  We develop a low-complexity polar coding scheme for the discrete memoryless
broadcast channel with confidential messages under strong secrecy and
randomness constraints. Our scheme extends previous work by using an optimal
rate of uniform randomness in the stochastic encoder, and avoiding assumptions
regarding the symmetry or degraded nature of the channels. The price paid for
these extensions is that the encoder and decoders are required to share a
secret seed of negligible size and to increase the block length through
chaining. We also highlight a close conceptual connection between the proposed
polar coding scheme and a random binning proof of the secrecy capacity region.
