[Physicist]

The privilege of the writ of habeas corpus shall not be suspended, unless when in cases of rebellion or invasion the public safety may require it.

Good catch. It is interesting that it is called here a privilege and not a right.

Two questions: does the present situation qualify as a rebellion or invasion, and which branch of government is thereby empowered to suspend the privilege?

[TheOtherOne]

Two questions: does the present situation qualify as a rebellion or invasion, and which branch of government is thereby empowered to suspend the privilege?

I think there is 1 question only: "does the present situation qualify as a rebellion or invasion"?

As for the other,

Article I Section 1. All legislative powers herein granted shall be vested in a Congress of the United States, which shall consist of a Senate and House of Representatives.

I would think therefore that Section 9 is considered a power granted to Congress.

[GVnana]

Two questions: does the present situation qualify as a rebellion or invasion, and which branch of government is thereby empowered to suspend the privilege?

Good questions. I can only offer the information that Congress approved the use of force in the so-called "Patriot Act" and this will most likely be the directive pointed to when called to justify the use of tribunals.