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Applicable Algebra in Engineering, Communication and Computing
Published in: Applicable Algebra in Engineering, Communication and Computing 1/2018

05-06-2017 | Original Paper

Verifiability-based conversion from CPA to CCA-secure predicate encryption

Authors: Mridul Nandi, Tapas Pandit

Published in: Applicable Algebra in Engineering, Communication and Computing | Issue 1/2018

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Abstract

Predicate encryption (PE), a generalization of attribute-based encryption (ABE), is a versatile tool for providing access control over data. The underlying predicate for a PE is parametrized by an index, called system parameter or simply system-index. A system-index, in general, consists of component(s) from \(\mathbb {N}\). Yamada et al. in PKC 2011 proposed a verifiability-based conversion from CPA to CCA-secure ABE. This conversion was generalized by Yamada et al. in PKC 2012 from ABE to PE. In the later conversion, the authors considered the system-index to be a single component. In practice, there are many schemes, e.g., functional encryption for general relations and hierarchical-inner product (HIP) encryption schemes of Okamoto-Takashima in CRYPTO 2010, CANS 2011 and EUROCRYPT 2012, where system-indices consist of more than a single component. Therefore, for these schemes, the conversion of Yamada et al. (in PKC, 2012) is out of scope. In this paper, we revisit the CPA to CCA conversion for PE and propose a new conversion based on verifiability. The proposed conversion works irrespective of the number of components in the system-indices. It generalizes the existing conversion of Yamada et al. (in PKC, 2011) from ABE to PE. The PE schemes which are realized by the conversion of Yamada et al. (2011) are also realized by our conversion. Therefore, the conversion of ours has more scope than the conversion proposed in 2012. We show that all the aforementioned CPA-secure schemes for general relations and HIP relation are easily converted to the corresponding CCA-secure schemes by our conversion. Further, we show a generic conversion from CPA to CCA-secure functional encryption for regular languages which captures the existing PE schemes for regular languages.
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Appendix
Available only for authorised users
Footnotes
1
A PE with public index hides only the message, whereas a PE with hidden index conceals both the message and the data-index.
 
2
These are 2-threshold gates, one may consider general threshold gates, e.g., t-threshold gates.
 
3
\(\mathcal {T}_0\) maps the system-index \(\varvec{j}\) of \(\mathsf{PE}\) to the system-index \(\varvec{j}'\) of \(\mathsf{PE}'\). However, we omit the technical details of \(\mathcal {T}_0\) throughout this chapter as it does not harm in understanding the actual conversion.
 
4
The ABE schemes [17] for circuits are not known to have either public verifiability or verifiability-1. So, the CCA-secure realization of the schemes is still unknown. We remark that if there is an efficient algorithm for testing the group membership of the underlying multilinear maps [16], then one can have the public verifiability using the property of the multilinear maps.
 
5
If \(0,1\in \varSigma \), then consider two special symbols say \(\tilde{\sigma }_0, \tilde{\sigma }_1\) such that \(\tilde{\sigma }_0, \tilde{\sigma }_1 \not \in \varSigma \) and set \(\varSigma ' := \varSigma \cup \{\tilde{\sigma }_0, \tilde{\sigma }_1\}\) and \(\mathsf{Tr}'\) is replaced by \(\mathsf{Tr}' := \mathsf{Tr}\cup \{(q'_{i-1}, q'_i, \tilde{\sigma }_{\mathsf{vk}[i]})\ :\ i\in [n]\}\)
 
6
A decrypt query on \((\mathsf{CT}, x)\) is called valid if its returned value is not \(\perp \). We note that for a decrypt query \((\mathsf{CT}, x)\) of the form \((\mathsf{CT}= \mathsf{CT}^*\wedge x\thicksim y)\) or https://static-content.springer.com/image/art%3A10.1007%2Fs00200-017-0330-2/MediaObjects/200_2017_330_IEq767_HTML.gif , the simulator always returns \(\perp \).
 
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Metadata
Title
Verifiability-based conversion from CPA to CCA-secure predicate encryption
Authors
Mridul Nandi
Tapas Pandit
Publication date
05-06-2017
Publisher
Springer Berlin Heidelberg
Published in
Applicable Algebra in Engineering, Communication and Computing / Issue 1/2018
Print ISSN: 0938-1279
Electronic ISSN: 1432-0622
DOI
https://doi.org/10.1007/s00200-017-0330-2

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