If you have the 3-loop case, you don't need to know the output of
the 3rd encryption before feeding a new input to the 1st -- so you can
be running 3 at a time, as your diagram showed. That's what gives you
3x the speed.
Perhaps the following term will help others understand what Carl is
getting at. (I get the impression that understanding is not yet
universal.)
Carl in essence wants to *pipeline* the 3 stage computation. While
latency for a single block remains the same, sustained throughput is
3x faster with 3 loops vs. 1.
-Ray