I am reading a paper in cryptography, there is something that I cannot understand well! here is the paragraph:
An inherently unobfuscatable function ensemble is an ensemble $\{H_k\}_{k∈N}$ of distributions $H_k$ on finite functions (from, say, $\{0, 1\}^{l_{in(k)}}$ to $\{0, 1\}^{l_{out(k)}}$) such that:
- Every function $f\xleftarrow{R}H_k$ is computable by a circuit of size poly(k)....
I could not understand the concept of ensembles and their difference with sets. It seams that an ensemble is a set with some parameter like k. For example here I see the ensemble $\{H_k\}_{k∈N}$ as a set $\{H_1, H_2, ...\}$. Am I right? If yes then why we need the concept of ensembles?
The other question is that what does the notation $f\xleftarrow{R}H_k$ implies for? Is it randomly sampling one element from the ensemble (set)?
I feel that I really need a concrete example to get the different between a set and ensemble. Let say there are some objects. If I put them in an ensemble what would I get more in compare to put them in a set?