I definitely have the impression that even if the hard problem a cryptosystem is based on actually is hard (which is yet to be proved, but I agree is almost certainly true), most of the time the algorithm used to actually encrypt stuff is not completely without flaws, which are successively patched and exploited. I thought this was obvious, just how everyone assumed it worked! Obviously an algorithm which (a) uses a long key length and (b) is optimised for simplicity rather than speed is more likely to be secure, but is it really the consensus that some cryptosystems are free from obscure flaws? Haven't now-broken systems in the past been considered nearly infalliable? Perhaps someone (or you if you do) who knows professional cryoptography systems can clear that up, which ought to be pretty obvious?