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

Wiretap and Gelfand-Pinsker Channels Analogy and its Applications

An analogy framework between wiretap channels (WTCs) and state-dependent point-to-point channels with non-causal encoder channel state information (referred to as Gelfand-Pinker channels (GPCs)) is proposed. A good sequence of stealth-wiretap codes is shown to induce a good sequence of codes for a corresponding GPC. Consequently, the framework enables exploiting existing results for GPCs to produce converse proofs for their wiretap analogs. The analogy readily extends to multiuser broadcasting scenarios, encompassing broadcast channels (BCs) with deterministic components, degradation ordering between users, and BCs with cooperative receivers. Given a wiretap BC (WTBC) with two receivers and one eavesdropper, an analogous Gelfand-Pinsker BC (GPBC) is constructed by converting the eavesdropper's observation sequence into a state sequence with an appropriate product distribution (induced by the stealth-wiretap code for the WTBC), and non-causally revealing the states to the encoder. The transition matrix of the state-dependent GPBC is extracted from WTBC's transition law, with the eavesdropper's output playing the role of the channel state. Past capacity results for the semi-deterministic (SD) GPBC and the physically-degraded (PD) GPBC with an informed receiver are leveraged to furnish analogy-based converse proofs for the analogous WTBC setups. This characterizes the secrecy-capacity regions of the SD-WTBC and the PD-WTBC, in which the stronger receiver also observes the eavesdropper's channel output. These derivations exemplify how the wiretap-GP analogy enables translating results on one problem into advances in the study of the other