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Tightly secure cryptographic schemes have been extensively studied in the fields of chosen-ciphertext secure public-key encryption (CCA-secure PKE), identity-based encryption (IBE), 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 schemes that are tightly secure in the multi-user and multi-challenge setting. In other words, the security of our schemes do not degrade even if an adversary obtains many ciphertexts generated by many users. Our schemes are 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 schemes, we can obtain the first tightly secure function-hiding IPFE schemes and multi-input IPFE (MIPFE) schemes 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 can obtain the first tightly secure function-hiding MIPFE schemes by applying our conversion to the tightly secure function-hiding IPFE schemes described above. |
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