# ElGamal signature - exploiting fallacious implementation

This question is related to ElGamal signature scheme as defined here ElGamal signature without calculating the inverse

Show how one could exploit an implementation ElGamal signature scheme in which it is not checked that $0 \leq \gamma \leq p-1.$

As far as I can see, we have to find a $\gamma$ such that $\alpha^{a\gamma-x}\gamma^\delta \equiv 1 \pmod{p}$ for a message $x$.

Anyone happens to see a good choice of $\gamma$?

Using that, you can solve this by finding a $\gamma$ satisfying
$$\gamma \equiv 0 \pmod{p-1}$$
$$\gamma \equiv \alpha^x \pmod{p}$$