  We investigate two source coding problems with secrecy constraints. In the
first problem we consider real--time fully secure transmission of a memoryless
source. We show that although classical variable--rate coding is not an option
since the lengths of the codewords leak information on the source, the key rate
can be as low as the average Huffman codeword length of the source. In the
second problem we consider causal source coding with a fidelity criterion and
side information at the decoder and the eavesdropper. We show that when the
eavesdropper has degraded side information, it is optimal to first use a causal
rate distortion code and then encrypt its output with a key.
