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arXiv:1501.07547 · IEEE Transactions on Information Theory

Individual Secrecy for Broadcast Channels With Receiver Side Information

Yanling Chen, O. Ozan Koyluoglu, Aydin Sezgin

Published Apr 28, 2017• 10 citations
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Abstract

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.

DOI
10.1109/tit.2017.2699201

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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.
In this paper, we study the problem of secure communication over the broadcast channel with receiver side information, under the lens of individual secrecy constraints (i.e., information leakage from each message to an eavesdropper is made vanishing). Several coding schemes are proposed by extending known results in broadcast channels to this secrecy setting. In particular, individual secrecy provided via one-time pad signal is utilized in the coding schemes. As a result, we obtain an achievable rate region together with a characterization of the capacity region for special cases of either a weak or strong eavesdropper (compared to both legitimate receivers). Interestingly, the capacity region for the former corresponds to a line and the latter corresponds to a square with missing corners; a phenomenon occurring due to the coupling between user's rates. At the expense of having a weaker notion of security, positive secure transmission rates are always guaranteed, unlike the case of the joint secrecy constraint.
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 individual secrecy capacity region of the broadcast channel with receiver side information. First, an achievable rate region is established for the discrete memoryless case by employing superposition coding. Further, it is extended to the corresponding Gaussian case, where the individual secrecy capacity region is characterized in case of a weak or strong eavesdropper (compared to two legitimate receivers). For the case left, inner and outer bounds are established and the individual secrecy capacity region is characterized for the low and high SNR regimes. Note that the last case is distinctive due to the individual secrecy constraint, in the sense that positive rate pair is still possible although the eavesdropper may have the advantage against at least one of the legitimate receivers over the channel, unlike the situation if the joint secrecy constraint is imposed.
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.
We study the transmission of a common message and three confidential messages over a broadcast channel with two legitimate receivers and an eavesdropper. Each legitimate receiver is interested in decoding two of the three confidential messages, while having the third one as side information. In order to measure the ignorance of the eavesdropper about the confidential messages, we investigate two different secrecy criteria: joint secrecy and individual secrecy. For both criteria, we provide a general achievable rate region. We establish both the joint and individual secrecy capacity if the two legitimate receivers are less noisy than the eavesdropper. We further investigate the scenario where the eavesdropper is less noisy than the two legitimate receivers. It is known that the joint secrecy constraints can not be fulfilled under this scenario, however, we manage to establish a non vanishing capacity region for the individual secrecy case.
We study secure communication in which two confidential messages are transmitted over a broadcast channel to two legitimate receivers, while keeping an eavesdropper ignorant. Each legitimate receiver is interested in decoding one confidential message, while having the other one as side information. In order to measure the secrecy of the communication, we investigate two different secrecy criteria: joint secrecy and individual secrecy. For both criteria, we provide an achievable rate region and a matching multi-letter outer bound presenting a multi-letter description for the capacity region. We further investigate the class of more capable channels and provide a single-letter converse establishing the secrecy capacity region, not only for more capable channels but less noisy and degraded channels as well. Our results indicate that the secrecy capacity for individual secrecy is higher than the one for joint secrecy, as one message can be used as a secret key for the other one.