This is almost exactly how my proposed NIP 87 works, except the group is recognized by p-tagged recipient, so members check directly for all keys for the group that have been shared with them. But I thought MLS solved this through the hierarchical key derivation stuff? My impression was that MLS made it possible to make the number of messages that need to be sent scale logarithmically with the number of recipients, without resorting to shared keys.

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Yes. This is true for crypto operations, and ratchets. But since nostr is the delivery service we need to make sure everyone has access to the messages they need. When they need them. P tagging shows basically the whole group membership publicly no?!