Trapdoor DDH groups from pairings and isogenies

Péter Kutas; Christophe Petit; Javier Silva

Paper 2019/1290

Trapdoor DDH groups from pairings and isogenies

Péter Kutas, Christophe Petit, and Javier Silva

Abstract

Trapdoor DDH groups are an appealing cryptographic primitive where DDH instances are hard to solve unless provided with additional information (i.e., a trapdoor). In this paper, we introduce a new trapdoor DDH group construction using pairings and isogenies of supersingular elliptic curves. The construction solves all shortcomings of previous constructions as identified by Seurin (RSA 2013). We also present partial attacks on a previous construction due to Dent--Galbraith, and we provide a formal security definition of the related notion of ``trapdoor pairings''.

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Published elsewhere. Minor revision. SAC 2020
Keywords: elliptic curve cryptography pairings isogenies trapdoor DDH
Contact author(s): christophe f petit @ gmail com
kutasp @ gmail com
javiersilvavelon @ gmail com
History: 2020-11-27: revised; 2019-11-07: received; See all versions
Short URL: https://ia.cr/2019/1290
License: CC BY

BibTeX

@misc{cryptoeprint:2019/1290,
      author = {Péter Kutas and Christophe Petit and Javier Silva},
      title = {Trapdoor {DDH} groups from pairings and isogenies},
      howpublished = {Cryptology {ePrint} Archive, Paper 2019/1290},
      year = {2019},
      url = {https://eprint.iacr.org/2019/1290}
}