article

Pairings for cryptographers

Authors:

Steven D. Galbraith,

Kenneth G. Paterson,

Nigel P. SmartAuthors Info & Claims

Discrete Applied Mathematics, Volume 156, Issue 16

Pages 3113 - 3121

https://doi.org/10.1016/j.dam.2007.12.010

Published: 01 September 2008 Publication History

Abstract

Many research papers in pairing-based cryptography treat pairings as a ''black box''. These papers build cryptographic schemes making use of various properties of pairings. If this approach is taken, then it is easy for authors to make invalid assumptions concerning the properties of pairings. The cryptographic schemes developed may not be realizable in practice, or may not be as efficient as the authors assume. The aim of this paper is to outline, in as simple a fashion as possible, the basic choices that are available when using pairings in cryptography. For each choice, the main properties and efficiency issues are summarized. The paper is intended to be of use to non-specialists who are interested in using pairings to design cryptographic schemes.

References

[1]

Barreto, P.S.L.M., Galbraith, S.D., O'Eigeartaigh, C. and Scott, M., Efficient pairing computation on supersingular Abelian varieties. Des. Codes Cryptogr. v42. 239-271.

[2]

In: Blake, I., Seroussi, G., Smart, N.P. (Eds.), Advances in Elliptic Curve Cryptography, Cambridge University Press.

[3]

Boneh, D. and Boyen, X., Efficient selective-ID secure identity-based encryption without random oracles. In: LNCS, vol. 3027. Springer-Verlag. pp. 223-238.

Digital Library

[4]

Boneh, D., Boyen, X. and Shacham, H., Short group signatures. In: LNCS, vol. 3152. Springer-Verlag. pp. 41-55.

Digital Library

[5]

Boneh, D. and Franklin, M., Identity-based encryption from the Weil pairing. In: LNCS, vol. 2139. Springer-Verlag. pp. 213-229.

Digital Library

[6]

Boneh, D., Lynn, B. and Shacham, H., Short signatures from the Weil pairing. J. Cryptology. v17. 297-319.

[7]

Boneh, D. and Shacham, H., Group signatures with verifier-local revocation. In: ACM CCS 2004, ACM Press. pp. 168-177.

Digital Library

[8]

Chen, L., Cheng, Z., Malone-Lee, J. and Smart, N.P., An efficient ID-KEM based on the Sakai-Kasahara key construction. IEE Proceedings, Information Security. v153. 19-26.

[9]

Chen, L., Cheng, Z. and Smart, N.P., Identity-based key agreement protocols from pairings. Int. J. Inf. Secur. v6. 213-242.

Digital Library

[10]

D. Freeman, M. Scott, E. Teske, A taxonomy of pairing-friendly elliptic curves, preprint 2006

[11]

Hess, F., Smart, N.P. and Vercauteren, F., The Eta pairing revisited. IEEE Trans. Inform. Theory. v52. 4595-4602.

[12]

Joux, A., A one round protocol for tripartite Diffie-Hellman. In: LNCS, vol. 1838. Springer-Verlag. pp. 385-394.

Digital Library

[13]

Lenstra, A.K., Key lengths. In: Handbook of Information Security, vol. 2, Wiley. pp. 617-635.

[14]

Luca, F. and Shparlinski, I., Elliptic curves with low embedding degree. J. Cryptology. v19. 553-562.

[15]

R. Sakai, K. Ohgishi, M. Kasahara, Cryptosystems based on pairing, in: The 2000 Symposium on Cryptography and Information Security, Okinawa, Japan, January 2000

[16]

R. Sakai, K. Ohgishi, M. Kasahara, Cryptosystems based on pairing over elliptic curve (in Japanese), in: The 2001 Symposium on Cryptography and Information Security, Oiso, Japan, January 2001

[17]

R. Sakai, M. Kasahara, ID based cryptosystems with pairing on elliptic curve, Cryptology ePrint Archive, Report 2003/054, 2003

[18]

H. Shacham, New paradigms in signature schemes, Ph.D. Thesis, Stanford, 2005

[19]

Smart, N.P. and Vercauteren, F., On computable isomorphisms in efficient pairing based systems. Discrete Appl. Math. v155. 538-547.

[20]

NIST Recommendation for Key Management Part 1: General, NIST Special Publication 800-57. August, 2005. Available from http://csrc.nist.gov/publications/nistpubs/800-57/SP800-57-Part1.pdf

[21]

ECRYPT Yearly Report on Algorithms and Keysizes (2004), March 2005. Available from http://www.ecrypt.eu.org/documents/D.SPA.10-1.1.pdf

Cited By

Zhang ZHuang YHuang WLiao YZhou S(2024)A Fully Auditable Data Propagation Scheme With Dynamic Vehicle Management for EC-ITSIEEE Transactions on Intelligent Transportation Systems10.1109/TITS.2024.335498425:7(7861-7877)Online publication date: 1-Jul-2024
https://dl.acm.org/doi/10.1109/TITS.2024.3354984
Shi RYang YLi YFeng HPang HDeng R(2024)AnoPasJournal of Systems Architecture: the EUROMICRO Journal10.1016/j.sysarc.2024.103184153:COnline publication date: 1-Aug-2024
https://dl.acm.org/doi/10.1016/j.sysarc.2024.103184
Liu JQin JWang WMei LWang H(2024)Key-aggregate based access control encryption for flexible cloud data sharingComputer Standards & Interfaces10.1016/j.csi.2023.10380088:COnline publication date: 1-Mar-2024
https://dl.acm.org/doi/10.1016/j.csi.2023.103800
Show More Cited By

Index Terms

Pairings for cryptographers

Recommendations

Short designated verifier proxy signature from pairings
EUC'05: Proceedings of the 2005 international conference on Embedded and Ubiquitous Computing

In a designated verifier proxy signature scheme, the original signer delegates her/his signing capability to the proxy signer in such a way that the latter can sign messages on behalf of the former, but only the designated verifier can believe the ...
On security proof of McCullagh Barreto's key agreement protocol and its variants

McCullagh and Barreto presented an identity-based authenticated key agreement protocol in CT-RSA 2005. Their protocol was found to be vulnerable to a key-compromise impersonation attack. In order to recover the weakness, McCullagh and Barreto and Xie ...
A strongly secure identity-based authenticated key agreement protocol without pairings under the GDH assumption

Among the existing identity-based authenticated key agreement ID-AKA protocols, there are only a few of them that can resist to leakage of ephemeral secret keys, which is about the protection of the session secret key after the ephemeral secret keys of ...

Comments

Information & Contributors

Information

Published In

cover image Discrete Applied Mathematics

Discrete Applied Mathematics Volume 156, Issue 16

September, 2008

85 pages

ISSN:0166-218X

Issue’s Table of Contents

Copyright © Elsevier B.V. © 2008.

Publisher

Elsevier Science Publishers B. V.

Netherlands

Publication History

Published: 01 September 2008

Author Tags

Qualifiers

Article

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

215
Total Citations
View Citations
0
Total Downloads

Downloads (Last 12 months)0
Downloads (Last 6 weeks)0

Reflects downloads up to 03 Sep 2024

Other Metrics

View Author Metrics

Citations

Cited By

Zhang ZHuang YHuang WLiao YZhou S(2024)A Fully Auditable Data Propagation Scheme With Dynamic Vehicle Management for EC-ITSIEEE Transactions on Intelligent Transportation Systems10.1109/TITS.2024.335498425:7(7861-7877)Online publication date: 1-Jul-2024
https://dl.acm.org/doi/10.1109/TITS.2024.3354984
Shi RYang YLi YFeng HPang HDeng R(2024)AnoPasJournal of Systems Architecture: the EUROMICRO Journal10.1016/j.sysarc.2024.103184153:COnline publication date: 1-Aug-2024
https://dl.acm.org/doi/10.1016/j.sysarc.2024.103184
Liu JQin JWang WMei LWang H(2024)Key-aggregate based access control encryption for flexible cloud data sharingComputer Standards & Interfaces10.1016/j.csi.2023.10380088:COnline publication date: 1-Mar-2024
https://dl.acm.org/doi/10.1016/j.csi.2023.103800
Shahrouz JAnaloui M(2024)An anonymous authentication scheme with conditional privacy-preserving for Vehicular Ad hoc Networks based on zero-knowledge proof and BlockchainAd Hoc Networks10.1016/j.adhoc.2023.103349154:COnline publication date: 12-Apr-2024
https://dl.acm.org/doi/10.1016/j.adhoc.2023.103349
Khamseh EReza AEsterabadi A(2024)Lightweight Certificateless Signcryption Scheme Using Type-3 Pairing on Elliptic CurveWireless Personal Communications: An International Journal10.1007/s11277-024-11120-4135:3(1497-1517)Online publication date: 1-Apr-2024
https://dl.acm.org/doi/10.1007/s11277-024-11120-4
Li JMa HWang JSong ZXu WZhang R(2023)Wolverine: A Scalable and Transaction-Consistent Redactable Permissionless BlockchainIEEE Transactions on Information Forensics and Security10.1109/TIFS.2023.324540618(1653-1666)Online publication date: 1-Jan-2023
https://dl.acm.org/doi/10.1109/TIFS.2023.3245406
Liu JYang JWu WHuang XXiang Y(2023)Lightweight Authentication Scheme for Data Dissemination in Cloud-Assisted Healthcare IoTIEEE Transactions on Computers10.1109/TC.2022.320713872:5(1384-1395)Online publication date: 1-May-2023
https://dl.acm.org/doi/10.1109/TC.2022.3207138
He XLi LPeng H(2023)An enhanced traceable CP-ABE scheme against various types of privilege leakage in cloud storageJournal of Systems Architecture: the EUROMICRO Journal10.1016/j.sysarc.2023.102833136:COnline publication date: 1-Mar-2023
https://dl.acm.org/doi/10.1016/j.sysarc.2023.102833
Ni NZhu Y(2023)Enabling zero knowledge proof by accelerating zk-SNARK kernels on GPUJournal of Parallel and Distributed Computing10.1016/j.jpdc.2022.10.009173:C(20-31)Online publication date: 1-Mar-2023
https://dl.acm.org/doi/10.1016/j.jpdc.2022.10.009
Yang PLi HHuang JZhang HAu MHuang Q(2023)Secure channel free public key authenticated encryption with multi-keyword search on healthcare systemsFuture Generation Computer Systems10.1016/j.future.2023.03.002145:C(511-520)Online publication date: 1-Aug-2023
https://dl.acm.org/doi/10.1016/j.future.2023.03.002
Show More Cited By

View Options

View options

Get Access

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Full Access

Get this Publication

Media

Figures

Other

Tables

View Issue’s Table of Contents