I am trying to understand the example given on this page:
https://en.wikipedia.org/wiki/Fiat%E2%80%93Shamir_heuristic
but the explanation says I need to be familiar with both multiplicative groups and Euler's totient theorem to understand it. Well I was familiar with neither, but after some searching I might understand the necessary operations now and I wanted to check my understanding here.
For Euler's totient theorem, if I'm plugging in values for $\varphi$ correctly, I should get results as follows:
$\varphi(4) = 2$
$\varphi(11) = 10$
And so on.
For multiplicative groups, if I'm understanding this page correctly:
https://cs.nyu.edu/~spencer/algebra07/zntimes.pdf
this symbol $\mathbb{Z}_q^*$ says "take all coprimes of $q$ and multiply them and take the remainder", but I'm unclear on how to proceed.
Is it possible to explain this operation to someone without a background in groups? If not, where should I start?