I'm trying to understand the Paillier Scheme but there's something I can't understand in the keyGen algorithm :
Ensure ${\displaystyle n}$ divides the order of $g$ by checking the existence of the following modular multiplicative inverse: $$\mu =(L(g^{\lambda }{\bmod n}^{2}))^{{-1}}{\bmod n},$$
I'm trying hard to find the relation between $n$ divides the order of $g$ and $gcd(n, L(g^\lambda \, mod \;n^2))=1$ but I can't find it. I hope that somebody can help me understand it. Good evening, ciao !!
