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

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

  • 4
    $\begingroup$ That's the cartesian product. $\endgroup$
    – SEJPM
    Commented Apr 10, 2020 at 20:49
  • $\begingroup$ @SEJPM as in X is looks something like a pair of (m,r) where m e M and r e R? $\endgroup$ Commented Apr 10, 2020 at 20:53
  • 1
    $\begingroup$ 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. $\endgroup$
    – poncho
    Commented Apr 10, 2020 at 21:34
  • $\begingroup$ 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.) $\endgroup$ Commented Apr 11, 2020 at 0:36

1 Answer 1


$\mathcal X=\mathcal M\times \mathcal R$ 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.


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