What does the "x" operator stands for in cryptography?

I am studying commitment scheme and in of the notes from the class this statement comes up.

I'd like to know exactly what the X = M x R mean, since I don't seem to understand how the "x" operator should be interpreted in here

• That's the cartesian product. Commented Apr 10, 2020 at 20:49
• @SEJPM as in X is looks something like a pair of (m,r) where m e M and r e R? Commented Apr 10, 2020 at 20:53
• Yes, $\mathbb{M} \times \mathbb{R}$ is the set of all values $(m, r)$ where $m \in \mathbb{M}$ and $r \in \mathbb{R}$. As such, it's not really an 'operator', instead, it's a notation of what elements a specific set is made up of. Commented Apr 10, 2020 at 21:34
• Note this is not specific to cryptography and is used in pretty much all of mathematics. (The concept is also used in RDBMS but usually with other notation.) Commented Apr 11, 2020 at 0:36

$$\mathcal X=\mathcal M\times \mathcal R$$ simply means that all elements of $$\mathcal X$$ have the form $$(m,r)$$ with $$m\in\mathcal M$$ and $$r\in\mathcal R$$. So this is an operator that takes two sets and then joins them in a tuple. This is also called Cartesian product.