What is the difference between $\in$ and $\in_{\small R}$? I have a simple question about basic math. When I read different papers bout ABE, I see different methods to choose a random exponent.

What is the difference between the following options?


Choose a random exponent $\,a \in \mathbb Z_p$.
Choose a random exponent $\,a \in_{\small R} \mathbb Z_p$.
Choose a random exponent $\,a \in \mathbb Z^*_p$.
Choose a random exponent $\,a \in_{\small R} \mathbb Z^*_p$.
As the comments pointed out $a\in_{R} M$ means picking a sample $a$ uniformly from some set $M$. If a non-uniform distribution is implied, this will be stated.

In case you are also asking about it, $\mathbb{Z}_p^\ast$ is the multiplicative group (nonzero elements) of the integers modulo $p.$ In general
$$
\mathbb{Z}_n^\ast=\{k: k \in \mathbb{Z}_n, \gcd(k,n)=1\}
$$
is the multiplicative group over the integers modulo $n,$ made up of exactly the integers $k$ such that $\gcd(k,n)=1,$ and there are $\varphi(n)$ of them. Of course $\varphi(p)=p-1.$