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This does not mean though, that it is illegal to reinvent the wheel and apply it yourself.

I'm sorry to say that yes, it *IS* illegal to reinvent the wheel and apply it yourself. In the US it is called "Patent Infringement". Now, this may not apply to EVERYTHING, but there are cases where people re-invented something that was classified and their work then became classified.... (I also believe there are stories where the opposite is true, but I don't want to belabor the point)