Paper 2022/1662
Revisiting cycles of pairing-friendly elliptic curves
, Dusk Network, Pompeu Fabra UniversityAbstract
A recent area of interest in cryptography is recursive composition of proof systems. One of the approaches to make recursive composition efficient involves cycles of pairing-friendly elliptic curves of prime order. However, known constructions have very low embedding degrees. This entails large parameter sizes, which makes the overall system inefficient. In this paper, we explore $2$-cycles composed of curves from families parameterized by polynomials, and show that such cycles do not exist unless a strong condition holds. As a consequence, we prove that no $2$-cycles can arise from the known families, except for those cycles already known. Additionally, we show some general properties about cycles, and provide a detailed computation on the density of pairing-friendly cycles among all cycles.
Metadata
- Available format(s)
-
PDF
- Category
- Public-key cryptography
- Publication info
- Preprint.
- Keywords
- elliptic curvespairing-friendly curveszero-knowledge proofsrecursive composition
- Contact author(s)
-
marta @ dusk network
jorge urroz @ upc edu
javier @ dusk network - History
- 2023-05-26: last of 3 revisions
- 2022-11-29: received
- See all versions
- Short URL
- https://ia.cr/2022/1662
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2022/1662,
author = {Marta Bellés-Muñoz and Jorge Jiménez Urroz and Javier Silva},
title = {Revisiting cycles of pairing-friendly elliptic curves},
howpublished = {Cryptology {ePrint} Archive, Paper 2022/1662},
year = {2022},
url = {https://eprint.iacr.org/2022/1662}
}
