Paper 2024/869
On cycles of pairing-friendly abelian varieties
, University College London, Microsoft ResearchAbstract
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.
Metadata
- Available format(s)
-
PDF
- Category
- Foundations
- Publication info
- Published by the IACR in CRYPTO 2024
- Keywords
- Zero-knowledge proofsSNARKsrecursive proof compositionabelian varietiessupersingular curves
- Contact author(s)
-
maria santos 20 @ ucl ac uk
craigco @ microsoft com
mnaehrig @ microsoft com - History
- 2024-06-05: approved
- 2024-06-01: received
- See all versions
- Short URL
- https://ia.cr/2024/869
- License
-
CC0
BibTeX
@misc{cryptoeprint:2024/869,
author = {Maria Corte-Real Santos and Craig Costello and Michael Naehrig},
title = {On cycles of pairing-friendly abelian varieties},
howpublished = {Cryptology {ePrint} Archive, Paper 2024/869},
year = {2024},
url = {https://eprint.iacr.org/2024/869}
}
