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JUCS - Journal of Universal Computer Science

E - Capacity - Equivocation Region of Wiretap Channel

Mariam E. Haroutunian

Published Nov 28, 2021• 1 citation
Publisher

Abstract

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.

DOI
10.3897/jucs.76605

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In a wire tap channel, the transmitter Alice communicates with the legitimate receiver, Bob, in the presence of another receiver, Eve. The goal is to keep the wiretapper, Eve, as ignorant as possible about the information sent to Bob. For communication channels where the adversary, Eve, eavesdrops on the information sent between the legitimate users by wiretapping at the Bob's end, Wyner introduced secure encoding schemes and showed that non zero reliable transmission rate is possible in perfect secrecy. Wyner also obtained the information theoretic achievable rate equivocation region (Rb, DeltaK) for discrete memoryless wire tap channels. The rate equivocation region (Rb, DeltaK) is a trade off between the rate Rb at which information is sent by Alice to Bob, and the level of equivocation (confusion) DeltaK at the wiretapper Eve about this information. In this dissertation, we propose an iterative algorithm to compute the rate equivocation region (Rb, DeltaK) for any finite input finite output discrete memoryless wiretap channels in Wyners model. First, we investigate the achievable region of Wyner's wire tap channel in both Wyners and Csiszar Korner form. We analyze the general form of the achievable region in both forms and show that both forms are equivalent. We also show that calculating the rate equivocation region can be reduced to the computing of a function Gamma Rb defined by Wyner. Computing the function Gamma Rb involves convex programming and there exists no analytic closed form solution. We transform the function Gamma Rb into a minimax problem and obtain the function Gamma Rb in its parametric form. Calculating the parametric expressions in terms of the Lagrange multiplier yields a point on the Gamma Rb curve. Next, we propose an iterative algorithm for computing the parametric expressions. The iterative procedure can be viewed as a generalization of the Arimoto Blahut method. We prove the convergence of the algorithm and derive upper and lower bounds on the optimum value as a stopping criteria of the iterative algorithm. We provide simulation results about the computation of the parametric expressions from the proposed algorithm and of the achievable rate equivocation region. We also analyze the speed of the convergence of the proposed algorithm. We further propose an accelerated iterative algorithm to compute the parametric expressions with improved performance. The iterative procedure can be regarded as a generalization of the accelerated Arimoto Blahut algorithm. We obtain a sufficient condition of the weighted parameter

Civil War Book Review•Apr 4, 2018•0 citations
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.
We study the Gaussian multiple-input multiple-output (MIMO) wiretap channel, which consists of a transmitter, a legitimate user, and an eavesdropper. In this channel, the transmitter sends a common message to both the legitimate user and the eavesdropper. In addition to this common message, the legitimate user receives a private message, which is desired to be kept hidden as much as possible from the eavesdropper. We obtain the entire capacity-equivocation region of the Gaussian MIMO wiretap channel. This region contains all achievable common message, private message, and private message's equivocation (secrecy) rates. In particular, we show the sufficiency of jointly Gaussian auxiliary random variables and channel input to evaluate the existing single-letter description of the capacity-equivocation region due to Csiszar–Korner.
We study the Gaussian multiple-input multiple-output (MIMO) wiretap channel, which consists of a transmitter, a legitimate user, and an eavesdropper. In this channel, the transmitter sends a common message to both the legitimate user and the eavesdropper. In addition to this common message, the legitimate user receives a private message, which is desired to be kept hidden as much as possible from the eavesdropper. We obtain the entire capacity-equivocation region of the Gaussian MIMO wiretap channel. This region contains all achievable common message, private message, and private message's equivocation (secrecy) rates. In particular, we show the sufficiency of jointly Gaussian auxiliary random variables and channel input to evaluate the existing single-letter description of the capacity-equivocation region due to Csiszar-Korner.
A simple four node network in which cooperation improves the information-theoretic secrecy is studied. The channel consists of two senders, a receiver, and an eavesdropper. One or both senders transmit confidential messages to the receiver, while the eavesdropper tries to decode the transmitted message. The main result is the derivation of a newly achievable rate-equivocation region that is shown to be larger than a rate-equivocation region derived by Lai and El Gamal for the relay-eavesdropper channel. When the rate of the helping interferer is zero, the new rate-equivocation region reduces to the capacity-equivocation region over the wire-tap channel, hence, the new achievability scheme can be seen as a generalization of a coding scheme proposed by Csiszar and Korner. This result can naturally be combined with a rate-equivocation region given by Tang et al. (for the interference assisted secret communication), yielding an even larger achievable rate-equivocation region.
In a wire tap channel, the transmitter Alice communicates with the legitimate receiver, Bob, in the presence of another receiver, Eve. The goal is to keep the wiretapper, Eve, as ignorant as possible about the information sent to Bob. For communication channels where the adversary, Eve, eavesdrops on the information sent between the legitimate users by wiretapping at the Bob's end, Wyner introduced secure encoding schemes and showed that non zero reliable transmission rate is possible in perfect secrecy. Wyner also obtained the information theoretic achievable rate equivocation region (Rb, DeltaK) for discrete memoryless wire tap channels. The rate equivocation region (Rb, DeltaK) is a trade off between the rate Rb at which information is sent by Alice to Bob, and the level of equivocation (confusion) DeltaK at the wiretapper Eve about this information. In this dissertation, we propose an iterative algorithm to compute the rate equivocation region (Rb, DeltaK) for any finite input finite output discrete memoryless wiretap channels in Wyners model. First, we investigate the achievable region of Wyner's wire tap channel in both Wyners and Csiszar Korner form. We analyze the general form of the achievable region in both forms and show that both forms are equivalent. We also show that calculating the rate equivocation region can be reduced to the computing of a function Gamma Rb defined by Wyner. Computing the function Gamma Rb involves convex programming and there exists no analytic closed form solution. We transform the function Gamma Rb into a minimax problem and obtain the function Gamma Rb in its parametric form. Calculating the parametric expressions in terms of the Lagrange multiplier yields a point on the Gamma Rb curve. Next, we propose an iterative algorithm for computing the parametric expressions. The iterative procedure can be viewed as a generalization of the Arimoto Blahut method. We prove the convergence of the algorithm and derive upper and lower bounds on the optimum value as a stopping criteria of the iterative algorithm. We provide simulation results about the computation of the parametric expressions from the proposed algorithm and of the achievable rate equivocation region. We also analyze the speed of the convergence of the proposed algorithm. We further propose an accelerated iterative algorithm to compute the parametric expressions with improved performance. The iterative procedure can be regarded as a generalization of the accelerated Arimoto Blahut algorithm. We obtain a sufficient condition of the weighted parameter