On pairing-friendly 2-cycles and SNARK-friendly 2-chains of elliptic curves containing a curve from a prime-order family

Tomáš Novotný; Vladimír Sedláček

Paper 2024/1697

On pairing-friendly 2-cycles and SNARK-friendly 2-chains of elliptic curves containing a curve from a prime-order family

Tomáš Novotný

, RWTH Aachen University

Vladimír Sedláček

, Masaryk University

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.
Keywords: Cycles of elliptic curves chains of elliptic curves pairing-friendly curves
Contact author(s): tomas novotny @ rwth-aachen de
vlada sedlacek @ mail muni cz
History: 2025-04-22: revised; 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 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}
}