Paper 2021/1130
A note on group membership tests for $\G_1$, $\G_2$ and $\G_T$ on BLS pairing-friendly curves
Abstract
Here we consider a method for quickly testing for group membership in the groups $\G_1$, $\G_2$ and $\G_T$ (all of prime order $r$) as they arise on a type-3 pairing-friendly curve. As is well known endomorphisms exist for each of these groups which allows for faster point multiplication for elements of order $r$. The endomorphism applies if an element is of order $r$. Here we show that, under relatively mild conditions, the endomorphism applies {\bf if and only if} an element is of order $r$. This results in a faster method of confirming group membership. In particular we show that the conditions are met for the popular BLS family of curves.
Note: Fixed typo. Added observation on G2
Metadata
- Available format(s)
-
PDF
- Category
- Implementation
- Publication info
- Preprint.
- Keywords
- Pairing-based cryptography
- Contact author(s)
- michael scott @ tii ae
- History
- 2022-10-01: last of 3 revisions
- 2021-09-06: received
- See all versions
- Short URL
- https://ia.cr/2021/1130
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2021/1130,
author = {Michael Scott},
title = {A note on group membership tests for $\G_1$, $\G_2$ and $\G_T$ on {BLS} pairing-friendly curves},
howpublished = {Cryptology {ePrint} Archive, Paper 2021/1130},
year = {2021},
url = {https://eprint.iacr.org/2021/1130}
}
