[adastra22]

From the actual problem description:

Note that the puzzle can be solved by performing t successive squarings modulo n, beginning with the value 2. That is, set

W(0) = 2

W(i+1) = (W(i) ^ 2) (mod n) for i=1, 2, ...

and compute W(t).

There is no known way to perform this computation more quickly than to perform the t squarings sequentially, unless the factorization of n is known.

[lucb1e]

Ah! Thanks. That immediately answers the second thing I was wondering about, since 2k RSA keys are still deemed safe (if barely / not for secrets that need to last a long time into the future)

[TacticalCoder]

In addition to what GP answered: note that I didn't crack anything. I just really did all the 79 trillion sequential computation needed to find the solution. That's the really need thing: you can encode the problem in a split second and yet decide how many sequential steps are needed to find the solution.

[adastra22]

Yeah the cost of breaking the time lock is presumably less than breaking the order of the group.