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Computer Science and Information Technologies (CSIT)

Outer Bound for E-capacity - Equivocation Region of the Wiretap Channel

Mariam E. Haroutunian

Published Sep 1, 2019• 3 citations
Publisher

Abstract

The basic wiretap channel model is considered. The aim is to maximize the rate of the reliable communication from the source to the legitimate receiver, while keeping the confidential information as secret as possible from the wiretapper (eavesdroper). The E-capacity - equivocation region, which is the generalization of the capacity - equivocation region, is investigated. The outer bound of this region is constructed.

DOI
10.1109/csitechnol.2019.8895005

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The concept of the wiretap channel was first proposed by Wyner. He considered the case in which data is to be transmitted reliably over a discrete memoryless main channel to a legitimate receiver. The wiretapper views the output of the main channel through another discrete memoryless channel. It is assumed that the wiretapper knows the code being used and his only handicap is the additional noise in his signal. The problem is to maximize the transmission rate R to the legitimate receiver and the equivocation d of the wiretapper. In this dissertation, the additive white Gaussian noise wiretap channel is introduced and the set of all achievable (R,d) pairs is determined explicitly through the use of certain special properties of the Gaussian channel. Some useful characterizations of a special class of wiretap channels are also explored. A model of the wiretap channel with feedback is proposed. It turns out that with the introduction of feedback, even when the main channel is inferior to the wiretapper's channel, it is still possible to reliably communicate with the legitimate receiver in complete secrecy. The binary erasure wiretap channel with feedback is examined and inner and outer bounds on the achievable (R,d) region are given. Finally, a scheme for enlarging the capacity region of multiple-access channels using feedback is analyzed. It is shown that conditions under which an enlargement is possible are fairly weak, indicating that feedback can almost increase the capacity region. (Author)

•Jan 1, 1976•19 citations
The basic wiretap channel model is considered. The aim is to maximize the rate of the reliable communication from the source to the legitimate receiver, while keeping the confidential information as secret as possible from the wiretapper (eavesdroper). The E-capacity - equivocation region, which is the generalization of the capacity - equivocation region, is investigated. The outer bound of this region is constructed.
One of the problems of information - theoretic security concerns secure communication over a wiretap channel. The aim in the general wiretap channel model is to maximize the rate of the reliable communication from the source to the legitimate receiver, while keeping the confidential information as secret as possible from the wiretapper (eavesdropper). We introduce and investigate the E - capacity - equivocation region and the E - secrecy capacity function for the wiretap channel, which are, correspondingly, the generalizations of the capacity - equivocation region and secrecy - capacity studied by Csiszár and Körner (1978). The E - capacity equivocation region is the closure of the set of all achievable rate - reliability and equivocation pairs, where the rate - reliability function represents the optimal dependence of rate on the error probability exponent (reliability). By analogy with the notion of E - capacity, we consider the E - secrecy capacity function that for the given E is the maximum rate at which the message can be transmitted being kept perfectly secret from the wiretapper.
Investigation of communication over a wiretap channel is one of the problems of information–theoretic security. The aim in the general wiretap channel model is to maximize the rate of the reliable communication from the source to the legitimate receiver, while keeping the confidential information as secret as possible from the wiretapper (eavesdropper). Here we consider the compound wiretap channel model, when the channels to the legitimate receiver and to the wiretapper depends on the number of possible states. We investigate the EEE -capacity–equivocation region which is the closure of the set of all achievable rate-reliability and equivocation pairs, where the rate-reliability function represents the optimal dependence of rate on the error probability exponent (reliability). Here the outer bound of this region is constructed in the case, when the states are not known to all terminals.
The action-dependent states (ADSs) in wiretap channel is revisited. The transmitter aims to convey a confidential message to the receiver and protect it from the wiretapper as possible as he can. Actions are taken by the transmitter to influence the channel state information. For such a channel, Dai et al. first got an outer bound on the capacity-equivocation region which contains all the achievable transmission rates. We find a new outer bound and prove it is better than Dai's in terms of approximating the maximum rate at which the confidential message can be transmitted in perfect secrecy. Furthermore, the new outer bound provides the engineer with a more precise target to achieve higher transmission rates in the capacity-equivocation region.
Information embedding on actions is a new channel model in which a specific decoder is used to observe the actions taken by the encoder and retrieve part of the message intended for the receiver. We revisit this model and consider a different scenario where a secrecy constraint is imposed. By adding a wiretapper in the model, we aim to send the confidential message to the receiver and keep it secret from the wiretapper as much as possible. We characterize the inner and outer bounds on the capacity-equivocation region of such a channel with noncausal (and causal) channel state information. Furthermore, the lower and upper bounds on the sum secrecy capacity are also obtained. Besides, by eliminating the specific decoder, we get a new outer bound on the capacity-equivocation region of the wiretap channel with action-dependent states and prove it is tighter than the existing outer bound. A binary example is presented to illustrate the tradeoff between the sum secrecy rate and the information embedding rate under the secrecy constraint. We find that the secrecy constraint and the communication requirements of information embedding have a negative impact on improving the secrecy transmission rate of the given communication link.
Information embedding on actions is a new channel model in which a specific decoder is used to observe the actions taken by the encoder and retrieve part of the message intended for the receiver. We revisit this model and consider a more practical scenario where secrecy constraints are imposed. By adding a wiretapper in the model, we aim to send the confidential message to the receiver and keep it secret from the wiretapper as much as possible. We characterize the inner and outer bounds on the capacity-equivocation region of such a channel with noncausal (and causal) channel state information. Furthermore, the lower and upper bounds on the secrecy capacity are also obtained. Besides, by eliminating the specific decoder, we get a new outer bound on the capacity-equivocation region of wiretap channel with action-dependent states and prove it is tighter than the existing outer bound.
The concept of the wiretap channel was first proposed by Wyner. He considered the case in which data is to be transmitted reliably over a discrete memoryless main channel to a legitimate receiver. The wiretapper views the output of the main channel through another discrete memoryless channel. It is assumed that the wiretapper knows the code being used and his only handicap is the additional noise in his signal. The problem is to maximize the transmission rate R to the legitimate receiver and the equivocation d of the wiretapper. In this dissertation, the additive white Gaussian noise wiretap channel is introduced and the set of all achievable (R,d) pairs is determined explicitly through the use of certain special properties of the Gaussian channel. Some useful characterizations of a special class of wiretap channels are also explored. A model of the wiretap channel with feedback is proposed. It turns out that with the introduction of feedback, even when the main channel is inferior to the wiretapper's channel, it is still possible to reliably communicate with the legitimate receiver in complete secrecy. The binary erasure wiretap channel with feedback is examined and inner and outer bounds on the achievable (R,d) region are given. Finally, a scheme for enlarging the capacity region of multiple-access channels using feedback is analyzed. It is shown that conditions under which an enlargement is possible are fairly weak, indicating that feedback can almost increase the capacity region. (Author)