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Is it mathematically possible to accomplish this without another party involved? I can't think of a way, but some mathematicians are pretty clever...
In the average case, couldn't you just randomly generate a pretty small key, encrypt the information, then throw the key away? Then you could start the process of randomly guessing at the key, and eventually you'd figure it out again. Just pick a key size based on the amount of computing you're willing to do to decrypt.