International Association for Cryptologic Research

International Association
for Cryptologic Research

CryptoDB

On cycles of pairing-friendly abelian varieties

Authors:
Maria Corte-Real Santos , University College London
Craig Costello , Microsoft Research
Michael Naehrig , Microsoft Research
Download:
DOI: 10.1007/978-3-031-68400-5_7 (login may be required)
Search ePrint
Search Google
Presentation: Slides
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
}