# Modelling of the Energy Depletion Process and Battery Depletion Attacks for Battery-Powered Internet of Things (IoT) Devices

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## Abstract

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## 1. Introduction

## 2. Energy Consumption Models for IoT Devices

#### 2.1. Power Consumption of an IoT Device

#### 2.2. Modelling of the Expected Lifetime of an IoT Device

#### 2.3. Stochastic Modelling of the Battery of an IoT Device

## 3. Energy Depletion Attacks in IoT Networks

## 4. Modelling the Energy Depletion Process for a Battery of an IoT Device

#### 4.1. Markovian Model of the Battery for IoT Devices

#### 4.2. Diffusion Approximation Model of the Battery for IoT Devices

## 5. Analysis of Ghost Energy Depletion Attacks on an IoT Network

- 1
- The energy consumption of the various hardware components of the IoT device (e.g., microcontrollers, radio transceivers, sensors, actuators, and other electronic components). Energy-demanding microcontrollers and radio transceivers will consume more energy than energy-efficient ones. They will drain the energy stored in the battery of the IoT device quickly during a battery depletion attack.
- 2
- The energy capacity of the IoT battery. For a given IoT device, the lifetime depends mainly on its battery’s energy capacity. With a high-capacity battery, the lifetime of the device could be longer. A ghost energy depletion attack will quickly shut down a device with a small battery capacity.
- 3
- Frequency of data collection (sensing), actuation (where necessary), processing, and communication (reception and transmission of information). The more frequent the device’s sensing, processing, actuation, processing, and communication operations, the higher the device’s energy consumption. A ghost attacker could compel victim IoT devices to perform such operations more frequently than during normal operations.
- 4
- The MAC protocol in the link layer. A ghost attacker can abuse the MAC protocol in the link layer to create collisions, thus increasing the energy consumption of the devices sharing the channel with it. A collision-free protocol at the link layer could reduce this kind of attack.
- 5
- The cryptographic algorithm is implemented on the IoT device to encrypt and decrypt information. The energy required to encrypt or decrypt a packet depends on the number of microcontroller clock cycles required to execute the algorithm (encryption or decryption) and the average current drawn by each cycle. Therefore, with information about the number of cycles required to execute the algorithm, the current drawn in each cycle, the microcontroller’s clock frequency, and the microcontroller’s operating voltage, the energy required to execute an encryption or decryption algorithm on an IoT device can be estimated. The more sophisticated or computationally intensive the cryptographic algorithm, the more quickly it can be leveraged by an attacker to drain the energy of an IoT device.
- 6
- The packet sizes. The longer the packet size, the more energy is required to transmit the packet and the longer the time required to transmit the packet. A ghost attacker could decide to create longer packets that take too long to transmit, causing other IoT devices sharing the channel with it to experience more collisions.

#### 5.1. Analysis of High Computational Load Ghost Energy Depletion Attack

#### 5.2. Analysis of MAC Misbehaviour Ghost Energy Depletion Attack

## 6. Numerical Examples

## 7. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 3.**The distribution ${P}_{n}\left(t\right)$, of the amount of energy n in Wh present in the battery at time t, for $t\in (0,\phantom{\rule{0.277778em}{0ex}}10]$, $n\in [0,100]$, $B=100$, and ${P}_{D}=1$.

**Figure 4.**The distribution ${P}_{n}\left(t\right)$, of the amount of energy n in Wh present in the battery at time t, for $t\in (0,\phantom{\rule{0.277778em}{0ex}}100]$, $n\in [0,100]$, $B=100$, and ${P}_{D}=1$.

**Figure 5.**Comparing the probability density of the lifetime of the IoT device ${\gamma}_{B,0}\left(t\right)$ for $B=100$ Wh and ${P}_{D}=0.2$ W, Markov and diffusion models.

**Figure 7.**An illustration of Equation (35) with ${\lambda}_{A}=5$, ${\lambda}_{0}=1$, $D=0.001$, $N=50$, $\lambda \in [0,\phantom{\rule{0.277778em}{0ex}}2000]$; the intersection points indicate the operating points of the system.

**Figure 8.**The relationship between the mean active time of the transmitter and the mean total effective traffic intensity in the channel: $1/\mu $ vs. $\lambda $, for $D=0.001$, ${T}_{c}=0.001$, ${T}_{r}=0.1$, ${T}_{tx}=0.01$, and $\lambda \in [0,\phantom{\rule{0.277778em}{0ex}}2000]$.

**Figure 9.**The distribution $\psi (x,t;B)$, of the amount of energy x present in the battery at time t, for $t\in (0,200]$ and $x\in [0,100]$.

**Figure 10.**The distribution $\psi (x,t;B)$, of the amount of energy x present in the battery at time t, for $t\in (0,500]$ and $x\in [0,100]$.

**Figure 11.**The distribution $\psi (x,t;B)$, of the amount of energy x present in the battery at time t for $t\in (0,1000]$ and $x\in [0,100]$.

**Figure 12.**The distribution $\psi (x,t;B)$, of the amount of energy x present in the battery at time t for $t\in (0,2000]$ and $x\in [0,100]$.

**Figure 13.**The influence of the active mode power, ${P}_{ACT}$, on the distribution of the lifetime of the IoT device.

**Figure 14.**The influence of the proportion of sleep time, ${R}_{SLEEP}$, on the distribution of the lifetime of the IoT device.

**Figure 15.**The influence of the proportion of sleep time, ${R}_{SLEEP}$, on the probability that the energy stored in the battery is completely depleted.

**Figure 16.**The influence of the squared coefficient of variance of the energy consumption ${C}_{B}^{2}$ on the distribution of the lifetime of the IoT device.

**Figure 17.**The influence of the battery capacity B on the probability that the energy stored in the battery is completely depleted.

**Figure 18.**Mean device lifetime ${\mu}_{T}$ versus battery capacity B for various values of sleep mode ratio ${R}_{SLEEP}$.

**Figure 19.**The probability density function ${\gamma}_{B,\eta B}\left(t\right)$ that after time t, the amount of energy present in the battery is $x=\eta B$; that is, the battery must have discharged to $1-\eta $ percent of its initial amount of energy.

**Figure 20.**The probability ${\mathsf{\Gamma}}_{B,\eta B}\left(t\right)$ that after time t, the amount of energy present in the battery is $x=\eta B$; that is, the battery must have discharged to $1-\eta $ percent of its initial amount of energy.

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## Share and Cite

**MDPI and ACS Style**

Kuaban, G.S.; Gelenbe, E.; Czachórski, T.; Czekalski, P.; Tangka, J.K.
Modelling of the Energy Depletion Process and Battery Depletion Attacks for Battery-Powered Internet of Things (IoT) Devices. *Sensors* **2023**, *23*, 6183.
https://doi.org/10.3390/s23136183

**AMA Style**

Kuaban GS, Gelenbe E, Czachórski T, Czekalski P, Tangka JK.
Modelling of the Energy Depletion Process and Battery Depletion Attacks for Battery-Powered Internet of Things (IoT) Devices. *Sensors*. 2023; 23(13):6183.
https://doi.org/10.3390/s23136183

**Chicago/Turabian Style**

Kuaban, Godlove Suila, Erol Gelenbe, Tadeusz Czachórski, Piotr Czekalski, and Julius Kewir Tangka.
2023. "Modelling of the Energy Depletion Process and Battery Depletion Attacks for Battery-Powered Internet of Things (IoT) Devices" *Sensors* 23, no. 13: 6183.
https://doi.org/10.3390/s23136183