Secrecy Coding Research Articles

Integrated physical-layer secure visible light communication and positioning system based on polar codes

Visible light communication (VLC) with physical-layer security can provide information-theoretic security for the optical wireless channel based on the characteristics of the channel instead of encryption algorithms and secret keys at application layer. Since precise location information of communication parties is crucial for estimating channel states and designing secure communication schemes, this paper proposes an integrated visible light communication and positioning system which provides triple functionalities of high-accuracy indoor positioning, physical-layer secure visible light communication, and flicker mitigation illumination. A heterogeneous signal hybrid line coding scheme is proposed for the transmitter to converge the high-speed communication data signals and the low-speed positioning data signals, and a hybrid heterogeneous signal extraction scheme is proposed for the receiver to separate the hybrid heterogeneous signals with a high-bandwidth photodetector and a low-pass complementary metal-oxide-semiconductor (CMOS) image sensor. Based on the positioning information and the communication scheme, a polar codes-based forward error correction coding scheme is designed to achieve physical-layer security and transmission reliability simultaneously. Numerical results show that the proposed system can reach a secrecy code rate of 0.76 for a single-input single-output indoor VLC channel and a transmission efficiency of 0.38 without perceivable flicker. Experimental results show that the proposed system can achieve an average positioning accuracy of 3.35 cm and decrease the bit error rate of a legitimate receiver to a near error-free level (lower than 10−7) while keeping the bit error rate of an eavesdropper at 0.4887 (nearly 0.5) with a transmission data rate of 1 Mbps, resulting in near-zero suppression of the eavesdropped information and a high secrecy capacity of 0.9994.

Optimizing Finite-Blocklength Nested Linear Secrecy Codes: Using the Worst Code to Find the Best Code.

Nested linear coding is a widely used technique in wireless communication systems for improving both security and reliability. Some parameters, such as the relative generalized Hamming weight and the relative dimension/length profile, can be used to characterize the performance of nested linear codes. In addition, the rank properties of generator and parity-check matrices can also precisely characterize their security performance. Despite this, finding optimal nested linear secrecy codes remains a challenge in the finite-blocklength regime, often requiring brute-force search methods. This paper investigates the properties of nested linear codes, introduces a new representation of the relative generalized Hamming weight, and proposes a novel method for finding the best nested linear secrecy code for the binary erasure wiretap channel by working from the worst nested linear secrecy code in the dual space. We demonstrate that our algorithm significantly outperforms the brute-force technique in terms of speed and efficiency.

Secrecy Performance for RIS-Based Integrated Satellite Vehicle Networks With a UAV Relay and MRC Eavesdropping

This work investigates the secrecy issues for the secrecy reconfigurable intelligent surface-based integrated satellite unmanned aerial vehicle (UAV) relay networks with multiple vehicle eavesdroppers. Particularly, the maximal ratio combining (MRC) eavesdropping is utilized to overhear the legitimate signal information. The UAV is applied to forward the legitimate signal to the destination user. Reconfigurable intelligent surface is applied to ensure the transmission. Relied on the proposed secrecy system model and MRC eavesdropping scheme, this paper gets the detailed investigations for the secrecy outage probability (SOP) through the whole signal-to-noise ratios (SNRs) to valuate the effects of important parameters on the SOP. Moreover, to achieve the further impacts of main parameters on the SOP at high SNRs, the approximate analysis for the SOP is also gotten together with the secrecy diversity order (SDO) and secrecy coding gain (SCG). At last, several typical Monte Carlo (MC) results are obtained to present the rightness of obtained theoretical analysis.

Secrecy Outage Probability for Two-Way Integrated Satellite Unmanned Aerial Vehicle Relay Networks with Hardware Impairments

In this paper, we investigate the secrecy outage performance for the two-way integrated satellite unmanned aerial vehicle relay networks with hardware impairments. Particularly, the closed-form expression for the secrecy outage probability is obtained. Moreover, to get more information on the secrecy outage probability in a high signal-to-noise regime, the asymptotic analysis along with the secrecy diversity order and secrecy coding gain for the secrecy outage probability are also further obtained, which presents a fast method to evaluate the impact of system parameters and hardware impairments on the considered network. Finally, Monte Carlo simulation results are provided to show the efficiency of the theoretical analysis.

Physical Layer Security Analysis of Multi-Hop Hybrid RF/FSO System in Presence of Multiple Eavesdroppers

In this paper, the physical layer security (PLS) analysis for a decode-and-forward (DF) protocol based multi-hop hybrid radio frequency (RF)/ free space optics (FSO) is presented. Herein, two different scenarios are considered for detecting the secured information at the destination. In the first scenario, at each hop, the received signals with higher secrecy capacity are selected. However, in the second scenario, the RF and FSO signals are simply decoded and forwarded to the next hop and selection is done at the last hop only. Each node in the system is connected to its subsequent node through parallel RF and FSO links. The FSO links and RF links are characterized by Málaga ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {M}$</tex-math></inline-formula> ) and Nakagami- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$m$</tex-math></inline-formula> composite distributions respectively. For both scenarios, the secrecy outage probability (SOP), strictly positive secrecy capacity (SPSC), intercept probability (IP), and effective secrecy throughput (EST) are obtained as performance metrics. These performance metrics are obtained by considering pointing error, different optical signal detection methods, turbulence effect, and the RF link fading parameter ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$m$</tex-math></inline-formula> ). Using the results, the security and reliability trade-off analysis is discussed for two scenarios. In addition, the asymptotic results are also obtained to study the system in depth. Further, the secrecy diversity order (SDO) and secrecy coding gain (SCG) are obtained to analyse the system in depth. Finally, Monte-Carlo Simulation is performed to verify the obtained results. The results manifest that the scenario with selection at each hop provides better secrecy performance than the scenario with selection at the last hop.

Coding for Secrecy in Remote State Estimation With an Adversary

We study the problem of remote state estimation in the presence of an eavesdropper. A sensor transmits state information over a packet-dropping link to a legitimate user. This information is randomly overheard by an eavesdropper. To reduce information leakage to the eavesdropper, previous studies have shown that by encoding the estimate with the acknowledgments (Acks), perfect secrecy can be achieved. However, this strategy greatly relies on the accuracy of the Acks and may easily fail if the Acks are compromised by cyberattacks. In this article, we tackle this issue by proposing to switch between sending an encoded state and sending the plain state to stay resilient against fake Acks. Specifically, we assume the Acks to be randomly attacked and derive recursive expressions for the minimum-mean-squared error estimates and error covariance matrices at the legitimate user and at the eavesdropper. Based upon this, we propose a transmission policy that depends on the probability of synchronization. We formulate a partially observable Markov decision process to model the evolution of the synchronization status and derive associated optimal transmission policies. Numerical examples are provided to verify the theoretical results.

Secrecy Coding Analysis of Short-Packet Full-Duplex Transmissions with Joint Iterative Channel Estimation and Decoding Processes.

This paper studies the secrecy coding analysis achieved by the self-jamming technique in the presence of an eavesdropper by considering a short-packet Full-Duplex (FD) transmission developed based on iterative blind or semi-blind channel estimation and advanced decoding algorithms. Indeed, the legitimate receiver and eavesdropper can simultaneously receive the intended signal from the transmitter and broadcast a self-jamming or jamming signal to the others. Unlike other conventional techniques without feedback, the blind or semi-blind algorithm applied at the legitimate receiver can simultaneously estimate, firstly, the Self-Interference (SI) channel to cancel the SI component and, secondly, estimate the propagation channel, then decode the intended messages by using 5G Quasi-Cyclic Low-Density Parity Check (QC-LDPC) codes. Taking into account the passive eavesdropper case, the blind channel estimation with a feedback scheme is applied, where the temporary estimation of the intended channel and the decoded message are fed back to improve both the channel estimation and the decoding processes. Only the blind algorithm needs to be implemented in the case of a passive eavesdropper because it achieves sufficient performances and does not require adding pilot symbols as the semi-blind algorithm. In the case of an active eavesdropper, based on its robustness in the low region of the Signal-to-Noise Ratio (SNR), the semi-blind algorithm is considered by trading four pilot symbols and only requiring the feedback for channel estimation processes in order to overcome the increase in noise in the legitimate receiver. The results show that the blind or semi-blind algorithms outperform the conventional algorithm in terms of Mean Square Error (MSE), Bit Error Rate (BER) and security gap (). In addition, it has been shown that the blind or semi-blind algorithms are less sensitive to high SI and self-jamming interference power levels imposed by secured FD transmission than the conventional algorithms without feedback.

The Suspension of the Portuguese Inquisition, 1674 to 1681: The Female Perspective

Abstract Using trials and wills of women arrested in the Portuguese inquisitorial purges of New Christian families between 1672 and 1674, which gave rise to negotiations for a General Pardon and unprecedented suspension of the Inquisition, this article argues that there was a concerted strategy of female education amongst New Christian families, teaching literacy and business savvy to girls. This was not as a tool of empowerment or self-determination against a paternalistic society, but a necessity for the family to function under the scrutiny of neighbors and threat of inquisitorial persecution. Literacy was both a political strategy, a tool that could be used to undermine and evade the inquisition’s codes of secrecy, and a way to ensure the family and its vitally important business networks survived in the diaspora. Exploring the idea that reading and writing can be political acts, I will examine here what literacy meant for the practicality of lives lived in the shadow of the inquisition and diaspora.

Black girls navigate the physical and emotional landscape of the neighbourhood: Normalized violence and strategic agency

This article considers how young Black women living in gang-affected neighbourhoods in an urban area in England, UK navigate their safety in public and private spaces, and how these spaces overlap and intersect. Drawing on a project with 18 participants aged 14–19, the research seeks to understand how the participants inhabit, navigate and strategize for their safety through their narratives of life and survival in an unsafe neighbourhood. Findings indicate that they experience sexual harassment in public spaces and gang-associated sexual and physical violence as common, accepted aspects of their everyday realities, from as young as 12. The narratives suggest that participants navigate complex friendship groups to protect each other and their families through tight codes of trust, secrecy, privacy and conflict-management strategies. This article seeks to bring attention to how young women utilize their agency to illuminate the coping strategies they draw on to navigate their physical environments. The article concludes with a discussion of the implications for interventions.

Physical-Layer Security in the Finite Blocklength Regime Over Fading Channels

This paper studies physical-layer secure transmissions from a transmitter to a legitimate receiver against an eavesdropper over slow fading channels, taking into account the impact of finite blocklength secrecy coding. A comprehensive analysis and optimization framework is established to investigate secrecy throughput for both single- and multi-antenna transmitter scenarios. Both adaptive and non-adaptive design schemes are devised, in which the secrecy throughput is maximized by exploiting the instantaneous and statistical channel state information of the legitimate receiver, respectively. Specifically, optimal transmission policy, blocklength, and code rates are jointly designed to maximize the secrecy throughput. Additionally, null-space artificial noise is employed to improve the secrecy throughput for the multi-antenna setup with the optimal power allocation derived. Various important insights are developed. In particular, 1) increasing blocklength benefits both reliability and secrecy under the proposed transmission policy; 2) secrecy throughput monotonically increases with blocklength; 3) secrecy throughput initially increases but then decreases as secrecy rate increases, and the optimal secrecy rate maximizing the secrecy throughput should be carefully chosen in order to strike a good balance between rate and decoding correctness. Numerical results are eventually presented to verify theoretical findings.

Implications of Coding Layers on Physical-Layer Security: A Secrecy Benefit Approach.

In this work, we consider the pros and cons of using various layers of keyless coding to achieve secure and reliable communication over the Gaussian wiretap channel. We define a new approach to information theoretic security, called practical secrecy and the secrecy benefit, to be used over real-world channels and finite blocklength instantiations of coding layers, and use this new approach to show the fundamental reliability and security implications of several coding mechanisms that have traditionally been used for physical-layer security. We perform a systematic/structured analysis of the effect of error-control coding, scrambling, interleaving, and coset coding, as coding layers of a secrecy system. Using this new approach, scrambling and interleaving are shown to be of no effect in increasing information theoretic security, even when measuring the effect at the output of the eavesdropper’s decoder. Error control coding is shown to present a trade-off between secrecy and reliability that is dictated by the chosen code and the signal-to-noise ratios at the legitimate and eavesdropping receivers. Finally, the benefits of secrecy coding are highlighted, and it is shown how one can shape the secrecy benefit according to system specifications using combinations of different layers of coding to achieve both reliable and secure throughput.

On (t, L)-fold perfect authentication and secrecy codes with arbitration

An authentication code with arbitration is t-fold perfect if the numbers of decoding rules and encoding rules meet the information-theoretic lower bounds with equality. A code has perfect L-fold secrecy if observing a set of $$L'\le L$$ messages in the channel gives no information to the opponent regarding the $$L'$$ source states. In this paper, we investigate (t, L)-fold perfect authentication and secrecy codes with arbitration which provide both t-fold perfect and perfect L-fold secrecy. We define a new design, L-secrecy perfect ordered restricted strong partially balanced t-design, which is used to construct a (t, L)-fold perfect authentication and secrecy code with arbitration. We also obtain some infinite classes of (t, 1)-fold perfect authentication and secrecy codes with arbitration, especially for $$t>2$$ .

Analysis of short blocklength codes for secrecy

In this paper, we provide secrecy metrics applicable to physical-layer coding techniques with finite blocklengths over Gaussian and fading wiretap channel models and analyze their secrecy performance over several cases of concatenated code designs. Our metrics go beyond some of the known practical secrecy measures, such as bit error rate and security gap, so as to make lower bound probabilistic guarantees on error rates over short blocklengths both preceding and following a secrecy decoder. Our techniques are especially useful in cases where application of traditional information-theoretic security measures is either impractical or simply not yet understood. The metrics can aid both practical system analysis, including cryptanalysis, and practical system design when concatenated codes are used for physical-layer security. Furthermore, these new measures fill a void in the current landscape of practical security measures for physical-layer security coding and may assist in the wide-scale adoption of physical-layer techniques for security in real-world systems. We also show how the new metrics provide techniques for reducing realistic channel models to simpler discrete memoryless wiretap channel equivalents over which existing secrecy code designs may achieve information-theoretic security.

On an Almost-Universal Hash Function Family with Applications to Authentication and Secrecy Codes

Universal hashing, discovered by Carter and Wegman in 1979, has many important applications in computer science. MMH[Formula: see text], which was shown to be [Formula: see text]-universal by Halevi and Krawczyk in 1997, is a well-known universal hash function family. We introduce a variant of MMH[Formula: see text], that we call GRDH, where we use an arbitrary integer [Formula: see text] instead of prime [Formula: see text] and let the keys [Formula: see text] satisfy the conditions [Formula: see text] ([Formula: see text]), where [Formula: see text] are given positive divisors of [Formula: see text]. Then via connecting the universal hashing problem to the number of solutions of restricted linear congruences, we prove that the family GRDH is an [Formula: see text]-almost-[Formula: see text]-universal family of hash functions for some [Formula: see text] if and only if [Formula: see text] is odd and [Formula: see text] [Formula: see text]. Furthermore, if these conditions are satisfied then GRDH is [Formula: see text]-almost-[Formula: see text]-universal, where [Formula: see text] is the smallest prime divisor of [Formula: see text]. Finally, as an application of our results, we propose an authentication code with secrecy scheme which strongly generalizes the scheme studied by Alomair et al. [J. Math. Cryptol. 4 (2010) 121–148], and [J.UCS 15 (2009) 2937–2956].

On the Impact of Adaptive Eavesdroppers in Multi-Antenna Cellular Networks

In this paper, the impact of adaptive smarter eavesdroppers on the secrecy performance of a multi-antenna cellular network is investigated. The eavesdroppers can act as either passive eavesdroppers or active jammers based on their distance to the active base stations (BSs). To analyze the secrecy performance, the BSs, cellular users, and eavesdroppers are modeled as independent Poisson point processes. The closed-form expressions of the connection outage probability and lower bound of the secrecy outage probability are derived using the stochastic geometry approach. Following that, the conditions under which the eavesdroppers can act as active jammers are obtained. Finally, the optimal power allocation between artificial noise and information signal and the secrecy code rate at each BS, as well as the guard zone of the eavesdroppers are obtained using the Stackelberg game approach, where the eavesdroppers are modeled as the leader and the BSs as the follower. The Stackelberg equilibrium is obtained through the proposed iterative algorithm. Numerical results verify the theoretical analysis and show that the secrecy performance can be degraded severely by the adaptive eavesdroppers.

Intercept Probability Analysis of Wireless Networks in the Presence of Eavesdropping Attack With Co-Channel Interference

In this paper, the joint effect of fading and co-channel interference on the secrecy performance of a wireless communications system is studied. Considering a practical setting where a transmitter (Alice) communicates with a multi-antenna legitimate receiver (Bob) in the presence of a multi-antenna eavesdropper (Eve), we study the secrecy performance of the proposed system when maximal ratio combining is employed. The probability density function and cumulative distribution function of the output signal-plus-interference-to-noise ratio are derived. Given these formulations, we derive a novel analytical expression for the exact intercept probability, which takes into account the number of interfering signals and the fading characteristics of the wireless environment. In addition, we provide a comprehensive diversity analysis, where we derive simple asymptotic intercept probability expressions and explicitly show the impact of system parameters on the diversity order and secrecy coding gain. Throughout the asymptotic analysis, we consider various scenarios based on the interfernece-to-noise ratios at the legitimate receiver and the eavesdropper, as well as the average signal-to-noise ratio of the eavesdropper and examine their impact on the physical layer security of the wireless system. Finally, Monte-Carlo simulations are conducted to assess our proposed analysis.

A construction for optimal c-splitting authentication and secrecy codes

Authentication and secrecy codes which provide both secrecy and authentication have been intensively studied in the case where there is no splitting; however the results concerning the case where there is splitting are far fewer. In this paper, we focus on the case with c-splitting, and obtain a bound on the number of encoding rules required in order to obtain maximum levels of security. A c-splitting authentication and secrecy code is called optimal if it obtains maximum levels of security and has the minimum number of encoding rules. We define a new design, called an authentication perpendicular multi-array, and prove that the existence of authentication perpendicular multi-arrays implies the existence of optimal c-splitting authentication and secrecy codes. Further, we study the constructions and existence of authentication perpendicular multi-arrays, and then obtain two new infinite classes of optimal c-splitting authentication and secrecy codes.

Individual Secrecy for Broadcast Channels With Receiver Side Information

This paper studies the problem of secure communication over the broadcast channel with receiver side information under the lens of individual secrecy constraints. That is, the transmitter wants to send two independent messages to two receivers which have, respectively, the desired message of the other receiver as side information, while keeping the eavesdropper ignorant of each message (i.e., the information leakage from each message to the eavesdropper is made vanishing). Building upon one-time pad, secrecy coding, and broadcasting schemes, achievable rate regions are investigated, and the capacity region for special cases of either a weak or strong eavesdropper (compared to both legitimate receivers) are characterized. Interestingly, the capacity region for the former corresponds to a line and the latter corresponds to a square with missing corners; a phenomenon occurring due to the coupling between user's rates. Moreover, the individual secrecy capacity region is also fully characterized for the case where the eavesdropper's channel is deterministic. In addition to discrete memoryless setup, Gaussian scenarios are studied. For the Gaussian model, in addition to the strong and weak eavesdropper cases, the capacity region is characterized for the low and high SNR regimes when the eavesdropper's channel is stronger than one receiver but weaker than the other. Remarkably, positive secure transmission rates are always guaranteed under the individual secrecy constraint, unlike the case of the joint secrecy constraint (i.e., the information leakage from both messages to the eavesdropper is made vanishing). Thus, this notion of secrecy serves as an appropriate candidate for trading off secrecy level and transmission rate; making secrecy more affordable but still acceptable to the end user.

Secure Degrees of Freedom Region of the Two-User MISO Broadcast Channel With Alternating CSIT

The two user multiple-input single-output (MISO) broadcast channel with confidential messages (BCCM) is studied, in which the nature of channel state information at the transmitter (CSIT) from each user can be of the form $I_{i}$ , $i=1,2$ where $I_{1}, I_{2}\in \{\mathsf {P}, \mathsf {D}, \mathsf {N}\}$ , and the forms $\mathsf {P}$ , $\mathsf {D}$ , and $\mathsf {N}$ correspond to perfect and instantaneous, completely delayed, and no CSIT, respectively. Thus, the overall CSIT can alternate between nine possible states corresponding to all possible values of $I_{1}I_{2}$ , with each state occurring for $\lambda _{I_{1}I_{2}}$ fraction of the total duration. We assume that perfect and instantaneous CSI is available at the all receivers. The main contribution of this paper is to establish the secure degrees of freedom (s.d.o.f.) region of the MISO BCCM with alternating CSIT with the symmetry assumption, where $\lambda _{I_{1} I_{2}}=\lambda _{I_{2}I_{1}}$ . The main technical contributions include developing 1) novel achievable schemes for MISO BCCM with alternating CSIT with security constraints, which also highlight the synergistic benefits of inter-state coding for secrecy; 2) new converse proofs via local statistical equivalence and channel enhancement; and 3) showing the interplay between various aspects of channel knowledge and their impact on s.d.o.f.

Individual Secrecy for the Broadcast Channel

This paper studies the problem of secure communications over broadcast channels under the individual secrecy constraints. That is, the transmitter wants to send two independent messages to two legitimate receivers in the presence of an eavesdropper, while keeping the eavesdropper ignorant of each message (i.e., the information leakage rate from each message to the eavesdropper is made vanishing). Building upon Carleial–Hellman’s secrecy coding, Wyner’s secrecy coding, and the framework of Marton’s coding together with techniques, such as rate splitting and indirect decoding, an achievable individual secrecy rate region is established with the characterization of capacity regions for some special cases. In particular, the individual secrecy capacity region for the linear deterministic model is fully characterized, and for the Gaussian model, a constant gap (i.e., 0.5 b within the individual secrecy capacity region) result is obtained. To illustrate the impact of different secrecy constraints on the corresponding capacity regions, comparisons are made with those satisfying joint secrecy and without secrecy constraints. Overall, when compared with the joint secrecy constraint, the results allow for trading off secrecy level and throughput in the system.