**Multi-Input Quadratic Functional Encryption from Pairings**

*Junichi Tomida*

**Abstract: **Multi-input functional encryption (MIFE) is a generalization of functional encryption and allows decryptor to learn only function values $f(x_{1},\ldots,x_{n})$ from ciphertexts of $x_{1},\ldots,x_{n}$.
We present the first MIFE schemes for quadratic functions (MQFE) from pairings.
We first observe that public-key MQFE can be obtained from inner product functional encryption in a relatively simple manner whereas obtaining secret-key MQFE from standard assumptions is completely nontrivial.
The main contribution of this paper is to construct the first secret-key MQFE scheme that achieves indistinguishability-based selective security against unbounded collusion under the standard bilateral matrix Diffie-Hellman assumption.
All previous MIFE schemes either support only inner products (linear functions) or rely on non-standard cryptographic assumptions such as indistinguishability obfuscation or multi-linear maps.
Thus, our schemes are the first MIFE for functionality beyond linear functions from polynomial hardness of standard assumptions.

**Category / Keywords: **public-key cryptography / functional encryption, quadratic function, pairings

**Date: **received 15 Oct 2020

**Contact author: **junichi tomida vw at hco ntt co jp

**Available format(s): **PDF | BibTeX Citation

**Version: **20201016:064808 (All versions of this report)

**Short URL: **ia.cr/2020/1285

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