Strong Secrecy for Multiple Access Channels

We show strongly secret achievable rate regions for two different wiretap multiple-access channel coding problems. In the first problem, each encoder has a private message and both together have a common message to transmit. The encoders have entropy-limited access to common randomness. If no common randomness is available, then the achievable region derived here does not allow for the secret transmission of a common message. The second coding problem assumes that the encoders do not have a common message nor access to common randomness. However, they may have a conferencing link over which they may iteratively exchange rate-limited information. This can be used to form a common message and common randomness to reduce the second coding problem to the first one. We give the example of a channel where the achievable region equals zero without conferencing or common randomness and where conferencing establishes the possibility of secret message transmission. Both coding problems describe practically relevant networks which need to be secured against eavesdropping attacks.Comment: 55 page

Byzantine Multiple Access Channels -- Part I: Reliable Communication

We study communication over a Multiple Access Channel (MAC) where users can possibly be adversarial. The receiver is unaware of the identity of the adversarial users (if any). When all users are non-adversarial, we want their messages to be decoded reliably. When a user behaves adversarially, we require that the honest users' messages be decoded reliably. An adversarial user can mount an attack by sending any input into the channel rather than following the protocol. It turns out that the $2$-user MAC capacity region follows from the point-to-point Arbitrarily Varying Channel (AVC) capacity. For the $3$-user MAC in which at most one user may be malicious, we characterize the capacity region for deterministic codes and randomized codes (where each user shares an independent random secret key with the receiver). These results are then generalized for the $k$-user MAC where the adversary may control all users in one out of a collection of given subsets.Comment: This supercedes Part I of arxiv:1904.1192