What is the notation $u \xleftarrow{\text{R}} \mathbb{Z}_n^{\ast}$ mean?

Question

I am reading a cryptography paper titled "Dealing Cards in Poker Games" by P. Golle. In the section titled "key generation", the author says "choose $u \xleftarrow{\text{R}} \mathbb{Z}_n^{\ast}$".

I am assuming it implies that $u$ is randomly generated from the given set but I am unsure. Can someone help clarify?

Answer 1

Everytime I've encountered the notation $x\xleftarrow{R}X$ it's always meant: sample a random element of $X$ according to some specified probability distribution on $X$, usually the uniform distribution if $X$ is finite and no further mention of the distribution is made. Thus I would expect the sentence in this paper to mean "choose $u$ at random in the set $\Bbb{Z}_n^*$ according to the uniform distribution".

Answer 2

that most likely means $u$ can be set to any non zero integer if it is divided by $n$ results in a remainder of +1 or -1 (modulo of that integer/n is either +1 or -1)

example if $n$ is 4 then an eligible non zero integer can be 5 because remainder of 5/4 is 1