Formal variant of 'under the hood'

I am working on my Bachelor thesis and I need to use the formal way of saying 'under the hood'. The context is similar to: The agent accepts the message, performs processing and relays it to DUA. Under the hood, it is done (achieved) by...

Or is that phrase 'under the hood' already appropriate for using in that formal writing? Thank you in advance

Solution 1:

Internally

While this is still figurative (in that a software mechanism does not have a literal inside), it is perhaps more formal than under the hood.

Internally, it is done by ...

(Hat tip to Mick's comment.)

Solution 2:

This is implemented by ...

Implementation involves ...

To implement this, ...

Per Wikipedia

In computer science, an implementation is a realization of a technical specification or algorithm as a program, software component, or other computer system through computer programming and deployment. Many implementations may exist for a given specification or standard.

In computer science (apparently the general field you're writing in), it's not just the algorithm or specs that are interesting. The way an algorithm is implemented is important too.

"Implement" is kind of a traditional word in such a context.