Paper 2020/1285

Multi-Input Quadratic Functional Encryption from Pairings

Shweta Agrawal, Rishab Goyal, and Junichi Tomida

Abstract

We construct the first multi-input functional encryption \allowbreak(MIFE) scheme for quadratic functions from pairings. Our construction supports polynomial number of users, where user $i$, for $i\in [n]$, encrypts input ${\text{bfx}}_i\in {\text{mbZ}}^m$ to obtain ciphertext ${\text{ct}}_i$, the key generator provides a key ${\text{sk}}_{\text{bfc}}$ for vector $\text{bfc}\in {\text{mbZ}}^{(mn{)}^2}$ and decryption, given ${\text{ct}}_1,\dots ,{\text{ct}}_n$ and ${\text{sk}}_{\text{bfc}}$, recovers $\text{ip}\text{bfc}\text{bfx}\otimes \text{bfx}$ 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.

Note: author updated, editorial revision