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.

• Can you link to the document and tell us what page? Or take a screenshot from the document? – mikeazo Jan 16 '17 at 20:43
• I typically see $\in_R$ when referring to something being randomly drawn from a set. But seeing the paper would help answer your question. P.S., I updated to use TeX equations instead of a picture. – mikeazo Jan 16 '17 at 20:45
• FYI to the community: downvotes on questions like this (with no comment) are what make people like me feel "unqualified" to even read this site, and take moths off at a time. I get that people insta downvote anything that looks like a "pure mathematics" question... but really? – Mike Ounsworth Jan 16 '17 at 21:22
• @MikeOunsworth: I didn't downvote this, but without an actual reference to the context in which the OP saw this symbol (and no, "in a scientific paper related to cryptographic field" doesn't count), I don't think this question is "useful and clear" enough to deserve an upvote, either. While mikeazo's and Yehuda Lindell's guess is probably right, without knowing the context that symbol could really mean anything. – Ilmari Karonen Jan 17 '17 at 4:08
• @IlmariKaronen Thank you. Your comment nicely (and politely) explains what's missing from the question. If more people left comments like that along with their downvote, I think that would go a long way to making crypto.SE feel more inviting. – Mike Ounsworth Jan 17 '17 at 14:38

1. $x \in S$ is used to denote that $x$ is in the set $S$.
2. $x \in_R\ S$ is used to denote that $x$ is chosen randomly from the set $S$.
3. 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.
• I believe I've seen $x \overset{\$}{\leftarrow} S$used for this, too, and I wouldn't be at all surprised if somebody used$x \in_{\$} S$. As with standards, the nice thing about math symbols is that there are so many to choose from. ;) – Ilmari Karonen Jan 17 '17 at 3:57