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 Apr 10 '20 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? $\endgroup$ – Wild Tarzan Apr 10 '20 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 Apr 10 '20 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.) $\endgroup$ – 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.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.