Article

Generalizing Homomorphic MACs for Arithmetic Circuits

Authors:

Dario Catalano,

Rosario Gennaro,

Luca NizzardoAuthors Info & Claims

Proceedings of the 17th International Conference on Public-Key Cryptography --- PKC 2014 - Volume 8383

Pages 538 - 555

https://doi.org/10.1007/978-3-642-54631-0_31

Published: 26 March 2014 Publication History

Abstract

Homomorphic MACs, introduced by Gennaro and Wichs in 2013, allow anyone to validate computations on authenticated data without knowledge of the secret key.Moreover, the secret-key owner can verify the validity of the computation without needing to know the original authenticated inputs. Beyond security, homomorphic MACs are required to produce short tags succinctness and to support composability i.e., outputs of authenticated computations should be re-usable as inputs for new computations.

At Eurocrypt 2013, Catalano and Fiore proposed two realizations of homomorphic MACs that support a restricted class of computations arithmetic circuits of polynomial degree, are practically efficient, but fail to achieve both succinctness and composability at the same time.

In this paper, we generalize the work of Catalano and Fiore in several ways. First, we abstract away their results using the notion of encodings with limited malleability, thus yielding new schemes based on different algebraic settings. Next, we generalize their constructions to work with graded encodings, and more abstractly with k-linear groups. The main advantage of this latter approach is that it allows for homomorphic MACs which are somewhat composable while retaining succinctness. Interestingly, our construction uses graded encodings in a generic way. Thus, all its limitations limited composability and non-constant size of the tags solely depend on the fact that currently known multilinear maps share similar constraints. This means, for instance, that our scheme would support arbitrary circuits polynomial depth if we had compact multilinear maps with an exponential number of levels.

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Feng SXu SZhang LSuga YSakurai KDing XSako K(2022)Multi-Key Homomorphic MACs with Efficient Verification for Quadratic Arithmetic CircuitsProceedings of the 2022 ACM on Asia Conference on Computer and Communications Security10.1145/3488932.3497770(17-27)Online publication date: 30-May-2022
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Catalano DFiore D(2018)Practical Homomorphic Message Authenticators for Arithmetic CircuitsJournal of Cryptology10.1007/s00145-016-9249-131:1(23-59)Online publication date: 1-Jan-2018
https://dl.acm.org/doi/10.1007/s00145-016-9249-1
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Index Terms

Generalizing Homomorphic MACs for Arithmetic Circuits
1. Security and privacy
  1. Cryptography
2. Theory of computation
  1. Design and analysis of algorithms

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

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cover image Guide Proceedings

Proceedings of the 17th International Conference on Public-Key Cryptography --- PKC 2014 - Volume 8383

March 2014

684 pages

ISBN:9783642546303

Editor:
Hugo Krawczyk
IBM Research, USA

Publisher

Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 26 March 2014

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Cited By

Feng SXu SZhang LSuga YSakurai KDing XSako K(2022)Multi-Key Homomorphic MACs with Efficient Verification for Quadratic Arithmetic CircuitsProceedings of the 2022 ACM on Asia Conference on Computer and Communications Security10.1145/3488932.3497770(17-27)Online publication date: 30-May-2022
https://dl.acm.org/doi/10.1145/3488932.3497770
Xie DYang HQin JMa J(2019)Privacy-Preserving and Publicly Verifiable Protocol for Outsourcing Polynomials Evaluation to a Malicious CloudInternational Journal of Digital Crime and Forensics10.4018/IJDCF.201910010211:4(14-27)Online publication date: 1-Oct-2019
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Catalano DFiore D(2018)Practical Homomorphic Message Authenticators for Arithmetic CircuitsJournal of Cryptology10.1007/s00145-016-9249-131:1(23-59)Online publication date: 1-Jan-2018
https://dl.acm.org/doi/10.1007/s00145-016-9249-1
Kim SWu D(2018)Multi-Theorem Preprocessing NIZKs from LatticesAdvances in Cryptology – CRYPTO 201810.1007/978-3-319-96881-0_25(733-765)Online publication date: 19-Aug-2018
https://dl.acm.org/doi/10.1007/978-3-319-96881-0_25
Li SWang XZhang R(2018)Privacy-Preserving Homomorphic MACs with Efficient VerificationWeb Services – ICWS 201810.1007/978-3-319-94289-6_7(100-115)Online publication date: 25-Jun-2018
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Catalano DFiore DNizzardo L(2018)On the Security Notions for Homomorphic SignaturesApplied Cryptography and Network Security10.1007/978-3-319-93387-0_10(183-201)Online publication date: 2-Jul-2018
https://dl.acm.org/doi/10.1007/978-3-319-93387-0_10
Tran NPang HDeng RChen XWang XHuang X(2016)Efficient Verifiable Computation of Linear and Quadratic Functions over Encrypted DataProceedings of the 11th ACM on Asia Conference on Computer and Communications Security10.1145/2897845.2897892(605-616)Online publication date: 30-May-2016
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Fiore DMitrokotsa ANizzardo LPagnin E(2016)Multi-key Homomorphic AuthenticatorsProceedings, Part II, of the 22nd International Conference on Advances in Cryptology --- ASIACRYPT 2016 - Volume 1003210.1007/978-3-662-53890-6_17(499-530)Online publication date: 4-Dec-2016
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Catalano DRaimondo MFaro S(2016)Verifiable Pattern Matching on Outsourced TextsProceedings of the 10th International Conference on Security and Cryptography for Networks - Volume 984110.1007/978-3-319-44618-9_18(333-350)Online publication date: 31-Aug-2016
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Gorbunov SVaikuntanathan VWichs DServedio RRubinfeld R(2015)Leveled Fully Homomorphic Signatures from Standard LatticesProceedings of the forty-seventh annual ACM symposium on Theory of Computing10.1145/2746539.2746576(469-477)Online publication date: 14-Jun-2015
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