We consider a 1-to-K communication scenario, where a source transmits private messages to K receivers through a broadcast erasure channel, and the receivers feedback strictly, causally, and publicly their channel states after each transmission. We explore the achievable rate region when we require that the message to each receiver remains secret-in the information theoretical sense-from all the other receivers. We characterize the capacity of secure communication in all the cases where the capacity of the 1-to-K communication scenario without the requirement of security is known. As a special case, we characterize the secret-message capacity of a single receiver point-to-point erasure channel with public state-feedback in the presence of a passive eavesdropper. We find that in all the cases where we have an exact characterization, we can achieve the capacity using linear complexity two-phase schemes: in the first phase, we create appropriate secret keys, and in the second phase, we use them to encrypt each message. We find that the amount of key we need is smaller than the size of the message, and equal to the amount of encrypted message the potential eavesdroppers jointly collect. Moreover, we prove that a dishonest receiver that provides deceptive feedback cannot diminish the rate experienced by the honest receivers. We also develop a converse proof which reflects the two-phase structure of our achievability scheme. As a side result, our technique leads to a new outer bound proof for the nonsecure communication problem.
We consider a 1-to-K communication scenario, where a source transmits private messages to K receivers through a broadcast erasure channel, and the receivers feedback strictly, causally, and publicly their channel states after each transmission. We explore the achievable rate region when we require that the message to each receiver remains secret-in the information theoretical sense-from all the other receivers. We characterize the capacity of secure communication in all the cases where the capacity of the 1-to-K communication scenario without the requirement of security is known. As a special case, we characterize the secret-message capacity of a single receiver point-to-point erasure channel with public state-feedback in the presence of a passive eavesdropper. We find that in all the cases where we have an exact characterization, we can achieve the capacity using linear complexity two-phase schemes: in the first phase, we create appropriate secret keys, and in the second phase, we use them to encrypt each message. We find that the amount of key we need is smaller than the size of the message, and equal to the amount of encrypted message the potential eavesdroppers jointly collect. Moreover, we prove that a dishonest receiver that provides deceptive feedback cannot diminish the rate experienced by the honest receivers. We also develop a converse proof which reflects the two-phase structure of our achievability scheme. As a side result, our technique leads to a new outer bound proof for the nonsecure communication problem.
We consider a 1-to-K communication scenario, where a source transmits private messages to K receivers through a broadcast erasure channel, and the receivers feed back strictly causally and publicly their channel states after each transmission. We explore the achievable rate region when we require that the message to each receiver remains secret - in the information theoretical sense - from all the other receivers. We characterize the capacity of secure communication in all the cases where the capacity of the 1-to-K communication scenario without the requirement of security is known. As a special case, we characterize the secret-message capacity of a single receiver point-to-point erasure channel with public state-feedback in the presence of a passive eavesdropper. We find that in all cases where we have an exact characterization, we can achieve the capacity by using linear complexity two-phase schemes: in the first phase we create appropriate secret keys, and in the second phase we use them to encrypt each message. We find that the amount of key we need is smaller than the size of the message, and equal to the amount of encrypted message the potential eavesdroppers jointly collect. Moreover, we prove that a dishonest receiver that provides deceptive feedback cannot diminish the rate experienced by the honest receivers. We also develop a converse proof which reflects the two-phase structure of our achievability scheme. As a side result, our technique leads to a new outer bound proof for the non-secure communication problem.
This paper presents exact capacity characterizations for the case, when a principal, Alice, wants to securely send a message to another principal, Bob, over three network configurations: the parallel edges network, the V-network, and the triangle network. We assume that: 1) a passive eavesdropper, Eve, overhears any one edge in the network; 2) each edge corresponds to an independent broadcast packet erasure channel with arbitrary erasure probabilities; and 3) all legitimate nodes can publicly but causally acknowledge whether they received each packet or not. We develop optimal achievability schemes that are expressed as linear programs (LPs) and share a two-phase structure, where at the first phase, we create secret keys, and at the second phase, we use them to encrypt the transmitted message. Our outer bounds are also expressed through LP formulations. We prove that our schemes are optimal by showing that the optimal solution of the outer bound LP and the optimal solution of the achievability scheme LP coincide.
We investigate the problem of information theoretically secure communication in a line network with erasure channels and state feedback. We consider a spectrum of cases for the private randomness that intermediate nodes can generate, ranging from having intermediate nodes generate unlimited private randomness, to having intermediate nodes generate no private randomness, and all cases in between. We characterize the secret message capacity when either only one of the channels is eavesdropped or all of the channels are eavesdropped, and we develop polynomial time algorithms that achieve these capacities. We also give an outer bound for the case where an arbitrary number of channels is eavesdropped. Our work is the first to characterize the secrecy capacity of a network of arbitrary size, with imperfect channels and feedback. As a side result, we derive the secret key and secret message capacity of an one-hop network, when the source has limited randomness.
This paper investigates the secure data transmission in the broadcast channel with noiseless feedback by using the information-theoretic method. We consider transmitting a private message and a common message to two receivers, of which the common message is to be decoded by both receivers while the private message is only for the intended receiver. The channel to the intended receiver is assumed to be independent of that to the other receiver. Feedback from the output of the intended receiver is used as a shared secret key to enhance the secrecy in the transmission. The capacity-equivocation region and the secrecy capacity of this new model are obtained. We find the secrecy capacity is enhanced by using feedback, even in the case that the other receiver is in a better position than the intended receiver. In addition, our results generalize the secrecy capacity of the degraded wiretap channel with secure feedback, and the capacity region of the degraded broadcast channel.
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.
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.