Paper 2021/130
Ready-Made Short Basis for GLV+GLS on High Degree Twisted Curves
Bei Wang, Songsong Li, Yi Ouyang, and Honggang Hu
Abstract
The crucial step in elliptic curve scalar multiplication based on scalar decompositions using efficient endomorphisms—such as GLV, GLS or GLV+GLS—is to produce a short basis of a lattice involving the eigenvalues of the endomorphisms, which usually is obtained by lattice basis reduction algorithms or even more specialized algorithms. Recently, lattice basis reduction is found to be unnecessary. Benjamin Smith (AMS 2015) was able to immediately write down a short basis of the lattice for the GLV, GLS, GLV+GLS of quadratic twists using elementary facts about quadratic rings. Certainly it is always more convenient to use a ready-made short basis than to compute a new one by some algorithm. In this paper, we extend Smith's method on GLV+GLS for quadratic twists to quartic and sextic twists, and give ready-made short bases for $4$-dimensional decompositions on these high degree twisted curves. In particular, our method gives a unified short basis compared with Hu et. al's method (DCC 2012) for $4$-dimensional decompositions on sextic twisted curves.
Metadata
- Available format(s)
-
PDF
- Category
- Public-key cryptography
- Publication info
- Preprint. MINOR revision.
- Keywords
- EndomorphismReady-made short basisTwistGLV+GLS
- Contact author(s)
- wangbei @ mail ustc edu cn
- History
- 2021-03-04: last of 3 revisions
- 2021-02-05: received
- See all versions
- Short URL
- https://ia.cr/2021/130
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2021/130,
author = {Bei Wang and Songsong Li and Yi Ouyang and Honggang Hu},
title = {Ready-Made Short Basis for {GLV}+{GLS} on High Degree Twisted Curves},
howpublished = {Cryptology {ePrint} Archive, Paper 2021/130},
year = {2021},
url = {https://eprint.iacr.org/2021/130}
}
