Very interesting, and there is PoC already! Thanks for sharing :)
Halseth is making an *actual* proposal for zk channel announcements in LN gossip! :
https://delvingbitcoin.org/t/zk-gossip-for-lightning-channel-announcements/1407/
This topic has fascinated me for the last couple years. LN has a kind of unique position to blaze the trail of creating pure cost based, fully private, anti Sybil/DOS of the type that every privacy network needs.
(Disclaimer: I don't believe PoW works, long term, for anything outside of bitcoin. Probably. )
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