Short signatures from the Weil pairing
type: Item
instance of: scholarly article
title: Short signatures from the Weil pairing
zbMATH Open document ID: 1070.94010
author: Dan Boneh
author: Ben Lynn
author: Hovav Shacham
published in: Journal of Cryptology
publication date: 2005-04-15T00:00:00Z
review text: In this article the authors introduce a new signature scheme based on the Weil pairing. The main feature of this new signature scheme is that it is shorter than other known schemes: following the authors, a 170 bit signature provides a level of security similar to that of the 320 bit DSA signature. The scheme is based on groups for which the computational Diffie-Hellman problem is hard, but the decisional Diffie-Hellman problem is easy. Such groups are called by the authors ``gap Diffie-Hellman'' (GDH) groups, and the main tools for constructing them are elliptic curves. For instance, explicit GDH groups arising from some families of elliptic curves are considered. To that end they define the ``security multiplier'', \(\alpha\) of a subgroup \(\langle P \rangle\) of \(E({\mathbb F}_q)\). If \(\alpha>1\) they take \(G^1=\langle P \rangle\), \(G^2=\langle Q \rangle\), for suitable \(P\) and \(Q\), and use the Weil pairing to obtain a GDH group. Explicit families of curves with \(\alpha=6\) are described. Constructing elliptic curves having a given security multiplier \(\alpha\) remains as an open problem.
reviewed by: Carlos Munuera
Mathematics Subject Classification ID: 94A62
Mathematics Subject Classification ID: 11T71
Mathematics Subject Classification ID: 14G50
zbMATH DE Number: 2157503
zbMATH Keywords: digital signatures
zbMATH Keywords: elliptic curves
zbMATH Keywords: pairings
Wikidata QID: Q60961118
MaRDI profile type: Publication
full work available at URL: s00145-004-0314-9
OpenAlex ID: W2014239329
DOI: 10.1007/S00145-004-0314-9
description: scientific article; zbMATH DE number 2157503