  Multilevel diversity coding is a classical coding model where multiple
mutually independent information messages are encoded, such that different
reliability requirements can be afforded to different messages. It is well
known that {\em superposition coding}, namely separately encoding the
independent messages, is optimal for symmetric multilevel diversity coding
(SMDC) (Yeung-Zhang 1999). In the current paper, we consider weakly secure SMDC
where security constraints are injected on each individual message, and provide
a complete characterization of the conditions under which superposition coding
is sum-rate optimal. Two joint coding strategies, which lead to rate savings
compared to superposition coding, are proposed, where some coding components
for one message can be used as the encryption key for another. By applying
different variants of Han's inequality, we show that the lack of opportunity to
apply these two coding strategies directly implies the optimality of
superposition coding. It is further shown that under a set of particular
security constraints, one of the proposed joint coding strategies can be used
to construct a code that achieves the optimal rate region.
