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2017 | OriginalPaper | Buchkapitel

Tightly-Secure Encryption in the Multi-user, Multi-challenge Setting with Improved Efficiency

verfasst von : Puwen Wei, Wei Wang, Bingxin Zhu, Siu Ming Yiu

Erschienen in: Information Security and Privacy

Verlag: Springer International Publishing

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Abstract

We construct a compact public-key encryption with tight CCA security in the multi-user, multi-challenge setting, where the reduction loss is a constant. Our scheme follows the Hofheinz-Jager framework but is compressed in the sense that only one of the underlying two-tier signatures needs to be committed. Considering the virtually unbounded simulations, e.g., \(2^{80}\), the ciphertext size of our scheme decreases to about 256 group elements, whereas the best known solution provided by Blazy et al. required about 625 group elements under the same standard assumptions. In particular, we formalize a new notion called simulatable two-tier signature, which plays a central role in the construction of our tree-based signature and public-key encryption. Combining simulatable two-tier signatures with additional “ephemeral” signatures, we provide a method of constructing commitments to a tree-based signature, where most parts of the tree-based signature can be simulated and sent in the clear. Our method can reduce the length of the commitments and the related proofs of knowledge in previous works by 60%.

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Nächstes Kapitel Hierarchical Functional Encryption for Linear Transformations

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The concrete ciphertext size of PKE in [10] is not explicit in their paper. We compute the ciphertext size according to the appendix of [10] when \(d=2\), \(f=1\) and \(\lambda =80\). Note that (d, f) are the parameters related to the underlying d-time two-tier signatures and \(2^{\lambda }\) denotes the maximal number of signatures.

The simulatable two-tier signature is different from the notion simulatable signature introduced in [2]. The latter is defined in the common reference string (CRS) model and allows to create valid signatures using the trapdoor associated with the CRS, while our simulatable two-tier signature does not require the CRS and the trapdoor.

For simplicity, we omit the description of state information. Indeed, we need to store the state information, such as \(v_h\), \((\widehat{\textsf {ppk}},\widehat{\textsf {psk}})\), and the secondary public/secret key pairs and corresponding two-tier signatures generated so far.

For more details on the definition of IND-CCA security in the multi-user/-challenge setting, we refer to [19].

k in the left side of Eq. (6).

Theorem 7 in [1] states that their scheme is IND-CCA secure in the multi-challenge setting. As explained in [1] it is trivial to preserve tightness when extending the security reduction from the single user setting to the multi-user setting.

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Titel: Tightly-Secure Encryption in the Multi-user, Multi-challenge Setting with Improved Efficiency
verfasst von: Puwen Wei
Wei Wang
Bingxin Zhu
Siu Ming Yiu
Verlag: Springer International Publishing
Buch: Information Security and Privacy
Print ISBN: 978-3-319-60054-3

Electronic ISBN: 978-3-319-60055-0

Copyright-Jahr: 2017
DOI: https://doi.org/10.1007/978-3-319-60055-0_1

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