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Compact IBBE and Fuzzy IBE from Simple Assumptions

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Security and Cryptography for Networks (SCN 2018)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 11035))

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Abstract

We propose new constructions for identity-based broadcast encryption (IBBE) and fuzzy identity-based encryption (FIBE) in bilinear groups of composite order. Our starting point is the IBBE scheme of Delerablée (Asiacrypt 2007) and the FIBE scheme of Herranz et al. (PKC 2010) proven secure under parameterised assumptions called generalised decisional bilinear Diffie-Hellman (GDDHE) and augmented multi-sequence of exponents Diffie-Hellman (aMSE-DDH) respectively. The two schemes are described in the prime-order pairing group. We transform the schemes into the setting of (symmetric) composite-order groups and prove security from two static assumptions (subgroup decision).

The Déjà Q framework of Chase et al. (Asiacrypt 2016) is known to cover a large class of parameterised assumptions (dubbed über assumption), that is, these assumptions, when defined in asymmetric composite-order groups, are implied by subgroup decision assumptions in the underlying composite-order groups. We argue that the GDDHE and aMSE-DDH assumptions are not covered by the Déjà Q über assumption framework. We therefore work out direct security reductions for the two schemes based on subgroup decision assumptions. Furthermore, our proofs involve novel extensions of Déjà Q techniques of Wee (TCC 2016-A) and Chase et al.

Our constructions have constant-size ciphertexts. The IBBE has constant-size keys as well and guarantees stronger security as compared to Delerablée’s IBBE, thus making it the first compact IBBE known to be selectively secure without random oracles under simple assumptions. The fuzzy IBE scheme is the first to simultaneously feature constant-size ciphertexts and security under standard assumptions.

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Notes

  1. 1.

    We believe our arguments showing that the assumptions under question are not covered by the Déjà Q framework are sufficient. Also, we do not know if there exist other parameterised assumptions in this class that could possibly be used to prove security of the IBBE and FIBE schemes.

  2. 2.

    Alternatively, the scheme of [26] can be proved secure in the standard model if the adversary also announces all its private keys queries (in addition to the target set of identities) before seeing the public parameters.

  3. 3.

    The proof of Wee’s broadcast encryption [62, Sect. 4] has a similar correlation between the \(\mathbb {G}_{p_2}\) components of private keys and public parameters but, in the final step, the statistical argument involved simpler-to-analyse Vandermonde matrices.

  4. 4.

    The assumption is originally given in symmetric groups. In order to work with the Déjà Q framework, one must transform it into asymmetric groups (using Abe et al.’s method [3] as suggested in [23]) which depends on the scheme and the reduction.

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Acknowledgements

We want to thank all anonymous reviewers for invaluable comments. This work was funded in part by the “Programme Avenir Lyon Saint-Etienne de l’Université de Lyon” in the framework of the programme “Investissements d’Avenir” (ANR-11-IDEX-0007) and by the French ANR ALAMBIC project (ANR-16-CE39-0006). Part of this work was done when the last author was at Laboratoire LIP, ENS de Lyon, France and Indian Institute of Technology Bhubaneswar, India.

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  1. ENS de Lyon, Laboratoire LIP (U. Lyon, CNRS, ENSL, INRIA, UCBL), Lyon, France

    Junqing Gong & Benoît Libert

  2. CNRS, Laboratoire LIP, Lyon, France

    Benoît Libert

  3. Indian Institute of Technology, Kharagpur, India

    Somindu C. Ramanna

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  1. Junqing Gong
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Correspondence to Junqing Gong , Benoît Libert or Somindu C. Ramanna .

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  1. University of Catania, Catania, Italy

    Dario Catalano

  2. University of Salerno, Fisciano, Italy

    Roberto De Prisco

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Gong, J., Libert, B., Ramanna, S.C. (2018). Compact IBBE and Fuzzy IBE from Simple Assumptions. In: Catalano, D., De Prisco, R. (eds) Security and Cryptography for Networks. SCN 2018. Lecture Notes in Computer Science(), vol 11035. Springer, Cham. https://doi.org/10.1007/978-3-319-98113-0_30

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