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Paper: Multi-Input Quadratic Functional Encryption from Pairings

Authors:
Shweta Agrawal , IIT Madras
Rishab Goyal , MIT
Junichi Tomida , NTT Secure Platform Labs
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Conference: CRYPTO 2021
Abstract: We construct the first multi-input functional encryption (MIFE) scheme for quadratic functions from pairings. Our construction supports polynomial number of users, where user $i$, for $i \in [n]$, encrypts input $\bfx_i \in \mbZ^m$ to obtain ciphertext $\ct_i$, the key generator provides a key $\sk_\bfc$ for vector $\bfc \in \mbZ^{({mn})^2}$ and decryption, given $\ct_1,\ldots,\ct_n$ and $\sk_\bfc$, recovers $\ip{\bfc}{\bfx \otimes \bfx}$ and nothing else. We achieve indistinguishability-based (selective) security against unbounded collusions under the standard bilateral matrix Diffie-Hellman assumption. All previous MIFE schemes either support only inner products (linear functions) or rely on strong cryptographic assumptions such as indistinguishability obfuscation or multi-linear maps.
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BibTeX
@inproceedings{crypto-2021-31100,
  title={Multi-Input Quadratic Functional Encryption from Pairings},
  publisher={Springer-Verlag},
  author={Shweta Agrawal and Rishab Goyal and Junichi Tomida},
  year=2021
}