With magic wormhole, I've discovered SPAKE(2) and I was wondering if it is possible to derive pairwise shared keys between multiple participants still using one password only. More precisely, amongst N participants, each node can broadcast the same handshake value to every other nodes. Reminder for node A and B:
A) x random, X = g^x, sends X* = X * N^pwd
B) y random, Y = g^y, sends Y* = Y * M^pwd (N & M are public and can be the same)
If everyone broadcast the same handshake (X*, Y*, Z*...), and make pair-wise shared key with every other participants (i.e. combining X* and Y*, X* and Z*, etc), is it still secure ? The paper does not say about x being unique, although I might have overlooked.