Paper 2021/1130
A note on group membership tests for $\G_1$, $\G_2$ and $\G_T$ on BLS pairing-friendly curves
Michael Scott
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: Some further simplification. Proper latex rendering of point-at infinity
Metadata
- Available format(s)
- Category
- Implementation
- Publication info
- Preprint. MINOR revision.
- 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