函数加密体制（一） (13-6)

论文贡献：最近，有多种系统超出传统加密的边界。比如，身份基加密、可搜索加密、属性基加密。它们以及一些相关的研究（例如[BW07]，[KSW08]）提出了特定的新系统，用于解决从表达访问控制到搜索加密数据等问题。在过去的几年里，术语(函数加密！)被用来形容这个新领域。

尽管这些成果包含着函数加密的特殊案例，一般性的概念还从来没有被形式化的定义或研究。本篇文章我们正式地提出这个课题一个形式化的处理，并讨论了许多尚存的挑战。从函数加密的一般框架和语法开始，展示如何将现有的加密概念(如基于属性的加密和许多其他概念)优雅地表示为函数加密的特定功能。

定义抽象函数加密的安全性是非常有意义的。自然地，从基于游戏的不可区分性定义开始(基于[lBW07],[KSW08]中安全谓词加密的定义)。不幸的是，我们表明这个简单的定义对于某些函数是不够的（因为存在满足这个安全定义的平凡结构是不安全的）。

Our Contributions. Recently, there have been multiple systems that suggest moving beyond the traditional boundaries of encryption. Some examples include Identity-BasedEncryption[Sha84,cO1],searchableencryption [BCOP04] and Attribute-Based Encryption [SW05].These and other related works such as [BW0Z,KSW08] propose specific new systems for problems ranging from expressive access control to searching on encrypted data. In the last few years, the term "functional encryptiorˡ”was adopted to describe this new area [LOS ⁺10.OT10.AL101.

While these results contain special cases of functional encryption,the general con- cept has never been formally defined or studied.In this paper we put forth a formal treatment of the subject and discuss many of the remaining challenges. We begin with a general framework and syntax for functional encryption and show how existing encryption concepts, such as attribute based encryption and many others,can be ele- gantly expressed as particular functionalities of functional encryption.

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