Is establishing a secret key possible given this characteristic primitive? I am wondering if there are any readily available solutions for the following problem:
I have a ring-topology network with several devices connected to it, some malicious, some legitimate. I want to authenticate / establish a shared key between two legitimate devices, without the malicious ones finding out the key. There are no preshared secrets or certificates or anything, only this: During startup (and perhaps in regular intervals) I can exchange several messages between two trusted devices knowing for certain that the messages were sent by that trusted device (due to device-specific characteristic voltage spikes on the network).
Is this sufficient to establish a shared secret or key? I personally dont see a way but wanted to ask. Thanks!
During startup (and perhaps in regular intervals) I can exchange several messages between two trusted devices knowing for certain that the messages were sent by that trusted device (due to device-specific characteristic voltage spikes on the network).
Is this sufficient to establish a shared secret or key?

Should be; during start-up, have each device select a random signature public key, and broadcast it (and have every other device remember the public keys that they can validate came from a specific device).
Assuming that honest device A knows honest device B's public key (and knows that it is, in fact, B's key), and B knows A's public key, then it becomes easy; for example, A can generate a Diffie-Hellman key share, sign it with his private signature key, and send it to B; B also picks a DH key share, and sends a signed copy to A.  A and B validate the signatures they received, and then compute the shared secret.
No third device can recover the shared secret based on the published key shares, signatures and public keys.  In addition, because the key shares are signed, no one can modify them without one of the signature verification steps giving an error.
Now, I suspect that doing the above may be a bit more than what you personally want to take on; however it is most assuredly a solvable problem.