My question is about commitment schemes for arbitrarily large integers. One scheme I know uses groups of unknown order (RSA or class group) and depends on the strong-RSA assumption.
You chose a random element $g$ in a group $\mathbb{G}$ of unknown order and define the commitment $Com(n):= g^n$ for any integer $n$. You can turn this into a hiding commitment by choosing an element $h\in \mathbb{G}$ such that the discrete log between $g$, $h$ is unknown and defining the Pedersen commitment $PedCom(n,r):= g^nh^r$ for a randomly chosen secret integer $r$.
Are there other commitment schemes for arbitrarily large integers?
One could decompose the integer and use a polynomial commitment of some sort that does not need hidden order groups, but I suspect such a scheme would not allow for efficient protocols to prove relations between the committed integers.