I've read a paper that says that one of the "assumptions" that it makes is secure broadcast. Why is this an assumption? Can't a broadcast channel be built with simple primitives--i.e. encrypt and sign messages with a shared key?
And, assuming that there is something more that I'm missing, how are broadcast channels usually approximated in practice?
The problem is not broadcast, but secure broadcast. Secure broadcast guarantees that every recipient ends up with the same message.
If you just sign the message and send it separately to each recipient, a malicious sender could send different messages to different recipients.
A simple solution is that each recipient counter-signs the message and re-sends it to the other recipients. Once everyone has everyone's signature on the message, they accept.
There are better solutions, but all of them have an associated cost.
