  We investigate the combination between causal/zero-delay source coding and
information-theoretic secrecy. Two source coding models with secrecy
constraints are considered. We start by considering zero-delay perfectly secret
lossless transmission of a memoryless source. We derive bounds on the key rate
and coding rate needed for perfect zero-delay secrecy. In this setting, we
consider two models which differ by the ability of the eavesdropper to parse
the bit-stream passing from the encoder to the legitimate decoder into separate
messages. We also consider causal source coding with a fidelity criterion and
side information at the decoder and the eavesdropper. Unlike the zero-delay
setting where variable-length coding is traditionally used but might leak
information on the source through the length of the codewords, in this setting,
since delay is allowed, block coding is possible. We show that in this setting,
separation of encryption and causal source coding is optimal.
