Paper 2022/794
Generation of "independent" points on elliptic curves by means of Mordell--Weil lattices
Abstract
This article develops a novel method of generating "independent" points on an ordinary elliptic curve $E$ over a finite field. Such points are actively used in the Pedersen vector commitment scheme and its modifications. In particular, the new approach is relevant for Pasta curves (of $j$-invariant $0$), which are very popular in the given type of elliptic cryptography. These curves are defined over highly $2$-adic fields, hence successive generation of points via a hash function to $E$ is an expensive solution. Our method also satisfies the NUMS (Nothing Up My Sleeve) principle, but it works faster on average. More precisely, instead of finding each point separately in constant time, we suggest to sample several points at once with some probability.
Metadata
- Available format(s)
-
PDF
- Category
- Implementation
- Publication info
- Preprint.
- Keywords
- elliptic curves "independent" points isotrivial elliptic surfaces Mordell--Weil lattices vector commitment schemes
- Contact author(s)
- dimitri koshelev @ gmail com
- History
- 2022-07-22: last of 3 revisions
- 2022-06-20: received
- See all versions
- Short URL
- https://ia.cr/2022/794
- License
-
CC0
BibTeX
@misc{cryptoeprint:2022/794,
author = {Dmitrii Koshelev},
title = {Generation of "independent" points on elliptic curves by means of Mordell--Weil lattices},
howpublished = {Cryptology ePrint Archive, Paper 2022/794},
year = {2022},
note = {\url{https://eprint.iacr.org/2022/794}},
url = {https://eprint.iacr.org/2022/794}
}
