### 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.

Available format(s)
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
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Short URL
https://ia.cr/2022/794

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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}
}

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