# 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. – SEJPM Apr 10 '20 at 20:49
• @SEJPM as in X is looks something like a pair of (m,r) where m e M and r e R? – Wild Tarzan Apr 10 '20 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. – poncho Apr 10 '20 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.) – dave_thompson_085 Apr 11 '20 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.