I'm having a difficult time trying to solve this problem.
Suppose Alice uses the Elgamal signature scheme with
$(\alpha, \beta, p) = (2, 33384, 65539)$.
She publishes the two signed messages:
$(m_1, r_1, s_1) = (809, 18357, 1042)$ and $(m_2, r_2, s_2) = (22505, 18357, 26272)$.
Find $a$ by setting up and solving appropriate linear congruences. (I.e., don't compute the discrete logarithm of beta directly)
I know that $\beta = \alpha^a \bmod p$, which in this case would be $33384 = 2^a \bmod 65539$. However, I have no idea how to use the messages to set up congruences to solve for $a$. Any help is appreciated.