Achieving Multi-Hop PRE via Branching Program

Abstract

Proxy re-encryption ( $\mathsf {PRE}$ PRE ) is a fundamental cryptographic primitive in secure data sharing and e-mail forwarding, etc. To our knowledge, most existing efficient lattice-based $\mathsf {PRE}$ PRE schemes focus on the construction of single-hop, key-private, multi-bit and chosen-ciphertext attack ( $\text{CCA}$ CCA ), etc. Few works of literature discussed the detailed multi-hop construction over lattices. Very recently, Chandran et al. (PKC'14) proposed a lattice-based $\mathsf {PRE}$ PRE scheme that builds upon the key switching mechanism of Brakerski (CRYPTO'12), and pointed out that their scheme can achieve multi-hop $\mathsf {PRE}$ PRE scheme by the ideal circuit family for a directed graph $G$ G . In this paper, we are still working along this line and achieving multi-hop $\mathsf {PRE}$ PRE via the branching program ( $\mathsf {BP}$ BP ), which is one type of NC1 circuit and can be used to compute encrypted data. To our knowledge, we proposed the first multi-hop $\mathsf {PRE}$ PRE scheme via $\mathsf {BP}$ BP which supports homomorphic evaluation. We also analyze the security of our scheme under decisional learning with errors ( $\mathsf {LWE}$ LWE ) assumption.