The concept of proxy re-encryption (PRE) dates back to the work of Blaze, Bleumer, and Strauss in 1998. PRE offers delegation of decryption rights, i.e., it securely enables the re-encryption of ciphertexts from one key to another, without relying on trusted parties. PRE allows a semi-trusted third party termed as a “proxy” to securely divert encrypted files of user A (delegator) to user B (delegatee) without revealing any information about the underlying files to the proxy. To eliminate the necessity of having a costly certificate verification process, Green and Ateniese introduced an identity-based PRE (IB-PRE). The potential applicability of IB-PRE sprung up a long line of intensive research from its first instantiation. Unfortunately, till today, there is no collusion-resistant unidirectional IB-PRE secure in the standard model, which can withstand quantum attack. In this paper, we present the first concrete constructions of collusion-resistant unidirectional IB-PRE, for both selective and adaptive identity, which are secure in standard model based on the hardness of learning with errors problem.

代理重新加密（PRE）的概念可以追溯到1998年Blaze，Bleumer和Strauss的工作。PRE提供了解密权的委派，即，它可以安全地将密文从一个密钥重新加密为另一个密钥，而无需重新加密。依靠可信赖的各方。PRE允许被称为“代理”的半信任第三方将用户A（委托人）的加密文件安全地转移到用户B（委托人），而无需向代理透露有关基础文件的任何信息。为了消除进行昂贵的证书验证过程的必要性，Green和Ateniese引入了基于身份的PRE（IB-PRE）。从首次实例化开始，IB-PRE的潜在适用性就涌现了长期的深入研究。不幸的是，直到今天，标准模型中还没有安全的可防止串通的单向IB-PRE，可以承受量子攻击。在本文中，我们提出了针对选择性和自适应身份的抗共谋单向IB-PRE的第一个具体结构，该结构在基于错误学习的难度的标准模型中是安全的。