The broadcast channel with independent secret keys is studied. In this scenario, a common message has to be securely broadcast to two legitimate receivers in the presence of an eavesdropper. The transmitter shares with each legitimate receiver an independent secret key of arbitrary rate. These keys can either be used as one-time pads to encrypt the common message or can be interpreted as fictitious messages used as randomization resources for wiretap coding. Both approaches are discussed and the secrecy capacity is derived for various cases. Depending on the qualities of the legitimate and eavesdropper channels, either a one-time pad, wiretap coding, or a combination of both turns out to be capacity-achieving.
The broadcast channel with independent secret keys is studied. In this scenario, a common message has to be securely broadcast to two legitimate receivers in the presence of an eavesdropper. The transmitter shares with each legitimate receiver an independent secret key of arbitrary rate. These keys can either be used as one-time pads to encrypt the common message or can be interpreted as fictitious messages used as randomization resources for wiretap coding. Both approaches are discussed and the secrecy capacity is derived for various cases. Depending on the qualities of the legitimate and eavesdropper channels, either a one-time pad, wiretap coding, or a combination of both turns out to be capacity-achieving.
The problem of secure broadcasting with independent secret keys is studied. The particular scenario is analyzed where a common message has to be broadcasted to two legitimate receivers, while keeping an external eavesdropper ignorant of it. The transmitter shares independent secret keys of arbitrary rates with both legitimate receivers, which can be used in different ways: They can be used as one-time pads to encrypt the common message or they can be used as randomization resources for wiretap coding. Both approaches are studied in this paper. If both legitimate channels are degraded versions of the eavesdropper channel, it is shown that the one-time pad approach is optimal for several cases yielding corresponding capacity expressions. Reversely, the wiretap coding approach is shown to be optimal if the eavesdropper channel is degraded with respect to both legitimate channels establishing capacity in this case as well.
The broadcast channel with independent secret keys models a communication scenario in which a common message has to be securely broadcast to two legitimate receivers keeping an eavesdropper ignorant of it.The transmitter shares an independent secret key of arbitrary rate with each legitimate receiver.Depending on the channel qualities of the legitimate receivers and the eavesdropper, these secret keys must be used as one-time pads to encrypt the message, as fictitious messages for randomization in wiretap coding, or a combination of both to achieve the secrecy capacity.In this paper, communication takes place over independent parallel subchannels and the secrecy capacity is established for these cases, in which all parallel channels follow the same order of degradation.
The problem of secure broadcasting with independent secret keys is studied. The particular scenario is analyzed in which a common message has to be broadcast to two legitimate receivers, while keeping an external eavesdropper ignorant of it. The transmitter shares independent secret keys of sufficiently high rates with both legitimate receivers, which can be used in different ways: they can be used as one-time pads to encrypt the common message, as fictitious messages for wiretap coding, or as a hybrid of these. In this paper, capacity results are established when the broadcast channels involving the three receivers are degraded. If both legitimate channels are degraded versions of the eavesdropper's channel, it is shown that the one-time pad approach is optimal for several cases, yielding corresponding capacity expressions. Alternatively, the wiretap coding approach is shown to be optimal if the eavesdropper's channel is degraded with respect to both legitimate channels, establishing capacity in this case as well. If the eavesdropper's channel is neither the strongest nor the weakest, an intricate scheme that carefully combines both concepts of one-time pad and wiretap coding with fictitious messages turns out to be capacity-achieving. Finally we also obtain some results for the general non-degraded broadcast channel.
The use of secret keys in broadcast channels with receiver side information is studied. The particular scenario is analyzed where a transmitter wants to send two confidential messages to two receivers, while keeping an external eavesdropper ignorant. Each receiver has one of the confidential messages as side information available for decoding. In addition to that, the transmitter shares independent secret keys of arbitrary rates with both receivers. The secret keys can be used in different ways: They can act as one-time pads to encrypt the confidential messages or they can be used as randomization resources for wiretap coding. Both approaches are discussed and an achievable rate region based on superposition coding is established for the one-time pad approach. For the wiretap coding approach, the secrecy capacity for degraded channels is derived. In the optimal coding scheme, the available secret keys are used as the randomization part of the wiretap code to keep the eavesdropper ignorant. In establishing the capacity region, a new upper bound on the sum-rate is derived. This bound shows that in an optimal coding scheme, in the degraded case, the total equivocation-rate of the (opposite) secret-keys at the legitimate receivers must equal the equivocation-rate of the secret-keys at the eavesdropper, when informed about the messages.
Confidentiality of information is a key consideration in many networking applications, including e-commerce, online banking, and intelligence operations. How can information be communicated reliably to the legitimate users, while keeping it secret from eavesdroppers? How does such a secrecy constraint on communication affect the limits on information flow in the network? In this chapter, we study these questions under the information theoretic notion of secrecy, which requires each eavesdropper to obtain essentially no information about the messages sent from knowledge of its received sequence, the channel statistics, and the codebooks used. We investigate two approaches to achieve secure communication. The first is to exploit the statistics of the channel from the sender to the legitimate receivers and the eavesdroppers. We introduce the wiretap channel as a 2-receiver broadcast channel with a legitimate receiver and an eavesdropper, and establish its secrecy capacity, which is the highest achievable secret communication rate. The idea is to design the encoder so that the channel from the sender to the receiver becomes effectively stronger than the channel to the eavesdropper; hence the receiver can recover the message but the eavesdropper cannot. This wiretap coding scheme involves multicoding and randomized encoding. If the channel from the sender to the receiver is weaker than that to the eavesdropper, however, secret communication at a positive rate is not possible. This brings us to the second approach to achieve secret communication, which is to use a secret key shared between the sender and the receiver but unknown to the eavesdropper. We show that the rate of such secret key must be at least as high as the rate of the confidential message. This raises the question of how the sender and the receiver can agree on such a long secret key in the first place. After all, if they had a confidential channel with sufficiently high capacity to communicate the key, then why not use it to communicate the message itself! We show that if the sender and the receiver have access to correlated sources (e.g., through a satellite beaming common randomness to them), then they can still agree on a secret key even when the channel has zero secrecy capacity. We first consider the source model for key agreement, where the sender communicates with the receiver over a noiseless public broadcast channel to generate a secret key from their correlated sources.
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.