AF: Small: A Theory of Cryptography and the Physical World

密码学的传统目标是为明确定义的任务（如公钥加密）设计密码算法。我们建议研究以下概念上有趣的问题：我们什么时候可以嵌入一个加密函数到一个函数，这不是为此目的而设计的，说一个功能创建的性质？在一个更抽象的设置，可能的概念或集合？物品？由函数类{f_c}表示，其中c是（未知）对象的描述。我们不能控制函数类{f_c}，而是由下式给出：自然？我们假设一个对象c被选择（由？性质？）从一个熵足够大的分布中每个输入x代表不同的测量，或者？查询？，可以对物体做出的改变。我们的目标是设计一个学习c（或a？良好的近似？通过查询x并观察答案y = f_c（x），该算法应具有以下非平凡隐藏属性。任何只观察查询和响应序列（x，y）的计算有限的窃听者不能学习任何东西？有用的信息？关于C。

The traditional goal of cryptography is to design cryptographic algorithms for well-defined tasks, such as public-key encryption. We propose to study the following conceptually intriguing question: when can we embed a cryptographic function into a function which was not designed for this purpose, say a function created by nature?In a more abstract setting, the collection of possible concepts or ?objects? is represented by a function class {f_c}, where c is a description of the (unknown) object. We do not have control over the function class {f_c}, but rather it is given by ?nature?. We assume that an object c is chosen (by ?nature?) from a distribution which has a sufficiently large entropy. Each input x represents a different measurement, or ?query?, that can be made to the object. The goal is to design an algorithm for learning c (or a ?good approximation? of c) by making queries x and observing the answers y = f_c(x). The algorithm should have the following nontrivial hiding property. Any computationally bounded eavesdropper who only observes the sequence of queries and responses (x,y) cannot learn any ?useful information? about c.