# Why $\alpha$ in ElGamal cryptosystem has to be a primitive root? [duplicate]

When choosing the public key for ElGamal, $$\alpha$$ must be chosen as a primitive mod p. What if $$\alpha$$ is not a primitive root ? How will it influence the encryption and decryption ?

## marked as duplicate by fgrieu, e-sushiOct 26 '18 at 7:29

It not hard to detect a $$g$$ is the generator or not.