This paper studies the problem of secure communication over a K-transmitter multiple access channel in the presence of an external eavesdropper, subject to a joint secrecy constraint (i.e., information leakage rate from the collection of K messages to an eavesdropper is made vanishing). As a result, we establish the joint secrecy achievable rate region. To this end, our results build upon two techniques in addition to the standard information-theoretic methods. The first is a generalization of Chia-El Gamal's lemma on entropy bound for a set of codewords given partial information. The second is to utilize a compact representation of a list of sets that, together with properties of mutual information, leads to an efficient Fourier-Motzkin elimination. These two approaches could also be of independent interests in other contexts.
This paper studies the problem of secure communication over a K-transmitter multiple access channel in the presence of an external eavesdropper, subject to a joint secrecy constraint (i.e., information leakage rate from the collection of K messages to an eavesdropper is made vanishing). As a result, we establish the joint secrecy achievable rate region. To this end, our results build upon two techniques in addition to the standard information-theoretic methods. The first is a generalization of Chia-El Gamal's lemma on entropy bound for a set of codewords given partial information. The second is to utilize a compact representation of a list of sets that, together with properties of mutual information, leads to an efficient Fourier-Motzkin elimination. These two approaches could also be of independent interests in other contexts.
Collective Secrecy Over the K -Transmitter Multiple Access Channel
This paper studies the problem of secure communication over a K -transmitter multiple access channel (MAC) in the presence of an external eavesdropper, subject to a collective secrecy constraint (i.e., information leakage rate to an eavesdropper on a collection of messages that are from a pre-specified subset of the K transmitters, say S⊆K={1,2,…,K} , is made vanishing). Since secrecy is of concern only to transmitters {i∣i∈S} but not to transmitters {i∣i∈Sc} , where Sc=K\S , different transmission strategies could be employed at transmitters {i∣i∈Sc} . Consider the following two scenarios: 1) transmitters {i∣i∈Sc} use deterministic encoders (which are conventionally used for MAC without secrecy), competing for the channel resource (i.e., being competitive) and 2) transmitters {i∣i∈Sc} use stochastic encoders, helping to hide other transmitters’ messages from the eavesdropper (i.e., being cooperative). As a result, we establish the respective S -collective secrecy achievable rate regions and demonstrate the advantage of being cooperative theoretically and numerically. To this end, in addition to the standard techniques, our results build upon two techniques. The first is a generalization of Chia-El Gamal’s lemma on entropy bound for a set of codewords given partial information. The second is to utilize a compact representation of a list of sets that, together with submodular properties of mutual information functions involved, leads to an efficient Fourier-Motzkin elimination. These two approaches allow us to derive achievable regions in this work, and could also be of independent interest in other context.
Motivated in part by the problem of secure multicast distributed storage, we analyze secrecy rates for a channel in which two transmitters simultaneously multicast to two receivers in the presence of an eavesdropper. Achievable rates are calculated via extensions of a technique due to Chia and El~Gamal and also the method of output statistics of random binning. An intriguing synergy is observed between the achievable rate expressions arising from the two techniques: the rate region of the latter is simplified via a constraint that is discovered while deriving the former rate region. Outer bounds are derived for both the degraded and non-degraded versions of the channel, and examples are provided in which the inner and outer bounds meet. The inner bounds recover known results for the multiple-access wiretap channel, broadcast channel with confidential messages, and the compound MAC channel. An auxiliary result is also produced that characterizes the minimal randomness necessary to achieve secrecy in multiple-access wiretap channels.
This paper strengthens the known secrecy results for a k-transmitter multiple access channel (MAC) with an external eavesdropper from weak to strong without any rate loss on the achievable region. More specifically, the results are derived under a strong secrecy metric defined by the information leakage to the eavesdropper, instead of the weaker secrecy criteria defined by the information leakage rate or the (average) variation distance. To this end, different approaches are taken to analyze the information leakage and the decoding error probability. Interestingly, both the secrecy and error exponents could be characterized by the (conditional) Rényi mutual information in a concise form. Thus, the region is guaranteed with both information leakage and decoding error probability decreasing exponentially in the code length. Our technique for strong secrecy analysis reflects the resolvability for the k-transmitter MAC; while our error exponent could be regarded as a generalization of Gallager's error exponent.
This paper studies the problem of secure communications over broadcast channels under theindividualsecrecy constraints. That is, the transmitter wants to send two independent messages to two legitimate receivers in the presence of an eavesdropper, while keeping the eavesdropper ignorant ofeachmessage (i.e., the information leakage rate fromeachmessage to the eavesdropper is made vanishing). Building upon Carleial–Hellman’s secrecy coding, Wyner’s secrecy coding, and the framework of Marton’s coding together with techniques, such as rate splitting and indirect decoding, an achievable individual secrecy rate region is established with the characterization of capacity regions for some special cases. In particular, the individual secrecy capacity region for the linear deterministic model is fully characterized, and for the Gaussian model, a constant gap (i.e., 0.5 b within the individual secrecy capacity region) result is obtained. To illustrate the impact of different secrecy constraints on the corresponding capacity regions, comparisons are made with those satisfying joint secrecy and without secrecy constraints. Overall, when compared with the joint secrecy constraint, the results allow for trading off secrecy level and throughput in the system.
This paper studies the problem of secure communication over broadcast channels under the lens of individual secrecy constraints (i.e., information leakage from each message to an eavesdropper is made vanishing). It is known that, for the communication over the degraded broadcast channels, the stronger receiver is able to decode the message of the weaker receiver. In the individual secrecy setting, the message for the weaker receiver can be further utilized to secure the partial message that is intended to the stronger receiver. With such a coding spirit, it is shown that more secret bits can be conveyed to the stronger receiver. In particular, for the corresponding Gaussian model, a constant gap (i.e., 0.5 bits within the individual secrecy capacity region) result is obtained. Overall, when compared with the joint secrecy constraint, the results allow for trading-off secrecy level and throughput in the system.
This paper studies the problem of secure communication over the broadcast channel with receiver-side information under the lens of individual secrecy constraints, that is, the transmitter wants to send two independent messages to two receivers, which have, respectively, the desired message of the other receiver as side information, while keeping the eavesdropper ignorant of each message (i.e., the information leakage rate from each message to the eavesdropper is made vanishing). Building upon one-time pad, secrecy coding, and broadcasting schemes, achievable rate regions are investigated, and the capacity region for special cases of either a weak or strong eavesdropper (compared to both legitimate receivers) is characterized. Interestingly, the capacity region for the former corresponds to a line and the latter corresponds to a rectangle with missing corners; a phenomenon occurring due to the coupling between user's rates. Moreover, the individual secrecy capacity region is also fully characterized for the case where the eavesdropper's channel is deterministic. In addition to discrete memoryless setup, Gaussian scenarios are studied. For the Gaussian model, in addition to the strong and weak eavesdropper cases, the capacity region is characterized for the low and high SNR regimes when the eavesdropper's channel is stronger than one receiver but weaker than the other. Remarkably, positive secure transmission rates are always guaranteed under the individual secrecy constraint, unlike the case of the joint secrecy constraint (i.e., the information leakage rate from both messages to the eavesdropper is made vanishing). Thus, this notion of secrecy serves as an appropriate candidate for trading off secrecy level and transmission rate, making secrecy more affordable but still acceptable to the end user.