# Safe generator for ElGamal signature

What are the properties a generator $g$ should have to be secure for ElGamal signatures (original scheme)?

I am aware that it is poorly chosen and not secure when $g|p-1$ or $g^{-1}|p-1$, where $p$ is the large prime so that $g$ generates $Z_p^*$ and $g$ has maximum order (that is, $p-1$).

Are there other properties one should consider? Additionally, should $g$ be picked randomly over $[1..p-1]$ or is it safe to choose it to be a small integer to start with?

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