Diffie-Hellman key exchange using addition instead of multiplication? I know that the additive finite group $(Zp,+)$ of prime order $p$ when I perform the Diffie-Hellman key exchange (DHKE) protocol is insecure. I didn't however find many sources online explain why it is insecure. Neither could I find information about what possible attacks can be performed in that case.

Can anybody explain why it is insecure and what possible attacks would be possible if I would use addition instead of multiplication?

Additionally, how can I make both Alice and Bob have the same key when performing the DHKE using $(Zp, +)$?
Why can't we use $(Z_p,+)$?

In the DH key Exchange Alice and Bob agree on a common generator g which allow to share a common key. In fact in $(Z_p,+)$ every non zero element is a generator.

If a common generator g is preallably chosen, when Alice chose a secret a, transmitting A=g.a, the secret a will be immediatly disclosed by any one in the public channel by simply Computing $a=\frac{A}{g}$ and key exchange will be violated which isn't the case in $(Z_p,*)$, as the inversion by the discret logarithm, is considered hard.