  This paper studies the problem of secure communication over the broadcast
channel with receiver side information under the lens of individual secrecy
constraints. That is, the transmitter wants to send two independent messages to
two receivers which have, respectively, the desired message of the other
receiver as side information, while keeping the eavesdropper ignorant of each
message (i.e., the information leakage from each message to the eavesdropper is
made vanishing). Building upon one-time pad, secrecy coding, and broadcasting
schemes, achievable rate regions are investigated, and the capacity region for
special cases of either a weak or strong eavesdropper (compared to both
legitimate receivers) are characterized. Interestingly, the capacity region for
the former corresponds to a line and the latter corresponds to a square with
missing corners; a phenomenon occurring due to the coupling between user's
rates. Moreover, the individual secrecy capacity region is also fully
characterized for the case where the eavesdropper's channel is deterministic.
In addition to discrete memoryless setup, Gaussian scenarios are studied. For
the Gaussian model, in addition to the strong and weak eavesdropper cases, the
capacity region is characterized for the low and high SNR regimes when the
eavesdropper's channel is stronger than one receiver but weaker than the other.
Remarkably, positive secure transmission rates are always guaranteed under the
individual secrecy constraint, unlike the case of the joint secrecy constraint
(i.e., the information leakage from both messages to the eavesdropper is made
vanishing). Thus, this notion of secrecy serves as an appropriate candidate for
trading off secrecy level and transmission rate; making secrecy more affordable
but still acceptable to the end user.
