# Strange notation using dollar sign

In the paper Multi-Signatures in the Plain Public-Key Model and a General Forking Lemma, the authors Bellare and Neven use notation which looks like left arrow with dollar sign above it.

Authors provide an explanation for one variable:

$s \overset{{\$}}{\longleftarrow S}$denotes the operation of assigning to$s$an element of$S$chosen at random However, in this paper they use it with multiple variables like this:$s_1, \ldots, s_N \overset{{\scriptstyle \$}}{\longleftarrow S}$

What is the definition of this notation? Can we chose dependent random variables for $s_i$? Do we must choose all variables $(s_1, \ldots, s_N)$ at once from the set $S^N$ with uniform distribution?

• Personally, I'd probably read this as "sample a random element of S into $s_i$ independently", but I don't know for sure.
– SEJPM
Jul 16 '16 at 21:09
• Note that uniformly choosing the individual $s_i$ independently as SEJPM suggests is equivalent to your interpretation of uniformly choosing tuples from $S^N$. Jul 16 '16 at 21:23

$s_1, ..., s_N \stackrel{\$}{\leftarrow} S$means coordinate-wise sampling:$s_1 \stackrel{\$}{\leftarrow} S$
$s_2 \stackrel{\$}{\leftarrow} S$...$s_N \stackrel{\$}{\leftarrow} S$
• Oh-- hopefully not to belabor the point, but e.g. in this second paper I linked, see Page 5 (left column preceding Section 4). The variable X_i actually cannot be regarded as a random variable over the uniform distribution over its domain -- unless $\stackrel{\$}{\leftarrow}\$ is interpreted as coordinate-wise sampling. Jul 18 '16 at 0:25