Arguing security of an encryption scheme I have an encryption scheme which masks the message m by multiplying it with a secret random group element i.e $g^r \cdot m$. I should allow decryption and get $g^r$ if I have a valid secret key; otherewise I will only reveal $(g^L)^r$, where $L \in Z_n$ and $g^L$ is known to the adversary.

Is this secure? If yes, how can I argue about the security.
If the adversary knows $L$, then he can find $L^{-1}$, the multiplicative inverse of $L$ modulo $q$ where $q$ is the order of $g$. Then he can compute $g^r =((g^L)^r)^{L^{-1}}$. Once he find $g^r$, he can compute $m$ by eliminating $g^r$ from $m\cdot g^r$.

If the adversary knows only $g^L$, then it is ok. This case is like El Gamal. Let $h=g^L$, what you reveal is $(h^r,m\cdot g^r)$. Your private key is $L^{-1}$.