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

Dmitrii Koshelev

Paper 2020/969

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

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.

Metadata

Available format(s): PDF
Category: Implementation
Publication info: Preprint. MINOR revision.
Keywords: Barreto--Naehrig curves constant-time implementation hashing to elliptic curves Kummer surfaces pairing-based cryptography quadratic imaginary orders rational curves and their parametrization vertical isogenies
Contact author(s): dishport @ yandex ru
History: 2021-08-08: last of 7 revisions; 2020-08-18: received; See all versions
Short URL: https://ia.cr/2020/969
License: CC BY

BibTeX

@misc{cryptoeprint:2020/969,
      author = {Dmitrii Koshelev},
      title = {Hashing to elliptic curves of $j=0$ and quadratic imaginary orders of class number $2$},
      howpublished = {Cryptology {ePrint} Archive, Paper 2020/969},
      year = {2020},
      url = {https://eprint.iacr.org/2020/969}
}