An analysis of the timed Z-channel

Abstract

Our timed Z-channel (a general case of the Z-channel) appears as the basis for a large class of covert channels. Golomb (1980) analyzed the Z-channel, a memoryless channel with two input symbols and two output symbols, where one of the input symbols is transmitted with noise while the other is transmitted without noise, and the output symbol transmission times are equal. We introduce the timed Z-channel, where the output symbol transmission times are different. Specifically, we show how the timed Z-channel applies to two examples of covert timing channel scenarios: a CPU scheduler and a token ring network. We then give a detailed analysis of our timed Z-channel. We report a new result expressing the capacity of the timed Z-channel as the log of the root of a trinomial equation. This changes the capacity calculation from an optimization problem into a simpler algebraic problem and illustrates the relationship between the noise and time factors. Further, it generalizes Shannon's (1948, 1949) work on noiseless channels for this special case. We also report a new result bounding the timed Z-channel's capacity from below. Finally, we show how an interesting observation that Golomb reported for the Z-channel also holds for the timed Z-channel.