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Constructions of Unconditionally Secure Broadcast Encryption from Key Predistribution Systems with Trade-Offs Between Communication and Storage

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Provable Security (ProvSec 2015)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 9451))

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Abstract

An \((\le n,\le \omega )\)-one-time secure broadcast encryption schemes (BESs) allows a sender to specify any subset of receivers so that only the specified recievers can decrypt a ciphertext. In this paper, we first show an efficient construction of a BES with general ciphertext sizes. Specifically, we propose a generic construction of a BES from key predistribution systems (KPSs) when its ciphertext size is equal to integer multiple of the plaintext size, and our construction includes all known constructions. However, there are many possible combinations of the KPSs to realize the BES in our construction methodology, and therefore, we show that which combination is the best one in the sense that secret-key size can be minimized.

Deriving a tight bound on the secret-key size required for \((\le n,\le \omega )\)-one-time secure BES with any ciphertext size still remains an open problem.Our result also means that we first show an upper bound on the size of secret keys for general ciphertext sizes.

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Notes

  1. 1.

    Unconditionally secure protocols usually require long secret keys, and therefore it is important to show the minimal key size (i.e. derive a tight lower bound on the secret-key size).

  2. 2.

    In general, for deriving a tight bound, it is necessary to show upper/lower bounds with tightness.

  3. 3.

    Although uk is not explicitly described in several papers on KPSs [2, 4, 5, 12, 14], we introduce uk for measuring actual sizes of secret keys which TA has to generate. It is reasonable to consider uk since Blundo and Cresti [3] also dealt with uk in another context. We note that uk is actually not used in the scheme, and hence we do not explicitly describe it in output. We can also see uk as a deterministic function for deriving secret keys \(uk_1,\ldots .uk_n\).

  4. 4.

    For example, when \(n=9\), \(\delta =3\), and \(\ell _i=3 \ (i=1,2,3)\), then \(\mathcal {U}_1:=\{U_1,U_2,U_3\}\), \(\mathcal {U}_2:=\{U_4,U_5,U_6\}\), and \(\mathcal {U}_3:=\{U_7,U_8,U_9\}\).

  5. 5.

    \(\varvec{L}\) is said to be even when \(\ell _1-\ell _\delta =0\) if \(n/\delta \in \mathbb {N}\) or \(\ell _1-\ell _\delta =1\) if \(n/\delta \notin \mathbb {N}\).

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Acknowledgments

We would like to thank anonymous referees for their helpful comments. We would also like to thank Shota Yamada and Goichiro Hanaoka for their valuable comments for the preliminary version of this paper. The first author is supported by JSPS Research Fellowships for Young Scientists. This work (Yohei Watanabe) was supported by Grant-in-Aid for JSPS Fellows Grant Number 25\(\cdot \)3998. This work (Junji Shikata) was supported by JSPS KAKENHI Grant Number 15H02710, and it was partially conducted under the auspices of the MEXT Program for Promoting the Reform of National Universities.

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Authors and Affiliations

  1. Graduate School of Environment and Information Sciences, Yokohama National University, Yokohama, Japan

    Yohei Watanabe & Junji Shikata

  2. Institute of Advanced Sciences, Yokohama National University, Yokohama, Japan

    Junji Shikata

Authors
  1. Yohei Watanabe
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  2. Junji Shikata
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Correspondence to Yohei Watanabe .

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Editors and Affiliations

  1. The Hong Kong Polytechnic University, Hong Kong, China

    Man-Ho Au

  2. Japan Advanced Inst. of Science and Tech, Ishikawa, Japan

    Atsuko Miyaji

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Watanabe, Y., Shikata, J. (2015). Constructions of Unconditionally Secure Broadcast Encryption from Key Predistribution Systems with Trade-Offs Between Communication and Storage. In: Au, MH., Miyaji, A. (eds) Provable Security. ProvSec 2015. Lecture Notes in Computer Science(), vol 9451. Springer, Cham. https://doi.org/10.1007/978-3-319-26059-4_27

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  • DOI: https://doi.org/10.1007/978-3-319-26059-4_27

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