You can't use a peer-to-peer network to hide information
Actually you can. Pick N nodes, perhaps using proof of stake weighting to avoid Sybil attacks, and do (N/2) / N
secret sharing over them. You can then add another operation of "rebalancing" by which the N nodes send the keys to M new nodes without the keys ever coming together (informally, you secret share the secret shares, and when every new node receives a share from each old node it can combine them into a secret share of the original computation).