LDGR
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Allowing nodes to join a network is vital to maintaining its health so that it can accommodate nodes exiting the network.  However, ensuring that new nodes are safe and not acting maliciously is difficult.
Using a blockchain could let the network to authenticate and verify new nodes.  This would allow for existing nodes to authenticate joining nodes via a hash to verify their identity and add them to the network.  Existing nodes in a network must re-certify after a certain TTK or be declared "dead" by the network and reshuffling will occur.  Nodes would store log(n) neighboring nodes (or use a hop-based binary search finger list like Chord) to allow for quicker lookup. 
Blockchain would allow for a verified, propagating ledger of the most recent active nodes which have been verified by the network.  This also has potential in verifying the lookup tables stored at nodes to verify they are still relaying accurate, non-malicious information to querying nodes.
Since blockchain is still an emergent technology, little has been done exploring its uses.  An example is the Ethereum Naming Service, which aims to reproduce the functionality provided by the Domain Naming Service.
I would like to explore the possibility of adding a Blockchain Overlay to a core-network to enhance security and ward off malicious actors.  This could either be an overlay on the existing DNS-framework or on a proposed P2P framework like the Chord Overlay Network.