Something like "The right of the people to be secure in their persons, houses, papers, and effects, against unreasonable searches and seizures, shall not be violated"
Eh it's kind of a technicality that passwords are protected at all. It's not a privacy thing.
If you keep incriminating documents in a safe, the police have every right (with a warrant) to cut it open and get the documents. If the safe has a code, you don't have to share the code, but only because SHARING the code requires you to be "a witness against yourself" in violation of the 5th amendment, not because you have a right to privacy in the safe.
It's hard to justify giving a fingerprint as being a "witness against yourself". So with a warrant or other relevant due process it's hard to object.
I disagree with this idea myself. I believe that any compelled action that leads to your incrimination should be considered being a witness against yourself. I realise this isn't the established caselaw, and I already have some obvious potential reasons bubbling up in my mind as to why. For instance how can you give someone a breathalyser test if they refuse? It defnitely creates problems.
That said, I think bigger problems with this standard are coming down the line eventually.
"any compelled action" would also preclude giving ID at a traffic stop. Maybe even stopping for police at all. A line needs to be drawn somewhere, and I think it must be a balancing of the various interests rather than a hard and fast rule. For example privacy vs successfully convicting wrongdoers vs preventing convicting the innocent vs preventing abuse of power vs public safety etc etc.