  This paper derives upper and lower bounds on the secrecy capacity-memory
tradeoff of a wiretap erasure broadcast channel (BC) with Kw weak receivers and
Ks strong receivers, where weak receivers, respectively strong receivers, have
same erasure probabilities and cache sizes. The lower bounds are achieved by
schemes that meticulously combine joint cache-channel coding with wiretap
coding and key-aided one-time pads. The presented upper bound holds more
generally for arbitrary degraded BCs and arbitrary cache sizes. When only weak
receivers have cache memories, upper and lower bounds coincide for small and
large cache memories, thus providing the exact secrecy capacity-memory tradeoff
for this setup. The derived bounds allow to further conclude that the secrecy
capacity is positive even when the eavesdropper is stronger than all the
legitimate receivers with cache memories. Moreover, they show that the secrecy
capacity-memory tradeoff can be significantly smaller than its non-secure
counterpart, but it grows much faster when cache memories are small. The paper
also presents a lower bound on the global secrecy capacity-memory tradeoff
where one is allowed to optimize the cache assignment subject to a total cache
budget. It is close to the best known lower bound without secrecy constraint.
For small total cache budget, the global secrecy capacity-memory tradeoff is
achieved by assigning all the available cache memory uniformly over all
receivers if the eavesdropper is stronger than all legitimate receivers, and it
is achieved by assigning the cache memory uniformly only over the weak
receivers if the eavesdropper is weaker than the strong receivers.
