On cycles of pairing-friendly abelian varieties

Maria Corte-Real Santos; Craig Costello; Michael Naehrig

Paper 2024/869 Original: eprint.iacr.org/2024/869 ↗

On cycles of pairing-friendly abelian varieties

Maria Corte-Real Santos

Craig Costello

Michael Naehrig

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.

Metadata

Available format(s): PDF
Category: Foundations
Publication info: Preprint.
History: 2024-06-01: last updated; 2024-06-01: published
Short URL: https://ia.cr/2024/869
License: https://creativecommons.org/publicdomain/zero/1.0/

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}
}