"National security" falls under the umbrella of "common Defence" (which appears twice in the Constitution). Indeed, one of the motivating forces behind the creation of a stronger federal government under the Constitution was Shay's Rebellion, which was a purely internal threat.
The term ("privacy") does not appear in the Constitution, and the specific limits on federal power that do appear can't be generalized to fit under the umbrella of that term. There is no indication that e.g. the founders intended the 5th amendment protection against self-incrimination to be rooted in a "privacy" concept. It's clearly based on a "due process" concept, which explains why there is no general right to refuse to testify (which is what you'd have if the right was based on privacy) but only a right to refuse to testify in a way that might incriminate yourself. The concern is about he extreme persuasiveness of confessions, and the potential for abuse from coerced confessions, not about the right to keep information from a government investigation.
Similarly, the 3rd and 4th are better understood as rights based on the sanctity of the home and person (notably since the 4th conspicuously omits any reference to communications).
Attempts to find a right of "privacy" in the Constitution are extremely strained, for the simple reason that there isn't one. The founders just weren't thinking of this overriding concept of "privacy" as an umbrella concept for rights as disparate as protection against search and seizure, self-incrimination, or a right to an abortion.
