between two supersingular elliptic curves over \mathbb{F}_p with common \mathbb{F}_p-endomorphism ring \mathcal{O}, given a description of their full endomorphism rings. This algorithm provides a reduction of the security of the CSIDH cryptosystem to the problem of computing endomorphism rings of supersingular elliptic curves. A similar reduction for SIDH appeared at Asiacrypt 2016, but relies on totally different techniques. Furthermore, we also show that any supersingular elliptic curve constructed using the complex-multiplication method can be located precisely in the supersingular isogeny graph by explicitly deriving a path to a known base curve. This result prohibits the use of such curves as a building block for a hash function into the supersingular isogeny graph.

ePrint: https://eprint.iacr.org/2019/1202

Talk: https://www.youtube.com/watch?v=XMuSQ-G5Xbk

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