Generalizing Multiple Access Wiretap and Wiretap II Channel Models: Achievable Rates and Cost of Strong Secrecy.

In this paper, new two-user multiple access wiretap channel models are studied. First, the multiple access wiretap channel II with a discrete memoryless main channel under different wiretapping scenarios is introduced. The wiretapper, as in the classical wiretap channel II model, chooses a fixed-size subset of the channel uses, in which it obtains noise-free observations of one of the codewords: a deterministic function, e.g., superposition, of the two codewords or each of the two codewords. A fourth wiretapping scenario is considered, in which the wiretapper, in each position it chooses, decides to observe either one of the codewords or both codewords, with an overall budget on the number of its noiselessly observed symbols. These, thus, extend the recently examined wiretap channel II with a noisy main channel to a multiple access setting with a variety of attack models for the wiretapper. Next, the proposed multiple access wiretap channel II models are further generalized to the case when the wiretapper observes the outputs of a discrete memoryless channel, instead of erasures, outside the subset of noiseless observations. Achievable strong secrecy rate regions for all the proposed models are derived. Achievability is established by solving dual multi-terminal secret key agreement problems in the source model and converting the solution to the original channel models using probability distribution approximation arguments. The derived achievable rate regions quantify the secrecy cost due to the additional capabilities of the wiretapper with respect to the previous multiple access wiretap models.