Prossimi Seminari

30 Marzo 2026

Aula 3

ore 15:30

 Marzio Mula

(Bundeswehr Un., München)

How (Not) to Sample Trapdoor-Free 

Supersingular Elliptic Curves

Abstract: 

An open problem in isogeny-based cryptography is to sample supersingular elliptic curves over finite fields of cryptographic size in such a way that no one — including the sampler itself! — can efficiently compute the endomorphism ring of the output. This "trapdoor-free" sampling would be a crucial ingredient, for example, to instantiate the Charles–Goren–Lauter isogeny-based hash function without relying on a trusted setup. In this talk, we survey the best-known approach (CM reduction à la Deuring/Bröker followed by random walks in supersingular isogeny graphs), which achieves near-uniform sampling but inherently fails to be trapdoor-free. We then discuss why alternative routes (e.g., via Hasse invariants or division polynomials, and related large-degree root-finding problems) currently seem to lead to exponential-time methods, leaving the core problem open.

Calendario Generale:

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