Code change:
9.1. <del> [[ OPEN ISSUE: Direct initialization is currently undefined.  A client can create a group by initializing its own state to reflect a group including only itself, then adding the initial members.  This has computation and communication complexity O(N log N) instead of the O(N) complexity of direct initialization. ]] </del> <ins> A group can always be created by initializing a one-member group and using adding members individually.  For cases where the initial list of members is known, the Init message allows a group to be created more efficiently. The creator of the group constructs an Init message as follows: Fetch a UserInitKey for each member (including the creator) Identify a protocol version and cipher suite that is supported by all proposed members. Construct a ratchet tree with its leaves populated with the public keys and credentials from the UserInitKeys of the members, and all other nodes blank. Generate a fresh leaf key pair for the first leaf Compute its direct path in this ratchet tree Each member of the newly-created group initializes its state from the Init message as follows: Note the group ID, protocol version, and cipher suite in use Construct a ratchet tree as above Update the cached ratchet tree by replacing nodes in the direct path from the first leaf using the direct path Update the cached ratchet tree by replacing nodes in the direct path from the first leaf using the information contained in the "path" attribute The update secret for this interaction, used with an all-zero init secret to generate the first epoch secret, is the "path_secret[i+1]" derived from the "path_secret[i]" associated to the root node.  The members learn the relevant path secrets by decrypting one of the encrypted path secrets in the DirectPath and working back to the root (as in normal DirectPath processing). [[ OPEN ISSUE: This approach leaks the initial contents of the tree to the Delivery Service, unlike the sequential-Add case. ]] [[ OPEN ISSUE: It might be desireable for the group creator to be able to "pre-warm" the tree, by providing values for some nodes not on its direct path.  This would violate the tree invariant, so we would need to figure out what mitigations would be necessary. ]] </ins> 9.2.

Related discussion:
text: This is something we've been meaning to do for a while, and just haven't gotten around to. The Init message directly creates a group with a specified member list. The cost of group creation is O(N) DH operations for the sender, and O(1) for receivers.
This now has an OPEN ISSUE regarding the fact that we'll need to add PKE encryption for that message, as agreed out of band, let's merge this and add encryption in the next iteration.
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