It's not a crypto problem. It's not about who you're talking to. It's what they tell you, and where they got the info they're telling you. Mutually mistrustful routing is very hard.
- and tell you about views of the Internet passed on from other neighbors
You can arrange to absolutely trust a given neighbor to be that neighbor, but until every BGP speaker in the world has that relationship, you can't trust the data that they pass on.
And every BGP speaker in the world has both direct controls (advertise this AS, don't advertise that AS) and influential controls (pretend that this AS is farther away than it is, prefer this AS here and not there because it's cheaper for us) that are both necessary and desirable, because money constrains what engineering can do.
Well stated. Cisco's docs go into great detail on this - they've spent a lot of time thinking about how to address the issues in plain ol' BGP with SoBGP (Secure Origin BGP), and they concluded that determining a BGP speaker is authorized to announce a particular route is impossible in a functioning internetwork.
