[Resource Topic] 2021/130: Ready-Made Short Basis for GLV+GLS on High Degree Twisted Curves

Welcome to the resource topic for 2021/130

Ready-Made Short Basis for GLV+GLS on High Degree Twisted Curves

Authors: Bei Wang, Songsong Li, Yi Ouyang, Honggang Hu


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.

ePrint: https://eprint.iacr.org/2021/130

See all topics related to this paper.

Feel free to post resources that are related to this paper below.

Example resources include: implementations, explanation materials, talks, slides, links to previous discussions on other websites.

For more information, see the rules for Resource Topics .