Function families Overview and some applications

Signs c denote inclusion of classes, black arrows denote constructions presented in detail in the following chapters, dashed arrows denote constructions in [ChHP92], and grey arrows other possible constructions. 

Apart from defining more such classes, one can also define details within each definition in different ways, e.g., requirements on the domains and membership tests (similar to the discrete-logarithm assumptions). In particular, all the following definitions contain sets Good and All of good keys or all acceptable keys, i.e., they make provisions for different interest groups the use of these sets is considered in Remark 8.38. Furthermore, not aU the simple relations between the definitions that one could prove are mentioned below. 

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Figure 8.5. Function families Overview and some applications.

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