Recovering the key in an ElGamal Signature Scheme variant
Well, we can approach it this way: if we denote the hashes of the two consecutive messages $H_1, H_2$, the signer used the internal values $k, k+2$, resulting in signatures $(r_1, s_1), (r_2, s_2)$, then we have (and all this arithmetic is modulo $p-1$):

$s_1 = (H_1 - x r_1) k^{-1}$

$s_2 = (H_2 - x r_2) (k+2)^{-1}$

where $x$ is the secret key we're interested in.  Rearranging, we get:

$s_1k = H_1 - x r_1$

$s_2(k+2) = H_2 - x r_2$

where we know the values of $r_1, s_1, r_2, s_2, H_1, H_2$; there's only two unknowns ($k, x$) which both appear as linear terms; we just solve the two simultaneous linear equations, which immediately gives us $x$.

It is easy to see that this observation can be extended to the case where the difference between two different internal $k$ values is something the attacker can guess.