On real-time and causal secure source coding

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.