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IEEE Transactions on Information Theory

A New Wiretap Channel Model and Its Strong Secrecy Capacity

Mohamed Nafea, Aylin Yener

Published Dec 22, 2017• 26 citations
Publisher

Abstract

In this paper, a new wiretap channel model is proposed, where the legitimate transmitter and receiver communicate over a discrete memoryless channel. The wiretapper has perfect access to a fixed-length subset of the transmitted code word symbols of her choosing. Additionally, she observes the remainder of the transmitted symbols through a discrete memoryless channel. This new model subsumes the classical wiretap channel and wiretap channel II with noisy main channel as its special cases, and is termed as the generalized wiretap channel for that reason. The strong secrecy capacity of the proposed channel model is identified. Achievability is established by solving a dual secret key agreement problem in the source model, and converting the solution to the original channel model using probability distribution approximation arguments. In the dual problem, a source encoder and decoder, who observe random sequences independent and identically distributed according to the input and output distributions of the legitimate channel in the original problem, communicate a confidential key over a public error-free channel using a single forward transmission, in the presence of a compound wiretapping source who has perfect access to the public discussion. The security of the key is guaranteed for the exponentially many possibilities of the subset chosen at the wiretapper by deriving a lemma which provides a doubly-exponential convergence rate for the probability that, for a fixed choice of the subset, the key is uniform and independent from the public discussion and the wiretapping source's observation. The converse is derived by using Sanov's theorem to upper bound the secrecy capacity of the generalized wiretap channel by the secrecy capacity when the tapped subset is randomly chosen by nature.

DOI
10.1109/tit.2017.2786541

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In this paper, a new wiretap channel model is proposed, where the legitimate transmitter and receiver communicate over a discrete memoryless channel. The wiretapper has perfect access to a fixed-length subset of the transmitted code word symbols of her choosing. Additionally, she observes the remainder of the transmitted symbols through a discrete memoryless channel. This new model subsumes the classical wiretap channel and wiretap channel II with noisy main channel as its special cases, and is termed as the generalized wiretap channel for that reason. The strong secrecy capacity of the proposed channel model is identified. Achievability is established by solving a dual secret key agreement problem in the source model, and converting the solution to the original channel model using probability distribution approximation arguments. In the dual problem, a source encoder and decoder, who observe random sequences independent and identically distributed according to the input and output distributions of the legitimate channel in the original problem, communicate a confidential key over a public error-free channel using a single forward transmission, in the presence of a compound wiretapping source who has perfect access to the public discussion. The security of the key is guaranteed for the exponentially many possibilities of the subset chosen at the wiretapper by deriving a lemma which provides a doubly-exponential convergence rate for the probability that, for a fixed choice of the subset, the key is uniform and independent from the public discussion and the wiretapping source's observation. The converse is derived by using Sanov's theorem to upper bound the secrecy capacity of the generalized wiretap channel by the secrecy capacity when the tapped subset is randomly chosen by nature.
In this paper, a new wiretap channel model is proposed, where the legitimate transmitter and receiver communicate over a discrete memoryless channel. The wiretapper has perfect access to a fixed-length subset of the transmitted codeword symbols of her choosing. Additionally, she observes the remainder of the transmitted symbols through a discrete memoryless channel. This new model subsumes the classical wiretap channel and wiretap channel II with noisy main channel as its special cases. The strong secrecy capacity of the proposed channel model is identified. Achievability is established by solving a dual secret key agreement problem in the source model, and converting the solution to the original channel model using probability distribution approximation arguments. In the dual problem, a source encoder and decoder, who observe random sequences independent and identically distributed according to the input and output distributions of the legitimate channel in the original problem, communicate a confidential key over a public error-free channel using a single forward transmission, in the presence of a compound wiretapping source who has perfect access to the public discussion. The security of the key is guaranteed for the exponentially many possibilities of the subset chosen at wiretapper by deriving a lemma which provides a doubly-exponential convergence rate for the probability that, for a fixed choice of the subset, the key is uniform and independent from the public discussion and the wiretapping source's observation. The converse is derived by using Sanov's theorem to upper bound the secrecy capacity of the new wiretap channel model by the secrecy capacity when the tapped subset is randomly chosen by nature.
A new model for the two-user multiple-access wiretap channel is considered. In this model, the legitimate (main) channel is a discrete memoryless channel (DMC), and the wiretapper chooses a fixed-length subset of the channel uses where she has perfect access to the transmitted symbols of the both users, while observing the remainder of the transmitted codewords through a second DMC. As such, it generalizes the existing multiple-access wiretap channel models and extends the recently proposed new wiretap channel model to a multiple access setting. An achievable strong secrecy rate region for the model is derived. The achievability is established by solving a dual multi-terminal secret key agreement problem in the source model, where two independent sources are communicating confidential keys to a common decoder over a public channel in the presence of a compound wiretapping source. The secrecy of the two keys in the dual source model is established by deriving a lemma which provides a doubly exponential convergence rate for the probability of the keys being uniform and independent from the public discussion and the wiretapping source observation.
In this paper, new two-user multiple access wiretap channel models are studied. First, the multiple access wiretap channel II with a discrete memoryless main channel under different wiretapping scenarios is introduced. The wiretapper, as in the classical wiretap channel II model, chooses a fixed-size subset of the channel uses, in which it obtains noise-free observations of one of the codewords: a deterministic function, e.g., superposition, of the two codewords or each of the two codewords. A fourth wiretapping scenario is considered, in which the wiretapper, in each position it chooses, decides to observe either one of the codewords or both codewords, with an overall budget on the number of its noiselessly observed symbols. These, thus, extend the recently examined wiretap channel II with a noisy main channel to a multiple access setting with a variety of attack models for the wiretapper. Next, the proposed multiple access wiretap channel II models are further generalized to the case when the wiretapper observes the outputs of a discrete memoryless channel, instead of erasures, outside the subset of noiseless observations. Achievable strong secrecy rate regions for all the proposed models are derived. Achievability is established by solving dual multi-terminal secret key agreement problems in the source model and converting the solution to the original channel models using probability distribution approximation arguments. The derived achievable rate regions quantify the secrecy cost due to the additional capabilities of the wiretapper with respect to the previous multiple access wiretap models.
In this paper, a new wiretap channel (WTC) model with a discrete memoryless (DM) main channel and a wiretapper who noiselessly observes a fixed portion, of her choice, of the transmitted symbols, while observing the remaining transmitted symbols through another DM channel (DMC), is considered. The strong secrecy capacity of the model is identified. The achievability is established using the output statistics of random binning framework which exploits the duality between source and channel coding problems. The converse is derived by upper bounding the secrecy capacity of an equivalent model with the secrecy capacity of a DM-WTC. This result generalizes both the classical DM-WTC and the WTC-II with a DM main channel.
The secrecy capacity of an extended communication model of wiretap channelII is determined. In this channel model, the source message is encoded into a digital sequence of length N and transmitted to the legitimate receiver through a discrete memoryless channel (DMC). There exists an eavesdropper who is able to observe arbitrary μ = N α digital symbols from the transmitter through a second DMC, where 0 ≤ α ≤ 1 is a constant real number. A pair of an encoder and a decoder is designed to let the receiver be able to recover the source message with a vanishing decoding error probability and keep the eavesdropper ignorant of the message. This communication model includes a variety of wiretap channels as special cases. The coding scheme is based on that designed by Ozarow and Wyner for the classic wiretap channel II.
A new broadcast wiretap channel (B-WTC) with a wiretapper who noiselessly taps into a fixed-length subset of the transmitted symbols of her choice, and observes the remainder through a noisy channel, is studied. An achievable strong secrecy rate region which extends Marton's inner bound to the proposed setting, is derived. Strong secrecy capacity regions for two classes of the new B-WTC, namely the new B-WTC with deterministic receivers, and the new B-WTC with degraded receivers and more noisy wiretapper, are identified. These results extend the recently proposed new wiretap channel model to the broadcast setting.