The physical layer security in the up-link of the wireless communication systems is often modeled as the multiple access wiretap channel (MAC-WT), and recently it has received a lot attention. In this paper, the MAC-WT has been re-visited by considering the situation that the legitimate receiver feeds his received channel output back to the transmitters via two noiseless channels, respectively. This model is called the MAC-WT with noiseless feedback. Inner and outer bounds on the secrecy capacity region of this feedback model are provided. To be specific, we first present a decode-and-forward (DF) inner bound on the secrecy capacity region of this feedback model, and this bound is constructed by allowing each transmitter to decode the other one's transmitted message from the feedback, and then each transmitter uses the decoded message to re-encode his own messages, i.e., this DF inner bound allows the independent transmitters to co-operate with each other. Then, we provide a hybrid inner bound which is strictly larger than the DF inner bound, and it is constructed by using the feedback as a tool not only to allow the independent transmitters to co-operate with each other, but also to generate two secret keys respectively shared between the legitimate receiver and the two transmitters. Finally, we give a sato-type outer bound on the secrecy capacity region of this feedback model. The results of this paper are further explained via a Gaussian example.
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 three different wiretapping scenarios, is introduced. The wiretapper, as in the classical wiretap channel II model, chooses a fixed-length subset of the channel uses on which she obtains noise-free observations of one of the codewords, a superposition of the two codewords, or each of the two codewords. These thus extend the recently examined wiretap channel II with a noisy main channel to a multiple access setting with a va…
Message Authentication Code (MAC) is a keyed function $f_K$ such that when Alice, who shares the secret $K$ with Bob, sends $f_K(M)$ to the latter, Bob will be assured of the integrity and authenticity of $M$. Traditionally, it is assumed that the channel is noiseless. However, Maurer showed that in this case an attacker can succeed with probability $2^{-\frac{H(K)}{\ell+1}}$ after authenticating $\ell$ messages. In this paper, we consider the setting where the channel is noisy. Specifically, Alice and Bob are connected by a discrete memoryless channel (DMC) $W_1$ and a noiseless but insecure …
This paper is concerned with the general multiple access wiretap channel and the existence of codes that accomplish reliability and strong secrecy. Information leakage to the eavesdropper is assessed by the variational distance metric, whereas the average error probability is bounded by modifying Feinsteins Lemma. We derive an achievable strong secrecy rate region by utilizing the resolvability theory for the multiple-access channel in terms of information-spectrum methods.
In this paper, we consider the secrecy capacity of a wiretap channel in the presence of causal state information and secure rate-limited feedback. In this scenario, the causal state information from the channel is available to both the legitimate transmitter and legitimate receiver. In addition, the legitimate receiver can send secure feedback to the transmitter at a limited rate Rf . We shown that the secrecy capacity is bounded. Moreover, when the channel to the legitimate receiver is less noisy than the channel to the eavesdropper, the bound is shown to be tight. The capacity achieving sche…
The finite state Markov channel (FSMC), where the channel transition probability is controlled by a state undergoing a Markov process, is a useful model for the mobile wireless communication channel. In this paper, we investigate the security issue in the mobile wireless communication systems by considering the FSMC with an eavesdropper, which we call the finite state Markov wiretap channel (FSM-WC). We assume that the state is perfectly known by the legitimate receiver and the eavesdropper, and through a noiseless feedback channel, the legitimate receiver sends his received channel output and…
This paper investigates the capacity region of a discrete memoryless (DM) multiple access wiretap (MAC-WT) channel where, besides confidential messages, the users have also open messages to transmit. All these messages are intended for the legitimate receiver but only the confidential messages need to be protected from the eavesdropper. By using random coding, we find an achievable secrecy rate region, within which perfect secrecy can be realized, i.e., all users can communicate with the legitimate receiver with arbitrarily small probability of error, while the confidential information leaked …
We study deterministic approximations of the Gaussian two-user multiple access wiretap channel (G-MAC-WT) and the Gaussian wiretap channel with a helper (G-WT-H). These approximations enable results beyond the recently shown 2/3 and 1/2 secure degrees of freedom (s.d.o.f.) for the G-MAC-WT and the G-WT-H, respectively. While the s.d.o.f. were obtained by real interference alignment, our approach uses signal-scale alignment. We show achievable schemes which are independent of the rationality of the channel gains. Moreover, our results can differentiate between channel strengths, in particular b…
In this paper, we consider a semi-deterministic wiretap channel where the main channel is noiseless and the eavesdropper's channel is a binary erasure channel (BEC). We provide a lower bound for the achievable secrecy rates of polar and Reed Muller codes and compare it to the second order coding rate for the semi-deterministic wiretap channel. To the best of our knowledge, this is the first work which demonstrates the secrecy performance of polar and Reed-Muller codes in short blocklengths. The results show that under a total variation secrecy metric, Reed Muller codes can achieve secrecy rate…
The adversarial wiretap channel (AWTC) model is a secure communication model in which adversary can directly read and write the transmitted bits in legitimate communication with fixed fractions. In this paper we propose a secure polar coding scheme to provide secure and reliable communication over the AWTC model. For the adversarial reading and writing action, we present a $ρ$ equivalent channel block and study its transformation under the channel polarization operation. We find that the generated channels are polarized in the sense that part of them are full-noise channels with probability al…
In this paper, we study a security problem on a simple wiretap network, consisting of a source node S, a destination node D, and an intermediate node R. The intermediate node connects the source and the destination nodes via a set of noiseless parallel channels, with sizes $n_1$ and $n_2$, respectively. A message $M$ is to be sent from S to D. The information in the network may be eavesdropped by a set of wiretappers. The wiretappers cannot communicate with one another. Each wiretapper can access a subset of channels, called a wiretap set. All the chosen wiretap sets form a wiretap pattern. A …
We study a deterministic approximation of the two-user multiple access wiretap channel. This approximation enables results beyond the recently shown $\tfrac{2}{3}$ secure degrees of freedom (s.d.o.f.) for the Gaussian multiple access channel. While the s.d.o.f. were obtained by real interference alignment, our approach uses signal-scale alignment. We show an achievable scheme which is independent of the rationality of the channel gains. Moreover, our result can differentiate between channel strengths, in particular between both users, and establishes a secrecy rate dependent on this difference…
In a point-to-point communication system which consists of a sender, a receiver and a set of noiseless channels, the sender wishes to transmit a private message to the receiver through the channels which may be eavesdropped by a wiretapper. The set of wiretap sets is arbitrary. The wiretapper can access any one but not more than one wiretap set. From each wiretap set, the wiretapper can obtain some partial information about the private message which is measured by the equivocation of the message given the symbols obtained by the wiretapper. The security strategy is to encode the message with s…
The Schalkwijk-Kailath (SK) scheme, which achieves the capacity of the point-to-point white Gaussian channel with feedback, is secure by itself and also achieves the secrecy capacity of the Gaussian wiretap channel with feedback, i.e., the SK scheme is a self-secure capacity-achieving (SSCA) feedback scheme for the Gaussian wiretap channel. For the multi-user wiretap channels, recently, it has been shown that Ozarow's capacity-achieving feedback scheme for the two-user Gaussian multiple-access channel (GMAC) is the SSCA feedback scheme for the two-user Gaussian multiple-access wiretap channel …
In this paper, we investigate the effects of an additional trusted relay node on the secrecy of multiple-access wiretap channel (MAC-WT) by considering the model of multiple-access relay wiretap channel (MARC-WT). More specifically, first, we investigate the discrete memoryless MARC-WT. Three inner bounds (with respect to decode-forward (DF), noise-forward (NF) and compress-forward (CF) strategies) on the secrecy capacity region are provided. Second, we investigate the degraded discrete memoryless MARC-WT, and present an outer bound on the secrecy capacity region of this degraded model. Finall…
In this paper, the problem of securely computing a function over the binary modulo-2 adder multiple-access wiretap channel is considered. The problem involves a legitimate receiver that wishes to reliably and efficiently compute a function of distributed binary sources while an eavesdropper has to be kept ignorant of them. In order to characterize the corresponding fundamental limit, the notion of secrecy computation-capacity is introduced. Although determining the secrecy computation-capacity is challenging for arbitrary functions, it surprisingly turns out that if the function perfectly matc…
We consider a two user multiple-access channel with an eavesdropper at the receiving end. We use previously transmitted messages as a key in the next slot till we achieve the capacity region of the usual Multiple Access Channel (MAC).
Recently, it has been shown that the time-varying multiple-access channel (MAC) with perfect channel state information (CSI) at the receiver and delayed feedback CSI at the transmitters can be modeled as the finite state MAC (FS-MAC) with delayed state feedback, where the time variation of the channel is characterized by the statistics of the underlying state process. To study the fundamental limit of the secure transmission over multi-user wireless communication systems, we re-visit the FS-MAC with delayed state feedback by considering an external eavesdropper, which we call the finite state …
Security constraint results in \textit{rate-loss} in wiretap channels. In this paper we propose a coding scheme for two user Multiple Access Channel with Wiretap (MAC-WT), where previous messages are used as a key to enhance the secrecy rates of both the users until we achieve the usual capacity region of a Multiple Access Channel (MAC) without the wiretapper (Shannon capacity region). With this scheme all the messages transmitted in the recent past are secure with respect to all the information of the eavesdropper till now. To achieve this goal we introduce secret key buffers at both the user…
We consider a two-user multiple-input multiple-output (MIMO) multiple access wiretap channel with $N$ antennas at each transmitter, $N$ antennas at the legitimate receiver, and $K$ antennas at the eavesdropper. We determine the optimal sum secure degrees of freedom (s.d.o.f.) for this model for all values of $N$ and $K$. We subdivide our problem into several regimes based on the values of $N$ and $K$, and provide achievable schemes based on real and vector space alignment techniques for fixed and fading channel gains, respectively. To prove the optimality of the achievable schemes, we provide …
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 sol…
We study the problem of two-user Gaussian multiple access channel (GMAC) in the presence of an external eavesdropper. In this problem, an eavesdropper receives a signal with a lower signal-to-noise ratio (SNR) compared to the legitimate receiver and all transmitted messages should be kept confidential against the eavesdropper. For this purpose, we propose a secure coding scheme on this channel which utilizes low-density parity-check (LDPC) codes by employing random bit insertion and puncturing techniques. At each encoder, the confidential message with some random bits as a random message are s…
We in this paper introduce an advanced eavesdropper that aims to paralyze the artificial-noise-aided secure communications. We consider the M-1-2 Gaussian MISO wiretap channel, which consists of a M-antenna transmitter, a single-antenna receiver, and a two-antenna eavesdropper. This type of eavesdropper, by adopting an optimal Grassmann manifold (OGM) filtering structure, can reduce the maximum achievable secrecy rate (MASR) to be zero by using only two receive antennas, regardless of the number of antennas at the transmitter. Specifically, the eavesdropper exploits linear filters to serially …
In this work, we consider a K-user Gaussian wiretap multiple-access channel (GW-MAC) in which each transmitter has an independent confidential message for the receiver. There is also an external eavesdropper who intercepts the communications. The goal is to transmit the messages reliably while keeping them confidential from the eavesdropper. To accomplish this goal, two different approaches have been proposed in prior works, namely, i.i.d. Gaussian random coding and real alignment. However, the former approach fails at moderate and high SNR regimes as its achievable result does not grow with S…
This paper investigates the secrecy capacity region of multiple access wiretap (MAC-WT) channels where, besides confidential messages, the users have also open messages to transmit. All these messages are intended for the legitimate receiver (or Bob for brevity) but only the confidential messages need to be protected from the eavesdropper (Eve). We first consider a discrete memoryless (DM) MAC-WT channel where both Bob and Eve jointly decode their interested messages. By using random coding, we find an achievable rate region, within which perfect secrecy can be realized, i.e., all users can co…
In this paper, we consider the Gaussian diamond-wiretap channel that consists of an orthogonal broadcast channel from a source to two relays and a Gaussian fast-fading multiple access-wiretap channel from the two relays to a legitimate destination and an eavesdropper. For the multiple access part, we consider both the case with full channel state information (CSI) and the case with no eavesdropper's CSI, at the relays and the legitimate destination. For both the cases, we establish the exact secure degrees of freedom and generalize the results for multiple relays. For the converse part, we int…
In this paper, we want to investigate classical-quantum multiple access wiretap channels (CQ-MA-WTC) under one-shot setting. In this regard, we analyze the CQ-MA-WTC using simultaneous position-based decoder for reliable decoding and using a newly introduced technique in order to decode securely. Also, for the sake of comparison, we analyze the CQ-MA-WTC using Sen's one-shot joint typicality lemma for reliable decoding. The simultaneous position-based decoder tends to a multiple hypothesis testing problem. Also, using convex splitting to analyze the privacy criteria in a simultaneous scenario …
Consider a communication network represented by a directed graph $\mathcal{G}=(\mathcal{V},\mathcal{E})$, where $\mathcal{V}$ is the set of nodes and $\mathcal{E}$ is the set of point-to-point channels in the network. On the network a secure message $M$ is transmitted, and there may exist wiretappers who want to obtain information about the message. In secure network coding, we aim to find a network code which can protect the message against the wiretapper whose power is constrained. Cai and Yeung \cite{cai2002secure} studied the model in which the wiretapper can access any one but not more th…
We consider the problem of multiterminal secret key agreement (SKA) in wiretapped source model where terminals have access to samples of correlated random variables from a publicly known joint probability distribution. The adversary has access to a side information variable, that is correlated with terminals' variables. We focus on a special type of terminal variables in this model, known as Tree-PIN, where the relation between variables of the terminals can be represented by a tree. The study of Tree-PIN source model is of practical importance as it can be realized in wireless network environ…
In this paper, we consider the problem of evaluating capacity expression of a multiple access channel (MAC) with noiseless feedback. So far, the capacity expression for this channel is known through a multi letter directed information by Kramer [1]. Recently, it was shown in [2] that one can pose it as a dynamic optimization problem, however, no dynamic program was provided as the authors claimed there is no notion of state that is observed by both the senders. In this paper, we build upon [2] to show that there indeed exists a state and therefore a dynamic program (DP) that decomposes this dy…
The model of wiretap channel (WTC) is important as it constitutes the essence of physical layer security (PLS). Wiretap channel with noiseless feedback (WTC-NF) is especially interesting as it shows what can be done when a private feedback is available. The already existing secret key based feedback coding scheme focuses on generating key from the feedback and using this key to protect part of the transmitted message. It has been shown that this secret key based feedback coding scheme is only optimal for the degraded WTC-NF, and finding an optimal feedback scheme for the general WTC-NF motivat…
We consider the problem of encoding a deterministic source sequence (a.k.a.\ individual sequence) for the degraded wiretap channel by means of an encoder and decoder that can both be implemented as finite--state machines. Our first main result is a necessary condition for both reliable and secure transmission in terms of the given source sequence, the bandwidth expansion factor, the secrecy capacity, the number of states of the encoder and the number of states of the decoder. Equivalently, this necessary condition can be presented as a converse bound (i.e., a lower bound) on the smallest achie…
This paper considers a Gaussian multi-input multi-output (MIMO) multiple access wiretap (MAC-WT) channel, where an eavesdropper (Eve) wants to extract the confidential information of all users. Assuming that both the legitimate receiver and Eve jointly decode their interested messages, we aim to maximize the sum secrecy rate of the system by precoder design. Although this problem could be solved by first using the iterative majorization minimization (MM) based algorithm to get a sequence of convex log-determinant optimization subproblems and then using some general tools, e.g., the interior po…
We determine the secrecy capacities under common randomness assisted coding of arbitrarily varying classical-quantum wiretap channels.Furthermore, we determine the secrecy capacity of a mixed channel model which is compound from the sender to the legal receiver and varies arbitrarily from the sender to the eavesdropper. As an application we examine when the secrecy capacity is a continuous function of the system parameters and show that resources, i.e., having access to a perfect copy of the outcome of a random experiment. are helpful for channel stability.
In this paper, we study the problem of secret communication over a multiple-access channel with a common message. Here, we assume that two transmitters have confidential messages, which must be kept secret from the wiretapper (the second receiver), and both of them have access to a common message which can be decoded by the two receivers. We call this setting as Multiple-Access Wiretap Channel with Common message (MAWC-CM). For this setting, we derive general inner and outer bounds on the secrecy capacity region for the discrete memoryless case and show that these bounds meet each other for a …
