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IBE with tight security against selective opening and chosen-ciphertext attacks

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Abstract

The simulation-based, selective opening and chosen-ciphertext (\(\mathsf {SIM}\text{- }\mathsf {SO}\text{- }\mathsf {CCA}\)) adversary runs in the multi-sender scenario, it may access to the decryption and user-secret key oracles, in addition to corrupt senders adaptively after seeing the ciphertext (hence it can obtain the encrypted messages together with the randomness). An \(\mathsf {SIM}\text{- }\mathsf {SO}\text{- }\mathsf {CCA}\) secure \(\mathsf {IBE}\) scheme aims to provide privacy for uncorrupted senders against such adversaries. In this work we present the first tightly \(\mathsf {SIM}\text{- }\mathsf {SO}\text{- }\mathsf {CCA}\) secure identity-based encryption (\(\mathsf {IBE}\)). Our \(\mathsf {SIM}\text{- }\mathsf {SO}\text{- }\mathsf {CCA}\) secure \(\mathsf {IBE}\) employs an identity-based key encapsulation mechanism (\(\mathsf {IBKEM}\)) as a building block, concretely,

  • Firstly, we define proper security requirements in the multi-challenge setting for an \(\mathsf {IBKEM}.\)

  • Then we transform an \(\mathsf {IBKEM}\) with such properties to a \(\mathsf {SIM}\text{- }\mathsf {SO}\text{- }\mathsf {CCA}\) secure \(\mathsf {IBE}\) in a tight way. The security definitions and transformation can be seen as an extension of the framework in the public encryption (PKE) setting (given by Lyu et al. in PKC 2018).

  • Finally, we propose an \(\mathsf {IBKEM}\) in prime order groups satisfying our requirements. The security of our \(\mathsf {IBKEM}\) can be tightly reduced to the standard matrix Diffie–Hellman assumption. Our \(\mathsf {IBKEM}\) leads to a tightly \(\mathsf {SIM}\text{- }\mathsf {SO}\text{- }\mathsf {CCA}\) secure \(\mathsf {IBE}\) and of independent interest.

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Notes

  1. Since there is only one instantiation of a tightly secure affine \(\mathsf {MAC},\) in this paper we give the construction based on the \(\mathsf {MDDH}\) assumption directly instead of via the primitive “affine \(\mathsf {MAC}\)”.

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Acknowledgements

We thank the anonymous reviewers for their helpful comments. We thank Dennis Hofheinz for pointing out a problem in an earlier version of the proof of Theorem 1. The authors were supported by the National Nature Science Foundation of China (Nos. 61502484, 61502480, 61572495, 61772515) and the National Cryptography Development Fund (No. MMJJ20170116). Part of this research was funded by the Indo-French Center for the Promotion of Advanced Research.

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Authors and Affiliations

  1. State Key Laboratory of Information Security, Institute of Information Engineering, CAS, Beijing, China

    Dingding Jia & Bao Li

  2. Data Assurance and Communication Security Research Center, CAS, Beijing, China

    Dingding Jia & Bao Li

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

    Dingding Jia

  4. HuaWei International, Singapore, Singapore

    Yamin Liu

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  1. Dingding Jia
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Correspondence to Dingding Jia.

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Communicated by R. Steinfeld.

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Jia, D., Liu, Y. & Li, B. IBE with tight security against selective opening and chosen-ciphertext attacks. Des. Codes Cryptogr. 88, 1371–1400 (2020). https://doi.org/10.1007/s10623-020-00755-6

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