Q:

About belonging symbol

could anyone please explain to me the difference between these two belonging symbols (one with R in index $\in_R$)  and the other (without R in index $\in$)
I have found them in a scientific paper related to cryptographic field.

A:

$x \in S$ is used to denote that $x$ is in the set $S$. 
$x \in_R\ S$ is used to denote that $x$ is chosen randomly from the set $S$.
Choosing a value randomly $x$ from $S$ is also sometimes denoted $x\leftarrow S$ or even $x\leftarrow_R\ S$. Sometimes this is used for choosing according to a distribution and not a set, but you need to look at the preliminaries of the paper to determine their notation.

In an ideal world, each paper would define what their notation means. However, this doesn't always happen. Nevertheless, the above should be a good guide for you.

