## Utku Tefek , Anshoo Tandon and Teng Joon Lim## |

Parameter | Value |
---|---|

[TeX:] $$\lambda_{D}$$ | [TeX:] $$10^{-3} \text {nodes } / m^{2}$$ |

[TeX:] $$\lambda_{R}$$ | [TeX:] $$2 \times 10^{-4} \text {nodes } / m^{2}$$ |

[TeX:] $$\lambda_{s}$$ | [TeX:] $$10^{-4} \text {nodes } / m^{2$$ |

[TeX:] $$\lambda_{B}$$ | [TeX:] $$4 \times 10^{-5} \text {nodes } / m^{2}$$ |

[TeX:] $$\delta_{D}$$ | [TeX:] $$0.05$$ |

[TeX:] $$\delta_{R}$$ | [TeX:] $$0.05$$ |

[TeX:] $$\eta$$ | [TeX:] $$3$$ |

[TeX:] $$\alpha$$ | [TeX:] $$4$$ |

Based on the solutions of (26) and (27), the minimum required sentinel density [TeX:] $$\lambda_{S}^{*}$$ to achieve a certain immediate detection probability is shown in Fig. 4. The isolated detection model is much more sensitive to the detection threshold, i.e., it requires significantly denser sentinel deployment to achieve a given detection probability.

In this section, Monte-Carlo simulations are presented to confirm the accuracy of the analytical results and to obtain insights on how system parameters affect the detection performance and end-to-end success rate of IoT transmissions. The parameters in Table 1 are used for simulations unless otherwise indicated in the plots.

In Fig. 5, the probability that a packet transmitted by devices or relays is captured by sentinels is plotted against the sentinel density. In general, the analytical plots follow the same trend as the Monte-Carlo plots. The limited discrepancy between the analytical and simulation plots of the isolated detection scheme is due to the PPP assumption of interfering nodes, and also due to the approximation (conjectured in (18)) on the distance distribution between a device and its associated sentinel.

Fig. 6 shows the detection probability of an attack, in comparison with the end-to-end success probability of IoT packets, plotted over the density of transmitting devices. As [TeX:] $$\lambda_{D} \delta_{D}$$ increases, the interference in device-to-relay and device-tosentinel links also increases, resulting in a lower capture probability in these links. Therefore, all three plots are decaying as transmitting device density is increasing. The rate of decay in sentinel detection probability is higher than that of end-to-end success probability, suggesting that the detection model is more sensitive to the interference level when capturing device packets.

Figs. 7 and 8 illustrate the detection probability of an attack, in comparison with the end-to-end success probability of IoT packets, plotted over the density of relays and ratio of transmitting relays respectively. Note that as relay density increases, typical device-to-relay distance decreases, resulting in a better capture probability for device-to relay links. On the other hand, increasing relay density increases the interference caused by the relays, reducing the capture probability at relay-to-AP links. The former effect is dominant up until [TeX:] $$\lambda_{R} \approx 2 \times 10^{-4}$$, whereas the latter dominates for larger [TeX:] $$\lambda_{R}$$ as can be seen from the end-to-end success probability plot (black squares). Both the attack detection probability and end-to-end success probability consistently decrease with the ratio of transmitting relays due to increased interference. At low relay densities, the analytical plot of the isolated detection scheme is less accurate due to the approximation in (18).

The foremost finding of this paper is that using passive sentinel nodes – even when they are much less in number than the relay nodes – to monitor data traffic in an IoT relay network is feasible from the communication theory perspective. This finding can be observed from Figs. 5–8, where [TeX:] $$\lambda_{S}<\lambda_{R}$$ leads to similar performance between the end-to-end success probability of the network and the attack detection probability of sentinels. It should also be noted that these Figures display the immediate detection probability of an attack performed on a single packet. As multiple packets are observed by the sentinel, the detection probability increases dramatically.

The sentinel-based detection is scalable because the task of each sentinel is simply to compare the transmitted MAC payload from a device in its vicinity with the corresponding payload forwarded by the relay. Even in co-operative detection, the sentinels only need to exchange certain messages locally, thus the increasing network area does not translate into a larger number of exchanged messages between the sentinels. The sentinelbased detection can also be considered in a multi-hop setting wherein sentinels compare the MAC payload transmitted by nodes with the corresponding payload forwarded by the respective next-hop-nodes in their vicinity. In this manner, the attack detection for each hop is an independent task, the probability of which is calculated in this paper.

Our sentinel approach has several advantages over other network intrusion detection systems and techniques [10]-[12]. Firstly, the proposed method does not require any change in the existing protocols or deployed devices but rather introduces a new set of sentinel nodes. Since the intrusion detection is performed only at the external sentinel devices, the IoT network is not burdened with computational load or signaling overhead unlike the prior work.

Secondly, the security of the users would be compromised if the intrusion detection system itself is compromised. It can be safely argued that the passive sentinel devices can be designed with the latest security technologies (e.g., Trusted Execution Environment), therefore, they would be less prone to attacks than any other wireless device in an IoT network. Privacy measures such as imposing hardware limitations on the transmit interfaces of the sentinel devices can be considered to protect the privacy of the IoT network. Therefore, integrity checking by sentinels would be a more secure approach than offloading such a critical task to the network whose integrity is questionable in the first place. On the other hand, we acknowledge that there will be a hardware cost (and bandwidth cost for co-operative detection) of deploying sentinels. Yet, the costs will be limited because very good attack detection performance can be achieved with [TeX:] $$\lambda_{S}<\lambda_{R}$$.

Thirdly, the false alarm rate in our sentinel based detection scheme is negligible as it occurs only in the unlikely scenario where the packet CRC fails to detect errors, even though the decoded packet is in error. Further, the detection scheme operates at the MAC layer and therefore remains effective even in scenarios where different wireless links may employ distinct modulation and coding schemes at the physical layer.

Finally, the other methods commonly relied on known channel parameters in their analysis which is unrealistic in a large IoT network. Through the use of stochastic geometry, we have demonstrated the feasibility of our sentinel-based method from a communication theoretical perspective. It should be noted however that, the use of stochastic geometry also has a downside. It only provides system-level insights (e.g., detection performance as a function of node densities) for an average network rather than suggesting precise refinements to a specific network. Hence, the fine-tuning of other useful parameters (e.g., finding exact sentinel locations, varying sentinel density based on the IoT network load) are not studied in this paper and will be investigated in future work.

In this paper, we have proposed sentinel based attack detection schemes to identify malicious relays that alter, drop or craft data packets in an IoT network. The proposed schemes are well suited to resource-constrained IoT networks and can supplement higher-layer security mechanisms. We have applied a stochastic geometry approach to interference modeling, and hence optimized the density of sentinel nodes for given densities of relay and IoT devices, as well as the desired attack detection probability. Co-operative detection performance is shown to be significantly better than that of isolated detection because the packet modifications can be detected in the co-operative scheme when the device and relay versions of the same packet are captured by different sentinels. On the other hand, isolated detection requires no communication among sentinels, except for the initial association region setup. Minimum sentinel density to achieve a certain attack detection performance was calculated for both schemes. It has been shown that the required sentinel density (especially in co-operative detection) can be much smaller than the relay density to achieve a detection probability approximately equal to the end-to-end success probability of the IoT network. This outcome, combined with the fact that sentinels do not add computational burden to the IoT network, confirms sentinels as viable solutions for preserving data integrity in IoT relay networks.

The intensity function of the interfering nodes is [TeX:] $$\lambda_{X}$$ outside [TeX:] $$\mathcal{V}_{Y_{0}}$$. Transforming into polar coordinates, we have intensity function of [TeX:] $$\Lambda(r)=2 \pi r \lambda_{X}$$ defined outside [TeX:] $$\mathcal{V}_{Y_{0}}, \text { with } r$$ denoting the distance from the origin (or [TeX:] $$Y_{0}$$). Let [TeX:] $$\rho_{X}, \forall X \in \Phi_{X}$$ denote the distances between the interfering nodes and their intended receivers. Therefore, [TeX:] $$\rho_{X}$$'s are i.i.d with a nearest Poisson point distribution, i.e., Rayleigh distribution,

The interfering nodes are outside [TeX:] $$\mathcal{V}_{Y_{0}}$$ if and only if they are farther from the origin than they are to their associated receivers at [TeX:] $$Y_{i} \in \Phi_{Y}$$ as specified by association rule in (3). Specifically, [TeX:] $$\|X\|>\rho_{X}, \forall X \in \Phi_{X} \backslash\left\{X_{0}\right\}$$. Hence, the intensity function of the interfering nodes defined in [TeX:] $$\mathbb{R}^{2} \text { is } \Lambda(r)=2 \pi r \lambda_{X} \mathbb{1}\left(r>\rho_{X}\right), \text { where } \mathbb{1}(\cdot)$$ is the indicator function. Using this intensity function, the Laplace transform of the interference distribution in (4) can be evaluated as follows.

where (a) follows from the i.i.d nature of [TeX:] $$\left\{h_{Y_{0}, X}\right\}$$s and their Moment Generating Function (MGF), (b) from using the Probability Generating Functional (PGFL) of the inhomogeneous PPP [TeX:] $$\Phi_{X} \backslash \mathcal{V}_{Y_{0}}$$ with intensity function [TeX:] $$\Lambda(r)=2 \pi r q \lambda_{X} \mathbb{1}\left(\mathbb{r}>\rho_{\mathbb{X}}\right)$$ ((A.3) in [37]) and (c) from the change of variables [TeX:] $$t \leftarrow r^{2} / \rho^{2}$$.

From (1), the capture probability [TeX:] $$1-\epsilon_{X} \rightarrow Y$$ can be calculated by de-conditioning on the typical transmitter/receiver distance [TeX:] $$\left\|Y_{0}-X_{0}\right\|=r$$,

where (a) follows from the complementary cumulative distribution function of the exponential random variable [TeX:] $$h_{Y_{0}, X_{0}}$$ and by substituting the nearest Poisson point distribution [TeX:] $$f_{\left\|Y_{0}-X_{0}\right\|}(r)=2 \pi \lambda_{Y} e^{-\pi \lambda_{Y} r^{2}}$$, and (b) is because the expression inside the expected value operator is in the form of the Laplace transform of the distribution of [TeX:] $$I_{Y_{0}}$$ evaluated at [TeX:] $$s=\eta r^{\alpha} / P_{X}$$.

We first show that,

here (a) follows from the change of variables [TeX:] $$r \leftarrow \rho^{2} / w$$, (b) from solving the inner integral by noting [TeX:] $$\mathrm{d}\left(\tan ^{-1}(\mathrm{rt})\right) / \mathrm{dt} = r /\left(1+r^{2} t^{2}\right)$$, (c) from integration by parts with [TeX:] $$u=\cot ^{-1}(r), \mathrm{d} \mathrm{v}=\exp (-\pi \lambda \mathrm{wr}) \mathrm{dr}$$, and the last step from expressing the integral in terms of the auxiliary function,

[TeX:] $$\mathcal{A}(x)=\int_{0}^{\infty} \frac{\exp (-x r)}{1+r^{2}} \mathrm{d} \mathrm{r}=\mathrm{Ci}(\mathrm{x}) \sin (\mathrm{x})+\left[\frac{\pi}{2}-\mathrm{Si}(\mathrm{x})\right] \cos (\mathrm{x})$$

Then, the above result with [TeX:] $$w=\sqrt{s P_{X}}$$ can be used in (5), to replace [TeX:] $$\mathbb{E}_{\rho}\left[\rho^{2} C_{\alpha}\left(s P_{X} \rho^{-\alpha}\right)\right] \text { with } \sqrt{s P_{X}}\left(\frac{\pi}{2}-\mathcal{A}\left(\pi \lambda_{Y} \sqrt{s P_{X}}\right)\right)$$,

Finally, (32) can be integrated over the distance distribution [TeX:] $$f_{\left\|Y_{0}-X_{0}\right\|}(r)=2 \pi \lambda_{Y} e^{-\pi \lambda_{Y} r^{2}} \text { for } r \geq 0$$ to obtain the capture probability in (8).

Utku Tefek received the B.Sc. degree with high hon- ors in Electrical and Electronics Engineering from Bilkent University, Turkey in 2013 and the Ph.D. de- gree from the National University of Singapore in 2017. From October 2017 to October 2018, he was a Postdoctoral Researcher at the National University of Singapore (NUS), Singapore. Since October 2018, he has been with ADSC (Advanced Digital Sciences Center), an affiliate of the University of Illinois. His research interests include the application of stochas- tic models to wireless networks, machine-to-machine communications and cyberphysical system security.

Anshoo Tandon received the B.E. degree in Computer Science and Engineering from Kumaun University, Nainital, India, in 1998, the M.E. degree in Signal Processing from the Indian Institute of Science, Bengaluru, India, in 2000, and the Ph.D. degree from the National University of Singapore (NUS), Singapore, in 2016. Between 2000 and 2011, he worked in different capacities in the industry towards developing efficient cellular and wireless connectivity solutions. He is currently a Research Fellow in the Department of Electrical and Computer Engineering at NUS, Singapore. His research interests include information theory, coding theory, and design of efficient communication systems. TengJoon(T.J.)Lim(S’92-M’95-SM’02-F’17) obtained the B.Eng. degree in Electrical Engineering with first-class honours from the National University of Singapore (NUS) in 1992, and the Ph.D. degree from the University of Cambridge in 1996. From September 1995 to November 2000, he was a Researcher at the Centre for Wireless Communications in Singapore, one of the predecessors of the Institute for Infocomm Research (I2R). From December 2000 to May 2011, he was Assistant Professor, Associate Professor, then Professor at the University of Toronto’s Edward S. Rogers Sr. Department of Electrical and Computer Engineering. From June 2011 to January 2020, he was a Professor at the Electrical Computer Engineering Department of NUS, where he served as a Deputy Head from July 2014 to August 2015. From September 2015 through December 2019, he served as Vice-Dean (Graduate Programs) in the NUS Faculty of Engineering. Since January 2020, he has served as Deputy Dean and Associate Dean (Education) at the Faculty of Engineering in the University of Sydney. Professor Lim is an Associate Editor for IEEE Potentials, was an Area Editor of the IEEE Transactions on Wireless Communications from September 2013 to September 2018, and previously served as an Associate Editor for the same journal. He has also served as an Associate Editor for IEEE Wireless Communications Letters, Wiley Transactions on Emerging Telecommunications Technologies (ETT), IEEE Signal Processing Letters and IEEE Transactions on Vehicular Technology. He has volunteered on the organizing committee of a number of IEEE conferences, including serving as the TPC co-chair of IEEE Globecom 2017. He chaired the Singapore chapter of the IEEE Communications Society in 2017 and 2018, and is a Distinguished Lecturer of the IEEE Vehicular Technology Society for 2019-20. His research interests span many topics within wireless communications, including cyber-security in the Internet of Things, heterogeneous networks, cooperative transmission, energy-optimized communication networks, multi-carrier modulation, MIMO, cooperative diversity, cognitive radio, and stochastic geometry for wireless networks, and he has published widely in these areas.

Teng Joon (T. J.) Lim (S’92-M’95-SM’02-F’17) ob- tained the B.Eng. degree in Electrical Engineering with first-class honours from the National Univer- sity of Singapore (NUS) in 1992, and the Ph.D. de- gree from the University of Cambridge in 1996. From September 1995 to November 2000, he was a Re- searcher at the Centre for Wireless Communications in Singapore, one of the predecessors of the Insti- tute for Infocomm Research (I2R). From December 2000 to May 2011, he was Assistant Professor, As- sociate Professor, then Professor at the University of Toronto’s Edward S. Rogers Sr. Department of Electrical and Computer Engi- neering. From June 2011 to January 2020, he was a Professor at the Electri- cal Computer Engineering Department of NUS, where he served as a Deputy Head from July 2014 to August 2015. From September 2015 through Decem- ber 2019, he served as Vice-Dean (Graduate Programs) in the NUS Faculty of Engineering. Since January 2020, he has served as Deputy Dean and Asso- ciate Dean (Education) at the Faculty of Engineering in the University of Syd- ney. Professor Lim is an Associate Editor for IEEE Potentials, was an Area Editor of the IEEE Transactions on Wireless Communications from Septem- ber 2013 to September 2018, and previously served as an Associate Editor for the same journal. He has also served as an Associate Editor for IEEE Wireless Communications Letters, Wiley Transactions on Emerging Telecommunications Technologies (ETT), IEEE Signal Processing Letters and IEEE Transactions on Vehicular Technology. He has volunteered on the organizing committee of a number of IEEE conferences, including serving as the TPC co-chair of IEEE Globecom 2017. He chaired the Singapore chapter of the IEEE Communica- tions Society in 2017 and 2018, and is a Distinguished Lecturer of the IEEE Vehicular Technology Society for 2019-20. His research interests span many topics within wireless communications, including cyber-security in the Internet of Things, heterogeneous networks, cooperative transmission, energy-optimized communication networks, multi-carrier modulation, MIMO, cooperative diver- sity, cognitive radio, and stochastic geometry for wireless networks, and he has published widely in these areas.

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