Paper 2024/1697 Original: eprint.iacr.org/2024/1697 ↗
On pairing-friendly 2-cycles and SNARK-friendly 2-chains of elliptic curves containing a curve from a prime-order family
Abstract
Cryptographic protocols such as zk-SNARKs use 2-cycles of~elliptic curves for efficiency, often relying on pairing computations. However, 2-cycles of~pairing-friendly curves are hard to find, and the only known cases consist of~an MNT4 and an MNT6 curve. In this work, we prove that a~2-cycle containing an MNT3, Freeman, or BN curve cannot be pairing-friendly. Thus we cannot hope to find new pairing-friendly 2-cycles using the current methods. Furthermore, we show that there are no SNARK-friendly 2-chains of elliptic curves from combinations of MNT, Freeman and BN curves of reasonable size, except for (MNT4, MNT6).
Metadata
- Available format(s)
PDF- Category
- Foundations
- Publication info
- Preprint.
- History
- 2025-04-22: last updated
- 2024-10-17: published
- Short URL
- https://ia.cr/2024/1697
- License
- https://creativecommons.org/licenses/by/4.0/
BibTeX
@misc{cryptoeprint:2024/1697,
author = {Tomáš Novotný and Vladimír Sedláček},
title = {On pairing-friendly 2-cycles and SNARK-friendly 2-chains of elliptic curves containing a curve from a prime-order family},
howpublished = {Cryptology {ePrint} Archive, Paper 2024/1697},
year = {2024},
url = {https://eprint.iacr.org/2024/1697}
}