I was just reading something about NP-hard problems and cryptosystems. I was thinking: Every NP-complete problem can be reduced to another and every NP-complete problem has NP-hard problem. Attack on the one NP-hard cryptosystem will mean that every NP-hard cryptosystem will be vulnerable to that attack after reducing it. That would actually mean that we will be able to extend Information Set Decoding attack of Code-based systems to any NP-hard based cryptosystem.

Is this consideration correct?