函数加密体制（一） (13-3)

Encryption is a method for a user to securely share data over an insecure network or storage site.Before the advent of public key cryptography, a widely held view was that for two users to communicate data confidentially they would need to a priori establish a mutually held secret key k.While this might be acceptable for some small or tightly knit organizations,such a solution was clearly infeasible for larger networks such as today's Internet consisting of billions of users. Over thirty years ago, Diffie and Hell- man [DH76a.DH76b] put forth a radically new idea in the concept of public key cryp- tography, where two parties can securely communicate with each other without having an a prior mutual secret— radically challenging the conventional wisdom of the time. Today public key encryption is an invaluable tool and its use is ubiquitous in building tools from secure web communication (e.g., SSH, SSL), to disk encryption, and secure software patch distribution.However,there is an ingrained view that:(1) Encryption is α method to send α messαge or dαtα to α single entity holding α secret key, and (2)Access to the encrypted dαtα is αll or nothing - one cαn either deανyei αnd rend the entire plαintext or one leαrns nothing αt αll αbout the plαintext other thαn its length.

对于许多新兴的应用（如云服务），公钥加密不够用了。例如，通常需要在密文中指定一个解密策略，只有当个体满足所指定的策略时才能解密。更一般地说，我们可能希望仅允许访问明文的一个函数，这取决于解密者的授权。现在来举一个具体的例子，考虑在云上存储的加密图像。执法部门可能需要在云上搜索包含特定人脸的图像。因此，云需要一个受限制的密钥来解密包含目标人脸的图像，但是不可以显示任何其他图像。更一般地说，这个密钥仅可以解密明文的一个函数，例如，除目标人脸外其余地方均模糊的图像。传统的公钥加密不能帮助我们完成这项任务。

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