No one knows at this very moment. (thanks @Terry)
It is highly possible that it is not even defined. There are several options, depending on what the Brazil government wants to do: do they want to stop spying, or do they want to stop spying from NSA ? (In the latter case, this means that Brazil could want to maintain possibility of spying by themselves).
The linked article contains the following excerpt:
Data will be stored on local servers.
and also that one:
For the user of the future service to actually be protected, however, the message recipient will also have to use Correios' email.
Both hint at some sort of network of decentralized encryption gateways. End users would connect to a specific gateway which would do all encryption and decryption, and ensure protection against spies on the big network links. However, the gateways would be in ideal place to spy on users. In a business context, we may imagine that each corporation would run its own gateway.
NSA spies would have to fall back to the methods that they.. already use... e.g. keyloggers or even simple bribery. Let it be a message: ye shall pay your sysadmins well, because they can see everything if they are such inclined.