[lxgr]

It's actually not that straightforward:

- How is the problem of key distribution solved? How does Bob know that the key is in fact Alices and not Mallorys?

- The scheme you propose does not provide forward secrecy.

- (How) is authentication performed? Are signatures used; if so, are they non-repudiable or deniable?

Secure instant messaging is not a solved problem (at least not in the form of a practical, usable implementation).