Paper 2024/1697
On pairing-friendly 2-cycles and SNARK-friendly 2-chains of elliptic curves containing a curve from a prime-order family
, RWTH Aachen UniversityAbstract
Cryptographic protocols such as zkSNARKs 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 curve cannot be pairing-friendly. For other curve families, we have a similar result for cryptographically attractive field sizes. 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 the (MNT4, MNT6) chains.
Metadata
- Available format(s)
-
PDF
- Category
- Foundations
- Publication info
- Preprint.
- Keywords
- zkSNARKsCycles of elliptic curvesChains of elliptic curvesPairing-friendly curves
- Contact author(s)
- tomas novotny @ rwth-aachen de
- History
- 2024-10-18: approved
- 2024-10-17: received
- See all versions
- Short URL
- https://ia.cr/2024/1697
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2024/1697,
author = {Tomáš Novotný},
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}
}
