Latin for "to Hide Complexity" as Related to "to Abstract"

Personally, I like the term to hide complexity which you already mentioned in the question. However, I find nothing wrong with the terms to abstract or to encapsulate. The meanings you listed are the literal meanings of their latin roots, but in the case of IT (and not only there), the meaning is used metaphorically:

In the case of abstracting, we detach/divert from some concrete thing into a more general idea. For example, John Doe is a concrete man while the term "man" describes any of a general group of persons and is therefore more abstract. You can point at John Doe with your finger because he's a concrete person. You can't point your finger at "man" in general because it's an abstract term - it is detached from the concrete. You can't see some of the details like you could with a specific person (like their hair color) but they are still there. The same happens with abstractions in computer science - details get hidden as we detach from concrete representations into a more general view of the issue (like going from byte representations to abstract "characters"). This is a perfectky valid usage for the term abstract.

Similarily, the term to encapsulate is widely used in computer science in the metaphorical sense. The "putting in" here has the meaning of putting something inside something else in order to hide details from view but to be able to use it more conveniently. It's like putting several small objects inside a box - you can't see the individual objects any more but they sure are more convenient to carry this way. This meaning of to encapsulate is also well established in the IT industry and perfectly valid.

The verb I suggest is to shield with the meaning of:

• To cover up; conceal.

  unluckily it has no latin origin, but it coneys the idea of covering and protecting ( the underlying data).