[Resource Topic] 2020/969: Hashing to elliptic curves of $j=0$ and quadratic imaginary orders of class number $2$

Resource Implementation
#1

Welcome to the resource topic for 2020/969

Title:
Hashing to elliptic curves of j=0 and quadratic imaginary orders of class number 2

Authors: Dmitrii Koshelev

Abstract:

In this article we produce the simplified SWU encoding to some Barreto–Naehrig curves, including BN512, BN638 from the standards ISO/IEC 15946-5 and TCG Algorithm Registry respectively. Moreover, we show (for any j-invariant) how to implement the simplified SWU encoding in constant time of one exponentiation in the basic field, namely without quadratic residuosity tests and inversions. Thus in addition to the protection against timing attacks, the new encoding turns out to be much more efficient than the (universal) SWU encoding, which generally requires to perform two quadratic residuosity tests.

ePrint: https://eprint.iacr.org/2020/969

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 .