Reveal all information up to n-th message
Is there a way to generate a sequence of keys that have the property that exposing any of those keys will reveal all previous keys, but no future key? 


One possibility: select a hard to factor value $n = pq$; publish the value $n$ (or include it with each day's "key"), and keep the factorization secret.  It'll make things easier if you select $p \equiv q \equiv 3 \pmod 4$

Then, select a random quadratic residue $r_0$ (which you can do by selecting a random value $t$ and computing $r_0 = t^2 \bmod n$)

Then, for each day's secret $r_i$, you can compute the next day's secret $r_{i+1} = \sqrt{r_i} \bmod n$ (that is, a modular square root); there are four such square roots; you'll want the one which is a quadratic residue.

That's actually easier than it sounds; if you took my advice about about $p \equiv q \equiv 3 \pmod 4$, then all you need to do is compute:

$$r_{i+1} \mod p = r_i^{(p+1)/4} \mod p$$

$$r_{i+1} \mod q = r_i^{(q+1)/4} \mod q$$

And combine $r_{i+1} \mod p$ and $r_{i+1} \mod q$ using CRT to reconstruct $r_{i+1}$

This addresses your problem, as:


Computing next keys is as difficult as factoring $n$
Computing previous keys is easy, as $r_{i-1} = r_i^2 \bmod n$
You can compute next keys as long as you want