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Paper: Tightly Secure Inner Product Functional Encryption: Multi-input and Function-Hiding Constructions

Authors:
Junichi Tomida
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DOI: 10.1007/978-3-030-34618-8_16
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Abstract: Tightly secure cryptographic schemes have been extensively studied in the fields of chosen-ciphertext secure public-key encryption, identity-based encryption, signatures and more. We extend tightly secure cryptography to inner product functional encryption (IPFE) and present the first tightly secure schemes related to IPFE.We first construct a new IPFE scheme that is tightly secure in the multi-user and multi-challenge setting. In other words, the security of our scheme does not degrade even if an adversary obtains many ciphertexts generated by many users. Our scheme is constructible on a pairing-free group and secure under the matrix decisional Diffie-Hellman (MDDH) assumption, which is the generalization of the decisional Diffie-Hellman (DDH) assumption. Applying the known conversions by Lin (CRYPTO 2017) and Abdalla et al. (CRYPTO 2018) to our scheme, we can obtain the first tightly secure function-hiding IPFE scheme and multi-input IPFE (MIPFE) scheme respectively.Our second main contribution is the proposal of a new generic conversion from function-hiding IPFE to function-hiding MIPFE, which was left as an open problem by Abdalla et al. (CRYPTO 2018). We obtain the first tightly secure function-hiding MIPFE scheme by applying our conversion to the tightly secure function-hiding IPFE scheme described above.Finally, the security reductions of all our schemes are fully tight, which means that the security of our schemes is reduced to the MDDH assumption with a constant security loss.
BibTeX
@article{asiacrypt-2019-30070,
  title={Tightly Secure Inner Product Functional Encryption: Multi-input and Function-Hiding Constructions},
  booktitle={Advances in Cryptology – ASIACRYPT 2019},
  series={Advances in Cryptology – ASIACRYPT 2019},
  publisher={Springer},
  volume={11923},
  pages={459-488},
  doi={10.1007/978-3-030-34618-8_16},
  author={Junichi Tomida},
  year=2019
}