函数加密体制（一） (13-5)

end,we explore the concept of functionαl encryption.In a functional encryption sys-tem, a decryption key allows a user to learn a function of the encrypted data. Briefly, in a functional encryption system for functionality F(·，·)(modeled as a Turing Ma- chine) an authority holding a master secret key can generate a key skₖ that enables the computation of the functionF(k，·)on encrypted data. More precisely,using skk the decryptor can computeF(k，x) from an encryption of uitively,the security of the system guarantees that one cannot learn anything more about x，inas we shall aee capturing this rigorously is quite challenging.

现在已经可以知道函数加密的能力了吧。再让我们考虑一下如果对于任意多项式时间的图灵机F(·，·) 可以实现函数加密的话，可以实现什么呢？在访问控制方面的应用中，可以设置 x＝(ind，m) 编码一个消息 m 以及一个任意复杂的访问控制程序 ind （作用是对用户凭证的描述）。函数 F 解释了程序 ind 在 k 上的作用，当且仅当 ind 接受 k 时输出消息 m 。此外， ind 还应该被隐藏起来，则人们不一定知道为什么成功解密或者那种密钥满足 ind 。在第3节中，我们给出了更多其他的例子。

We can now see the power of functional encryption.Let us consider what can be achieved if we could realize functional encryption for any polynomial-time Turing Ma- chine F(·，·).In applications of access control,one could let x= (ind，m) encode a message m as well as an arbitraly complex access control program ind that will act over the description of a user's credentials.The functionality F would interpret the program ind over k and output the message m if and only if ind accepts on input k. Moreover, the program ind would be hidden and thus one would not necessarily know why decryption was successful or what other keys would satisfy ind. We give many more examples in Section 3

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