Breaking cryptosystems? That exact construct would be so much more useful than that. It'd let you have a ticking time-lock encryption service -- I encrypt a message using the keys from the next block until block number N at some point in the future. You now have a message that will decrypt at a specified time in the future automatically and without intervention. That is a tremendous public resource to say nothing of its use within the system as a smart contracting primitive.
Unfortunately known methods of achieving this (e.g. breaking low-bit EC keys using Pallard's rho algorithm) don't meet the basic requirements of a proof of work system, the chief problem here being non-progress-free.
If it's worth saying, but not worth its own post, then it goes here.
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