Nodes can come and go. They just have to talk few neighbors. If you want every node over some time period participating, you can't do faster than than log2(n)

Nodes can come and go. They just have to talk few neighbors. If you want every node over some time period participating, you can't do faster than than log2(n) XOR operations. (in above comment I said O(n) xor's, that's obviously wrong. You need only log(N) xor's)