What is the definition of function index

Question

I'm reading through Indistinguishability Obfuscation from Well-Founded Assumptions and in Definition 3.1 describing sPRG, it mentions "samples a function index I." Can someone explain what a function index is in this context?

Answer 1

A sPRG as defined there describes a family of functions, i.e. a set of many functions $f_I$. The index $I$ identifies one such function from the family and the algorithm $\mathsf{IdSamp}$ describes how you would sample such an index. The $\mathsf{Eval}$ algorithm given $I$ and $\mathsf{sd}$ then evaluates the function $f_I$ on input $\mathsf{sd}$.