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  • Cet exposé a été présenté le 28 mars 2025 (13:45 - 14:45).

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  • Orateur

    Maria Corte-Real Santos - ENS Lyon

A promising avenue for realising scalable proof systems relies on the existence of 2-cycles of pairing-friendly elliptic curves. More specifically, such a cycle consists of two elliptic curves E/Fp and E’/Fq that both have a low embedding degree and also satisfy q = #E(Fp) and p = #E’(Fq). These constraints turn out to be rather restrictive; in the decade that has passed since 2-cycles were first proposed for use in proof systems, no new constructions of 2-cycles have been found. 

In this talk, we present joint work with Costello and Naehrig, where we generalise the notion of cycles of pairing-friendly elliptic curves to study cycles of pairing-friendly abelian varieties, with a view towards realising more efficient pairing-based SNARKs. We show that considering abelian varieties of dimension larger than 1 unlocks a number of interesting possibilities for finding pairing-friendly cycles, and we give several new constructions that can be instantiated at any security level.


 

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