Paper 2024/1572

Bounded Collusion-Resistant Registered Functional Encryption for Circuits

Abstract

As an emerging primitive, Registered Functional Encryption (RFE) eliminates the key-escrow issue that threatens numerous works for functional encryption, by replacing the trusted authority with a transparent key curator and allowing each user to sample their decryption keys locally. In this work, we present a new black-box approach to construct RFE for all polynomial-sized circuits. It considers adaptive simulation-based security in the bounded collusion model (Gorbunov et al. - CRYPTO'12), where the security can be ensured only if there are no more than Q >= 1 corrupted users and $Q$ is fixed at the setup phase. Unlike earlier works, we do not employ unpractical Indistinguishability Obfuscation (iO). Conversely, it can be extended to support unbounded users, which is previously only known from iO. Technically, our general compiler exploits garbled circuits and a novel variant of slotted Registered Broadcast Encryption (RBE), namely global slotted RBE. This primitive is similar to slotted RBE, but needs optimally compact public parameters and ciphertext, so as to satisfy the efficiency requirement of the resulting RFE. Then we present two concrete global slotted RBE from pairings and lattices, respectively. With proposed compiler, we hence obtain two bounded collusion-resistant RFE schemes. Here, the first scheme relies on k-Lin assumption, while the second one supports unbounded users under LWE and evasive LWE assumptions.