Article

Optimal authenticated data structures with multilinear forms

Authors:

Charalampos Papamanthou,

Roberto Tamassia,

Nikos TriandopoulosAuthors Info & Claims

Pairing'10: Proceedings of the 4th international conference on Pairing-based cryptography

Pages 246 - 264

Published: 13 December 2010 Publication History

Abstract

Cloud computing and cloud storage are becoming increasingly prevalent. In this paradigm, clients outsource their data and computations to third-party service providers. Data integrity in the cloud therefore becomes an important factor for the functionality of these web services. Authenticated data structures, implemented with various cryptographic primitives, have been widely studied as a means of providing efficient solutions to data integrity problems (e.g., Merkle trees). In this paper, we introduce a new authenticated dictionary data structure that employs multilinear forms, a cryptographic primitive proposed by Silverberg and Boneh in 2003 [10], the construction of which, however, remains an open problem to date. Our authenticated dictionary is optimal, that is, it does not add any extra asymptotic cost to the plain dictionary data structure, yielding proofs of constant size, i.e., asymptotically equal to the size of the answer, while maintaining other relevant complexities logarithmic. Instead, solutions based on cryptographic hashing (e.g., Merkle trees) require proofs of logarithmic size [40]. Because multilinear forms are not known to exist yet, our result can be viewed from a different angle: if one could prove that optimal authenticated dictionaries cannot exist in the computational model, irrespectively of cryptographic primitives, then our solution would imply that cryptographically interesting multilinear form generators cannot exist as well (i.e., it can be viewed as a reduction). Thus, we provide an alternative avenue towards proving the nonexistence of multilinear form generators in the context of general lower bounds for authenticated data structures [40] and for memory checking [18], a model similar to the authenticated data structures model.

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Cited By

Albrecht MFarshim PHofheinz DLarraia EPaterson K(2016)Multilinear Maps from ObfuscationProceedings, Part I, of the 13th International Conference on Theory of Cryptography - Volume 956210.1007/978-3-662-49096-9_19(446-473)Online publication date: 10-Jan-2016
https://dl.acm.org/doi/10.1007/978-3-662-49096-9_19
Zhang LSafavi-Naini REmura KHanaoka GZhao Y(2014)Generalized homomorphic MACs with efficient verificationProceedings of the 2nd ACM workshop on ASIA public-key cryptography10.1145/2600694.2600697(3-12)Online publication date: 3-Jun-2014
https://dl.acm.org/doi/10.1145/2600694.2600697
Zhang LSafavi-Naini R(2013)Private Outsourcing of Polynomial Evaluation and Matrix Multiplication Using Multilinear MapsProceedings of the 12th International Conference on Cryptology and Network Security - Volume 825710.1007/978-3-319-02937-5_18(329-348)Online publication date: 20-Nov-2013
https://dl.acm.org/doi/10.1007/978-3-319-02937-5_18
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Index Terms

Optimal authenticated data structures with multilinear forms
1. Security and privacy
  1. Cryptography
2. Theory of computation
  1. Computational complexity and cryptography

Index terms have been assigned to the content through auto-classification.

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Published In

cover image Guide Proceedings

Pairing'10: Proceedings of the 4th international conference on Pairing-based cryptography

December 2010

466 pages

ISBN:364217454X

Editors:
Marc Joye
Technicolor, Security and Content Protection Labs, Cesson-Sévigné Cedex, France
,
Atsuko Miyaji
Japan Advanced Institute of Science and Technology, Nomi, Ishikawa, Japan
,
Akira Otsuka
National Institute of Advanced Industrial Science and Technoloy, Tokyo, Japan

Sponsors

NICT: National Institute of Information and Communications Technology
Voltage Security: Voltage Security
Hitachi
National Institute of Advanced Industrial Science and Technology
NTT

Publisher

Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 13 December 2010

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Cited By

Albrecht MFarshim PHofheinz DLarraia EPaterson K(2016)Multilinear Maps from ObfuscationProceedings, Part I, of the 13th International Conference on Theory of Cryptography - Volume 956210.1007/978-3-662-49096-9_19(446-473)Online publication date: 10-Jan-2016
https://dl.acm.org/doi/10.1007/978-3-662-49096-9_19
Zhang LSafavi-Naini REmura KHanaoka GZhao Y(2014)Generalized homomorphic MACs with efficient verificationProceedings of the 2nd ACM workshop on ASIA public-key cryptography10.1145/2600694.2600697(3-12)Online publication date: 3-Jun-2014
https://dl.acm.org/doi/10.1145/2600694.2600697
Zhang LSafavi-Naini R(2013)Private Outsourcing of Polynomial Evaluation and Matrix Multiplication Using Multilinear MapsProceedings of the 12th International Conference on Cryptology and Network Security - Volume 825710.1007/978-3-319-02937-5_18(329-348)Online publication date: 20-Nov-2013
https://dl.acm.org/doi/10.1007/978-3-319-02937-5_18
Hess F(2012)Generalised jacobians in cryptography and coding theoryProceedings of the 4th international conference on Arithmetic of Finite Fields10.1007/978-3-642-31662-3_1(1-15)Online publication date: 16-Jul-2012
https://dl.acm.org/doi/10.1007/978-3-642-31662-3_1
Papamanthou CTamassia RTriandopoulos N(2011)Optimal verification of operations on dynamic setsProceedings of the 31st annual conference on Advances in cryptology10.5555/2033036.2033045(91-110)Online publication date: 14-Aug-2011
https://dl.acm.org/doi/10.5555/2033036.2033045

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