Why $\alpha$ in ElGamal cryptosystem has to be a primitive root? 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 ?
Everything works, except the key and signature space, reduced greatly;


  The result is that the signature space (when the key is used for     signing) or the public key space (when the key is used for encryption)     may be greatly reduced from its expected size of log(p) bits, possibly     down to 1 bit (the worst case if the order of g is 2)1.


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