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On cycles of pairing-friendly abelian varieties
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| Conference: | CRYPTO 2024 |
| Abstract: | One of the most promising avenues for realizing scalable proof systems relies on the existence of 2-cycles of pairing-friendly elliptic curves. Such a cycle consists of two elliptic curves E/GF(p) and E'/GF(q) that both have a low embedding degree and also satisfy q = #E and p = #E'. 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 paper, we generalize the notion of cycles of pairing-friendly elliptic curves to study cycles of pairing-friendly abelian varieties, with a view towards realizing 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. |
BibTeX
@inproceedings{crypto-2024-34288,
title={On cycles of pairing-friendly abelian varieties},
publisher={Springer-Verlag},
doi={10.1007/978-3-031-68400-5_7},
author={Maria Corte-Real Santos and Craig Costello and Michael Naehrig},
year=2024
}