Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

International Conference on Communications

The individual secrecy capacity of degraded multi-receiver wiretap broadcast channels

Ahmed S. Mansour, Rafael F. Schaefer, Holger Boche

Published Jun 1, 2015• 17 citations
Publisher

Abstract

We study secure communication over a degraded wiretap broadcast channel with multiple receivers and an eavesdropper. We consider two different secrecy measures: the traditional joint secrecy where the mutual information leakage of all messages must be small; and individual secrecy where the sum of the information leakage of each individual message must be small. At first, we investigate the joint secrecy criterion, where we present the capacity region established before and provide a simpler converse proof. We then consider the individual secrecy criterion and establish its capacity region, by combining the techniques of wiretap random coding and Shannon's one time pad principle. Our results indicate that the individual secrecy capacity region is bigger than the joint one. Further, we show that the established capacity regions are valid for any degraded wiretap broadcast channel, regardless of the degradedness order of the eavesdropper. Finally, we extend our results to Gaussian channels.

DOI
10.1109/icc.2015.7248979

Related papers

On the Individual Secrecy Capacity Regions of the General, Degraded, and Gaussian Multi-Receiver Wiretap Broadcast Channel

Ahmed S. Mansour, Rafael F. Schaefer, Holger Boche

In this paper, secure communication over a broadcast channel with multiple legitimate receivers and an external eavesdropper is investigated. Two different secrecy measures are considered. The first criterion is a conservative one known as joint secrecy, where the mutual leakage of all confidential messages must be small. The second criterion is a less conservative constraint known as individual secrecy, where the individual leakage of each confidential message must be small. At first, we consider the degraded multi-receiver wiretap broadcast channel and manage to establish the individual secrecy capacity region. Our encoding scheme applies a careful combination of the standard techniques of wiretap random coding and Shannon's one time pad encoding, where the confidential messages of the weak receivers are used as secret keys for the stronger ones. The validity of this technique is due to the properties of the degraded broadcast channel and the secrecy requirements of the individual secrecy criterion. Our result indicates that the individual secrecy capacity region is in fact larger than the joint one established in earlier literature. The established capacity region is then used to derive the individual secrecy capacity regions of the Gaussian single-input single-output and degraded Gaussian multiple-input multiple-output multi-receiver wiretap broadcast channels. Furthermore, we present an achievable rate region for the general two-receiver wiretap broadcast channel under both the joint and the individual secrecy criterion. Comparing these two rate regions suggests that even for the general case, the individual secrecy criterion might be able to provide a larger rate region compared with the joint one.

IEEE Transactions on Information Forensics and Security•May 10, 2016•16 citations

Secrecy Capacity of a Class of Broadcast Channels with an Eavesdropper

Ersen Ekrem, Şennur Ulukuş

We study the security of communication between a single transmitter and multiple receivers in a broadcast channel in the presence of an eavesdropper. We consider several special classes of channels. As the first model, we consider the degraded multi-receiver wiretap channel where the legitimate receivers exhibit a degradedness order while the eavesdropper is more noisy with respect to all legitimate receivers. We establish the secrecy capacity region of this channel model. Secondly, we consider the parallel multi-receiver wiretap channel with a less noisiness order in each sub-channel, where this order is not necessarily the same for all sub-channels. We establish the common message secrecy capacity and sum secrecy capacity of this channel. Thirdly, we study a special class of degraded parallel multi-receiver wiretap channels and provide a stronger result. In particular, we study the case with two sub-channels two users and one eavesdropper, where there is a degradedness order in each sub-channel such that in the first (resp. second) sub-channel the second (resp. first) receiver is degraded with respect to the first (resp. second) receiver, while the eavesdropper is degraded with respect to both legitimate receivers in both sub-channels. We determine the secrecy capacity region of this channel. Finally, we focus on a variant of this previous channel model where the transmitter can use only one of the sub-channels at any time. We characterize the secrecy capacity region of this channel as well.

arXiv:0812.0319•Dec 1, 2008•2 citations

On secure broadcasting

Ersen Ekrem, Şennur Ulukuş

We study the security of communication between a single transmitter and multiple receivers in a broadcast channel in the presence of an eavesdropper. We consider several special classes of channels. As the first model, we consider the degraded multi-receiver wiretap channel where the legitimate receivers exhibit a degradedness order while the eavesdropper is more noisy with respect to all legitimate receivers. We establish the secrecy capacity region of this channel model. Secondly, we consider the parallel multi-receiver wiretap channel with a less noisiness order in each sub-channel, where this order is not necessarily the same for all sub-channels. We establish the common message secrecy capacity and sum secrecy capacity of this channel. Thirdly, we study a special class of degraded parallel multi-receiver wiretap channels and provide a stronger result. In particular, we study the case with two sub-channels two users and one eavesdropper, where there is a degradedness order in each sub-channel such that in the first (resp. second) sub-channel the second (resp. first) receiver is degraded with respect to the first (resp. second) receiver, while the eavesdropper is degraded with respect to both legitimate receivers in both sub-channels. We determine the secrecy capacity region of this channel.

Asilomar Conference on Signals, Systems and Computers (ACSSC)•Oct 1, 2008•18 citations

The individual secrecy capacity of the Gaussian SISO and degraded Gaussian MIMO multi-receiver wiretap channel

Ahmed S. Mansour, Rafael F. Schaefer, Holger Boche

We study secure communication in which a transmitter wants to send confidential messages to an arbitrary number of receivers in the presence of an external eavesdropper. We consider two classes of Gaussian channels: the Gaussian single-input single-output (SISO) multi-receiver wiretap channel and the degraded Gaussian multiple-input multiple-output (MIMO) multi-receiver wiretap channel. These two channels belong to the class of degraded multi-receiver wiretap channels. In previous literature the secrecy capacity regions of these two channels were established under the conservative joint secrecy constraint. Thus, we focus our work on the less conservative individual secrecy constraint, which is characterized by a higher throughput. We establish the individual secrecy capacity region for these two cases. The achievability follows from the individual secrecy capacity established for the discrete memoryless degraded wiretap channels where coding is performed using Gaussian signals. On the other hand, the converse is established by adapting the techniques used for formulating the joint secrecy capacity region to the individual secrecy constraint.

IEEE International Workshop on Signal Processing Advances in Wireless Communications (SPAWC)•Jun 1, 2015•5 citations

Secrecy Capacity of a Class of Broadcast Channels with an Eavesdropper

Ersen Ekrem, Şennur Ulukuş

We study the security of communication between a single transmitter and many receivers in the presence of an eavesdropper for several special classes of broadcast channels. As the first model, we consider the degraded multireceiver wiretap channel where the legitimate receivers exhibit a degradedness order while the eavesdropper is more noisy with respect to all legitimate receivers. We establish the secrecy capacity region of this channel model. Secondly, we consider the parallel multireceiver wiretap channel with a less noisiness order in each subchannel, where this order is not necessarily the same for all subchannels, and hence the overall channel does not exhibit a less noisiness order. We establish the common message secrecy capacity and sum secrecy capacity of this channel. Thirdly, we study a class of parallel multireceiver wiretap channels with two subchannels, two users and an eavesdropper. For channels in this class, in the first (resp., second) subchannel, the second (resp., first) receiver is degraded with respect to the first (resp., second) receiver, while the eavesdropper is degraded with respect to both legitimate receivers in both subchannels. We determine the secrecy capacity region of this channel, and discuss its extensions to arbitrary numbers of users and subchannels. Finally, we focus on a variant of this previous channel model where the transmitter can use only one of the subchannels at any time. We characterize the secrecy capacity region of this channel as well.

EURASIP Journal on Wireless Communications and Networking•Aug 6, 2009•94 citations

Joint and individual secrecy in broadcast channels with receiver side information

Ahmed S. Mansour, Rafael F. Schaefer, Holger Boche

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.

IEEE International Workshop on Signal Processing Advances in Wireless Communications (SPAWC)•Jun 1, 2014•11 citations
We study secure communication over a degraded wiretap broadcast channel with multiple receivers and an eavesdropper. We consider two different secrecy measures: the traditional joint secrecy where the mutual information leakage of all messages must be small; and individual secrecy where the sum of the information leakage of each individual message must be small. At first, we investigate the joint secrecy criterion, where we present the capacity region established before and provide a simpler converse proof. We then consider the individual secrecy criterion and establish its capacity region, by combining the techniques of wiretap random coding and Shannon's one time pad principle. Our results indicate that the individual secrecy capacity region is bigger than the joint one. Further, we show that the established capacity regions are valid for any degraded wiretap broadcast channel, regardless of the degradedness order of the eavesdropper. Finally, we extend our results to Gaussian channels.
In this paper, secure communication over a broadcast channel with multiple legitimate receivers and an external eavesdropper is investigated. Two different secrecy measures are considered. The first criterion is a conservative one known as joint secrecy, where the mutual leakage of all confidential messages must be small. The second criterion is a less conservative constraint known as individual secrecy, where the individual leakage of each confidential message must be small. At first, we consider the degraded multi-receiver wiretap broadcast channel and manage to establish the individual secrecy capacity region. Our encoding scheme applies a careful combination of the standard techniques of wiretap random coding and Shannon's one time pad encoding, where the confidential messages of the weak receivers are used as secret keys for the stronger ones. The validity of this technique is due to the properties of the degraded broadcast channel and the secrecy requirements of the individual secrecy criterion. Our result indicates that the individual secrecy capacity region is in fact larger than the joint one established in earlier literature. The established capacity region is then used to derive the individual secrecy capacity regions of the Gaussian single-input single-output and degraded Gaussian multiple-input multiple-output multi-receiver wiretap broadcast channels. Furthermore, we present an achievable rate region for the general two-receiver wiretap broadcast channel under both the joint and the individual secrecy criterion. Comparing these two rate regions suggests that even for the general case, the individual secrecy criterion might be able to provide a larger rate region compared with the joint one.
We study the security of communication between a single transmitter and multiple receivers in a broadcast channel in the presence of an eavesdropper. We consider several special classes of channels. As the first model, we consider the degraded multi-receiver wiretap channel where the legitimate receivers exhibit a degradedness order while the eavesdropper is more noisy with respect to all legitimate receivers. We establish the secrecy capacity region of this channel model. Secondly, we consider the parallel multi-receiver wiretap channel with a less noisiness order in each sub-channel, where this order is not necessarily the same for all sub-channels. We establish the common message secrecy capacity and sum secrecy capacity of this channel. Thirdly, we study a special class of degraded parallel multi-receiver wiretap channels and provide a stronger result. In particular, we study the case with two sub-channels two users and one eavesdropper, where there is a degradedness order in each sub-channel such that in the first (resp. second) sub-channel the second (resp. first) receiver is degraded with respect to the first (resp. second) receiver, while the eavesdropper is degraded with respect to both legitimate receivers in both sub-channels. We determine the secrecy capacity region of this channel. Finally, we focus on a variant of this previous channel model where the transmitter can use only one of the sub-channels at any time. We characterize the secrecy capacity region of this channel as well.
We study the security of communication between a single transmitter and multiple receivers in a broadcast channel in the presence of an eavesdropper. We consider several special classes of channels. As the first model, we consider the degraded multi-receiver wiretap channel where the legitimate receivers exhibit a degradedness order while the eavesdropper is more noisy with respect to all legitimate receivers. We establish the secrecy capacity region of this channel model. Secondly, we consider the parallel multi-receiver wiretap channel with a less noisiness order in each sub-channel, where this order is not necessarily the same for all sub-channels. We establish the common message secrecy capacity and sum secrecy capacity of this channel. Thirdly, we study a special class of degraded parallel multi-receiver wiretap channels and provide a stronger result. In particular, we study the case with two sub-channels two users and one eavesdropper, where there is a degradedness order in each sub-channel such that in the first (resp. second) sub-channel the second (resp. first) receiver is degraded with respect to the first (resp. second) receiver, while the eavesdropper is degraded with respect to both legitimate receivers in both sub-channels. We determine the secrecy capacity region of this channel.
We study secure communication in which a transmitter wants to send confidential messages to an arbitrary number of receivers in the presence of an external eavesdropper. We consider two classes of Gaussian channels: the Gaussian single-input single-output (SISO) multi-receiver wiretap channel and the degraded Gaussian multiple-input multiple-output (MIMO) multi-receiver wiretap channel. These two channels belong to the class of degraded multi-receiver wiretap channels. In previous literature the secrecy capacity regions of these two channels were established under the conservative joint secrecy constraint. Thus, we focus our work on the less conservative individual secrecy constraint, which is characterized by a higher throughput. We establish the individual secrecy capacity region for these two cases. The achievability follows from the individual secrecy capacity established for the discrete memoryless degraded wiretap channels where coding is performed using Gaussian signals. On the other hand, the converse is established by adapting the techniques used for formulating the joint secrecy capacity region to the individual secrecy constraint.
We study the security of communication between a single transmitter and many receivers in the presence of an eavesdropper for several special classes of broadcast channels. As the first model, we consider the degraded multireceiver wiretap channel where the legitimate receivers exhibit a degradedness order while the eavesdropper is more noisy with respect to all legitimate receivers. We establish the secrecy capacity region of this channel model. Secondly, we consider the parallel multireceiver wiretap channel with a less noisiness order in each subchannel, where this order is not necessarily the same for all subchannels, and hence the overall channel does not exhibit a less noisiness order. We establish the common message secrecy capacity and sum secrecy capacity of this channel. Thirdly, we study a class of parallel multireceiver wiretap channels with two subchannels, two users and an eavesdropper. For channels in this class, in the first (resp., second) subchannel, the second (resp., first) receiver is degraded with respect to the first (resp., second) receiver, while the eavesdropper is degraded with respect to both legitimate receivers in both subchannels. We determine the secrecy capacity region of this channel, and discuss its extensions to arbitrary numbers of users and subchannels. Finally, we focus on a variant of this previous channel model where the transmitter can use only one of the subchannels at any time. We characterize the secrecy capacity region of this channel as well.
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.