## Cryptology ePrint Archive: Report 2020/1285

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