Towards Multi-Hop Homomorphic Identity-Based Proxy Re-Encryption via Branching Program

Identity-based proxy re-encryption (IBPRE) is a powerful cryptographic tool for various applications, such as access control system, secure data sharing, and secure e-mail forwarding. Most of the existing efficient IBPRE schemes are based on the Diffie-Hellman assumption, and they only focus on the single-hop construction. Based on the work of Chandran et al.'s lattice-based proxy re-encryption (PRE) scheme (PKC'14) and Yamada's lattice-based identity-based encryption (IBE) scheme (EUROCRYPT'16), in this paper, we first show the possibility of assembling lattice-based IBE into lattice-based PRE. Then, we present the construction of a new efficient single-hop homomorphic IBPRE from learning with errors (LWEs) via key homomorphic computation. Furthermore, using branching program (BP), we obtain an efficient multi-hop IBPRE scheme. To the best of our knowledge, our scheme is the first multi-hop homomorphic IBPRE scheme via BP. Our scheme supports homomorphic evaluation and is proved secure under the decisional LWE assumption.