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.

中文翻译：

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通过分支程序实现多跳 PRE

代理重加密（$\mathsf {PRE}$预科) 是安全数据共享和电子邮件转发等中的基本密码原语。据我们所知，大多数现有的高效基于格的 $\mathsf {PRE}$预科 方案侧重于构建单跳、密钥私有、多位和选择密文攻击（$\text{CCA}$CCA) 等。很少有文献讨论格子上详细的多跳结构。最近，钱德兰等人。(PKC'14) 提出了一种基于格的$\mathsf {PRE}$预科 该方案建立在 Brakerski (CRYPTO'12) 的密钥切换机制之上，并指出他们的方案可以实现多跳 $\mathsf {PRE}$预科 有向图的理想电路族方案 $G$G. 在本文中，我们仍在沿着这条路线工作，并实现多跳$\mathsf {PRE}$预科 通过分支程序（$\mathsf {BP}$BP)，这是一种 NC1 电路，可用于计算加密数据。据我们所知，我们提出了第一个多跳$\mathsf {PRE}$预科 方案通过 $\mathsf {BP}$BP它支持同态评估。我们还分析了在有错误的决策学习下我们方案的安全性（$\mathsf {LWE}$LWE） 假设。