Outgoing messages contain no explicit address of the recipient of the message. Therefore, every network participant tries to decrypt every message passing through the network even if the message was not originally intended for that network participant. Since only the actual recipient can successfully decrypt the messages intended for him, all network participants know that if they fail to decrypt the message then the message was not intended for them.
From Jonathan Warren's original paper:
We propose a system where users exchange a hash of a public key that also functions as the user’s address. If the public key can be obtained by the underlying protocol, then it can easily be hashed to verify that it belongs to the intended recipient... an example address would be:
It appears that a user's public key (or, a hash of their public key) is their messaging address. Thus, there is nothing to verify: when you send a message to user with public key
P, you don't need to verify that your recipient's public key is really
P, because you have identified your recipient solely by his public key.
As for how to tell if a public key belongs to a particular real-world entity: you can't, just as you can't easily verify that a particular email address belongs to a particular real-world entity.
For example, you want to send Alice a message. Alice advertises her Bitmessage address (e.g., on her business cards, on her public website, etc.) as
BM‐2nTX1KchxgnmHvy9ntCN9r7sgKTraxczzyE. You make a P2P Bitmessage request to get the public key associated with
BM‐2nTX1KchxgnmHvy9ntCN9r7sgKTraxczzyE. When you have fetched the key, you quickly verify that its fingerprint matches the one in Alice's address. then, you use the Bitmessage system to encrypt your message so it is readable only by Alice's private key.
But how did you know that
BM‐2nTX1KchxgnmHvy9ntCN9r7sgKTraxczzyE is really Alice's address? Maybe someone printed out fake business cards, or hijacked Alice's website to change her address. Maybe so, but if they did, that's not a problem that Bitmessage is designed to solve.
In fact, the lack of connection between an address and a real-world entity seems to be branded as a feature:
Hiding one’s identity is difficult. Even if throw-away email addresses are used, users must connect to an email server to send and retrieve messages, revealing their IP address...
And when talking about broadcast messages (emphasis mine):
This would allow an individual or organization to anonymously publish content using an authenticated identity to everyone who wishes to listen.
The primary use for BitMessage (as presented in the paper, anyway) seems to be the ability to sent messages that are from a cryptographically verified source, but that source is free to avoid identifying themselves in any real-world way.
I think that something like PGP's web of trust could be implemented on top of BitMessage to provide identity verification: such authentication is not incompatible with BitMessage, but it seems to be a service that would exists independent of BitMessage (i.e., step 1: verify that
BM‐2nTX1Kc... really is Alice's address; step 2: send a message to
BM‐2nTX1Kc... using BitMessage).