**1. Introduction**

The ability to authenticate electronic information-processing devices based on their unique characteristics attracts the attention of researchers who work to ensure the cybersecurity of information systems. The uniqueness of electronic devices at the physical level makes it possible to carry out authentication using various methods, namely physically non-cloneable functions for the Internet of Things (IoT) [1,2], error vector trajectories of the Global System for Mobile Communications (GSM) mobile phone signals [3], the spectrum of noise in the signal of radioactivity sensors [4], spontaneous electromagnetic radiation from operating mobile phones, light-emitting diode (LED) screens, laptops [5], wireless fidelity transmitters [6], etc. Authentication accuracy depends on the chosen method and conditions of experiments, but usually does not reach 100 percent.

The implementation of the idea of authentication by individual characteristics is based on a preliminary measurement of a physical quantity; for example, electromagnetic

**Citation:** Maksymovych, V.; Nyemkova, E.; Justice, C.; Shabatura, M.; Harasymchuk, O.; Lakh, Y.; Rusynko, M. Simulation of Authentication in Information-Processing Electronic Devices Based on Poisson Pulse Sequence Generators. *Electronics* **2022**, *11*, 2039. https://doi.org/10.3390/ electronics11132039

Academic Editor: Krzysztof Szczypiorski

Received: 24 May 2022 Accepted: 26 June 2022 Published: 29 June 2022

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interference from operating units of the device, the so-called internal electrical noise. The method of authentication for electronic information-processing devices (personal computers) by the individual forms of correlograms of their internal electrical noise is known [7]. The device authenticator—noise bit template—is calculated from the normalized autocorrelation function of noise. In the future, bit templates could be compared with each other using the selected metric; this is the Hamming distance in the simplest case. An important property of the bit template set, obtained from sequential measurements of the internal noise of a single device, is their closeness in the sense that the Hamming distances between possible pairs of bit templates are small, while the distances between pairs of templates for different devices are much larger. This makes it possible to reliably distinguish these devices, i.e., to authenticate them. The reference templates from each electronic device are pre-recorded on the server. During authentication, the device presents a real-time template, which is compared with a reference template. Authentication is confirmed if the distance between templates is less than a threshold value for the claimed device. Bit template variations provide dynamic authentication because the templates do not repeat exactly, and thus the authenticator reuse attack is eliminated. There are known experiments, a result of which made it possible to authenticate stationary personal computers of the same series with an accuracy of 98.6% [8].

An integrated sound card can be used to measure the internal noise of computers. Usually, noise bit templates of desktop computers are stable over time. For laptops the situation is slightly different. If the laptop gets into a location with a strong external electromagnetic field that significantly affects the internal noise of the laptop, then authentication errors occur [8]. In addition, not all electronic information-processing devices have integrated ADCs, for example, many microprocessors do not have an integrated ADC. For them, the use of internal noise as a sign of authentication is not possible. Therefore, in this study, the problem of modeling authentication features based on Poisson pulse sequence generators was formulated.

Generators of random or pseudo-random pulse sequences have been used for a long time to solve a wide range of problems in science and technology. Almost all standard program libraries have the embedded generators of pseudo-random sequences, which users could utilize. One of the most important generators is the Poisson pulse sequence generator (PPSG). These generators are widely used in different branches of techniques for simulating different processes that have a random temporal and spatial nature [9], for sociological and scientific research [10,11]. Such generators are effectively used to solve cybersecurity problems [12,13], to simulate the output signals of dosimetric detectors when designing them, and testing devices for measuring the parameters of ionizing radiation [14–19], because the number of radioactive decay particles detected by the detector over a period of time is subject to the Poisson distribution law.

In recently published works quite effective principles of realization of software and hardware PPSG are presented. Their structures, based on the use of pseudo-random number generators (PRNGs), were proposed [20–27] and methods for assessing the quality of their output signals were developed [28–31]. In this case the effectiveness of the possible application of the PPSG significantly depends on the quality of the designed generator and on the main characteristics of its output sequence.

The aim of this study was to model bit templates for the authentication of electronic information-processing devices based on a Poisson pulse sequence generator. The following tasks were solved to achieve this aim.


In this research, based on previously obtained results concerning Poisson pulse sequence generators and the development of the control code theory, the needed sequences were programmatically generated. Sample device bit templates were simulated based on these sequences and authentication was also performed programmatically. The examination consisted of calculating pairs of possible Hamming distances between the templates of the same device (intradistances) and for different devices (interdistances) and comparing them one with another.

Comparing the set of intradistances with the set of interdistances confirmed the main idea, that the generated templates could be unmistakably classified as being related to different devices. The threshold of distances was determined, according to which classification was made for specific parameters of the PPSG.

In this research the Poisson Pulse Sequence Generator was used for the first time to create device authentication templates based on the principle of biometrics. Compared with the best practices, which were using the measured values—electromagnetic radiation, internal electrical noise—the proposed method had several advantages. Benefits included 100% authentication, significantly more devices, and no time delay for measurements.

#### **2. Materials and Methods**

#### *2.1. Structural Scheme PPSG and the Principle of Its Operation*

The generator [16–18], whose structural scheme is illustrated in Figure 1, consisted of a modified additive Fibonacci generator (MAFG), which contained registers Rg1–Rg5, adders Ad1–Ad3, logical scheme LS, as well as a comparing scheme CS and logical element &. All the structural MAFG elements, except LS, worked in binary-decimal code.

**Figure 1.** PPSG structural scheme based on MAFG.

On MAFG output, e.g., on Rg5 output, a sequence of pseudo-random numbers was formed in accordance with the following expression:

$$\mathbf{x}\_{j+1} = \left(\mathbf{x}\_{j} + \mathbf{x}\_{j-1} + \mathbf{x}\_{j-2} + \mathbf{x}\_{j-3} + a\right) \text{mod}m \tag{1}$$

where *xj*, *xj*−1, *xj*−2, *xj*−<sup>3</sup> are the numbers in registers Rg4, Rg3, Rg2, Rg1, correspondingly, *m* = 10*q*, and *q* is the number of decades of the scheme's structural elements. The value of the variable *a* is determined by the logical equation

$$a = \left(a\_{0\_0} \oplus a\_{0\_1} \oplus a\_{0\_2} \oplus a\_{0\_3}\right) \oplus \dots \oplus \left(a\_{q-1\_0} \oplus a\_{q-1\_1} \oplus a\_{q-1\_2} \oplus a\_{q-1\_3}\right) \tag{2}$$

where *aij* (*i* = 0, 1, 2, 3; *j* = 0, 1, . . . , *q* − 1) is the value of bits of the binary-decimal number in Rg5. The number of members of Equation (2) can be selected from the range 0 . . . 4 · *q*.

The theoretical average value of the pulse frequency at the PPSG output is determining from the following Equation [16]:

$$f\_{out} = \frac{G}{10^4} f\_m \tag{3}$$

where *G* is the control code, *fm* is the clock pulse frequency.

*2.2. Output Signal Parameters and Internal Parameters of the Generator and Their Relationship*

The main parameters of the output pulse sequence were as follows:


The parameters of the output pulse sequence were determined by the following internal parameters of the generator (Figure 1):


The three internal parameters were clearly defined:


Based on the principle of PPSG construction, it could be argued that the repetition period of the output pulse sequence was equal to the repetition period of numbers in the MAFG output.

The repetition period and statistical characteristics of the sequence of numbers in the MAFG output determined the compliance of the output PPSG pulse sequence with the Poisson distribution law. However, that compliance significantly depended on the average frequency of an output sequence *fout*, whose theoretical value was determined by Equation (3) and, therefore, depended on the correlation between control code value *G* and value 10*q*. In fact, when value *G* was approaching the value 10*q*, then *fout* was approaching the clock frequency *fm* and, under such conditions, the output sequence started losing its pseudo-random properties. From the other side, the lower the frequency of the output sequence *fout*, the greater the time interval needed to be to determine its statistical characteristics. In this case such an interval should not exceed the repetition period of this sequence. Thus, in principle (theoretically), the original PPSG pulse sequence might conform to the Poisson distribution law for arbitrarily small average values *fout*, however, the sequence repetition period should be of a sufficiently large value. As a limit, if the average value *fout* went to zero, the repetition period should go to infinity.

These statements were practical in nature, satisfied most PPSG applications, and are confirmed below by specific calculations and simulation results. Theoretically, a more general approach to determine the correspondence of the output sequence to the Poisson distribution law could be considered, taking into account the value of the average repetition frequency, repetition period, observation time, and the chosen method of estimating statistical characteristics. However, such an approach needs to be refined to be applied in practice.

Taking into account the above, the average frequency *fout*, the range of its values, and the step change could be calculated theoretically using Equation (3). The real values of these quantities were determined as a result of simulation and/or experimentally.

#### *2.3. Estimation Method for Statistical Characteristics of the Output Signal*

This research was carried out using a generalized method of studying the parameters of the output PPSG pulse sequence for compliance with the Poisson distribution law using Pearson's test [32].

In accordance with the proposed method, the flow of input pulses of the PPSG was divided into *n* equal groups, each of which consisted of *imax* pulses. The maximum number of groups was *nmax*. The groups of input pulses corresponded to the groups of output pulses with the number of pulses *k*1, *k*2, ... *knmax* . The proposed method was based on the classical testing method of the hypothesis of the distribution of the general totality according to Poisson's law using Pearson's criterion (*χ*<sup>2</sup> criterion) [32–34]. In this case, taking into account the specifics of the PPSG construction, the following additions were proposed:


$$i\_{\max} = \frac{10^q}{\mathcal{G}} k\_{\mathcal{c}} \, . \tag{4}$$

As a result of the application of this method we obtained the value *χ*2*c* . According to the tables of critical distribution points of *χ*2 [33,34], according to the selected level of significance *α* (usually *α* is assigned one of the three following values: 0.1; 0.05; 0.01), the number of degrees of freedom *k* could be obtained using the critical value *<sup>χ</sup>*2*cr*. If *χ*2*c* < *<sup>χ</sup>*2*cr* there was no reason not to accept the hypothesis that the pulse flux corresponded to the Poisson distribution law.

When determining the statistical characteristics of the PPSG output signal in the range of values of the control code *G*, it was useful to average the last (current) *h* values of *χ*2*c* . Obtained by such a way, variable *<sup>χ</sup>*2*cav* was comparable with *<sup>χ</sup>*2*cr*. The averaging of the values *χ*2*c* was necessary for a certain "smoothing" of the results. Based on the simulation experience, one could select value *h* = 5, which could be changed if needed for a clearer (more integrated) determination of the control code range *G*, in which the output pulse sequence corresponded to the Poisson distribution law.

When designing a PPSG, it is also useful to pre-determine the statistical characteristics of the number sequence, in this case at the MAFG output. This could be achieved using standard statistical tests, such as NIST statistical tests [22–27,32,35].

#### *2.4. Defining the Limits of the Range of the Control Code Values*

Lower *G*1 and upper *G*2 limits of the control code values *G*, in which the statistical characteristics of the output pulse sequence corresponded to the Poisson distribution law, could be determined based on the following.

The sequence evaluation time should not be longer than its repetition period *Tn*. That is, based on the above methodology, the following inequality must be satisfied:

$$
\dot{u}\_{\text{max}} \cdot \boldsymbol{n}\_{\text{max}} \le T\_{\text{n}} \tag{5}
$$

From Equation (4) and inequality (5) we obtain

$$G \ge \frac{10^q \cdot k\_c \cdot n\_{\text{max}}}{T\_n} \tag{6}$$

This meant that the value *G*1 was the smallest integer number satisfying Inequality (6). As a result of PPSG simulation, it was found that the value *G*2 satisfied the following condition:

$$G \le G\_2 = s \cdot 10^q \tag{7}$$

In this case the value of the coefficient *s* was determined separately for a concrete number of MAFG decades *q*, and depended on the initial settings of the registers Rg1–Rg5, the number of involved members of Equation (2) and, under certain conditions, was close to 0.1.
