Two chaotic systems which interact by mutually exchanging a signal built from
their delayed internal variables, can synchronize. A third unit may be able to
record and to manipulate the exchanged signal. Can the third unit synchronize
to the common chaotic trajectory, as well? If all parameters of the system are
public, a proof is given that the recording system can synchronize as well.
However, if the two interacting systems use private commutative filters to
generate the exchanged signal, a driven system cannot synchronize. It is shown
that with dynamic private filters the chaotic trajectory even cannot be
calculated. Hence two way (interaction) is more than one way (drive). The
implication of this general result to secret communication with chaos
synchronization is discussed
