On the study of the law of decrease of the electromagnetic field in real operating conditions..
Goryachev Sergey Vyacheslavovich
ON THE RESEARCH OF THE LAW OF DECAY OF THE ELECTROMAGNETIC FIELD IN REAL OPERATING CONDITIONS
The article is interesting for its practical results of measurements of electromagnetic field propagation in real conditions of a typical room. The presented results can be used by a wide range of specialists working in the field of information security.
On factors influencing electromagnetic field propagation in a real environment
Among the possible channels of information leakage that must be protected, a special place is occupied by the channel of leakage due to side electromagnetic radiation. This is determined by the fact that almost every electrical device during operation emits electromagnetic waves into space, one way or another connected with its functioning. The sources of signal radiation can be various elements of the product that process information.
As examples, we will consider several elementary cases of the functioning of such sources.
Example One
A current of strength Io flows through a section of an electric wire. A magnetic field is created around it, the intensity of which is determined by the formula:
where:
Io is the current flowing through a section of the conductor;
r is the distance from the conductor;
p is a constant, 3.14……
The intensity of the electric field created by such a source is determined by the formula:
where t is the linear charge density calculated by the formula:
where:
l is the length of the conductor;
e is the permittivity.
From the given formulas (1) and (2) it follows that the field strength created by this source decreases with distance from it according to a linear law depending on the distance r.
Example two
Two parallel conductors located at a distance a from each other, having a static charge density on each of them +t and -t.
In this case, the electric field strength at an arbitrary point in space, located at a distance r from the conductors, will be determined by the formula:
where a is the distance between the conductors.
The magnetic field strength created by two conductors laid in parallel at a distance a from each other, through which a current of force Io flows, is determined by the formula:
As follows from the given formulas (3) and (4), the field strength decreases according to a quadratic law as it moves away from such a source.
Example three
Several annular turns of the conductor, through which a current of force Io flows, create a magnetic field, the strength of which is determined by the formula:
where:
r is the distance to the emitter in question in the direction perpendicular to the plane of the turns;
R is the radius of the circle of the turns;
n is the number of turns.
In this case, the decrease in the field depending on the distance is determined by the cubic law.
The simplest examples given above demonstrate the difference in the laws of field decay depending on the distance for different elementary sources. In practice, the picture of the electromagnetic field created by a real source looks much more complicated.
If we conditionally divide any functional unit of the equipment that processes information into separate sections and consider them as independent sources of the electromagnetic field, then we can note the following points:
1) The spatial configuration of such an independent source is usually very complex. Even the simplest connecting assembly of elements on a printed circuit board has a very branched and tortuous structure. The electromagnetic field strength from such a spatially extended source will also have a rather complex structure.
2) The intensity of the electromagnetic field at an arbitrary point in space is determined by the superposition of fields determined by the radiation of elementary sections of the independent radiation source under consideration.
3) The pattern of the electromagnetic field of radiation from a product processing information will differ significantly in different directions from it.
Consideration of the protection criterion
Let us now turn to the consideration of the criterion of protection of the equipment processing information from its leakage due to side electromagnetic radiation. It is obvious that at some point in space, removed from the radiation source at some distance, the radiation field strength of the source will have some specific value Ec, which is a function of several variables, including the distance from the source.
At the same point in space, there will be a field strength of the interference signal Eп. The nature of this interference signal is determined by the presence of extraneous sources of electromagnetic radiation, and their nature is quite complex in itself and requires separate consideration.
The field strength at the point in question will be determined by the sum of two components:
Eo = Es + En, (6)
where:
Eo is the electromagnetic field strength at the point in question in space;
Es is the electromagnetic field strength created by the informative radiation source at the point in question in space;
En is the electromagnetic field strength created by the interference source at the point in question in space.
In order to be able to register a signal created by an information source at the point under consideration, at least two conditions must be met:
1) The magnitude of the field strength of the signal created by the information source must be sufficient for it to be recorded by the technical means available to the potential interceptor of the information. This in turn is determined by the sensitivity of the receiving device Epr, i.e. this condition can be expressed by the following simple relationship:
Es > Epr, (7)
where:
Ес – signal field strength of the information source;
Епр – sensitivity of the receiving device of the potential interceptor.
2) On the other hand, the possibility of registering a source signal at the point under consideration is determined by the ratio of the values of the field strength of the signal of the information source and the field strength of the interference signal. The criterion for information security from the point of view of its leakage due to side electromagnetic radiation is the ratio:
Ес/Еп < d, (8)
where:
d is a certain value of the specified ratio (the so-called maximum permissible ratio), when exceeded, it becomes possible for a potential enemy to intercept information signals due to side electromagnetic emissions from the equipment processing the information.
Let us consider in more detail the values included in criterion (8).
Maximum permissible ratio “signal/interference”.
This conditional value can be determined by a number of factors. Among them may be:
1) The value of the protected information. Obviously, the more valuable the information to be protected is, the greater the degree of interference over the information signal at the point of its possible interception by a potential enemy should be ensured from the point of its protection.
2) The nature of the signal transmitting information and its characteristics. Among such characteristics are the following: analog signal, digital signal, unconverted signal, non-informative signal, modulated by an informative signal, and a number of others.
3) The ability to repeat fragments of an information message and the entire message as a whole. These may be some typical phrases during a telephone conversation, a sequence of commands during standard operations carried out during the operation of the product, and the like.
Other factors are also possible.
The field strength of the jamming signal at the location of possible interception of information by a potential enemy.
This value is determined by the influence of a number of third-party sources and is their superposition. The nature of these sources can be twofold: they can be interference of natural and artificial origin. Among the natural sources, the following can be noted:
— the magnetic field of the earth and other planets;
— the radiation of energy of some natural elements;
— other sources.
The nature of artificial sources was discussed at the very beginning of this work. Almost every electrical device in the process of its operation creates electromagnetic radiation, which determines the interference environment of the electromagnetic field at an arbitrary point in space, including at the point of possible operation of a potential enemy.
The nature of the interference signal may also vary. It may be an analog signal (voice during a telephone conversation, a signal emitted during the operation of an electric motor) or discrete (a signal emitted during the operation of a device that processes signals in the form of pulse codes). It may be either periodic (for example, radiation from a car ignition system) or random.
The interference signal may be monoharmonic (carrier frequency of a radio station) or emitted in a wide frequency spectrum.
To reduce the level of the interference signal at the output of the interception receiver (and, consequently, to increase the actual signal-to-interference ratio at the reception point), various hardware and mathematical methods can be used.
These include:
— methods of averaging the interference signal with a random distribution law;
— subtraction (compensation) of periodic interference from the signal-to-interference mixture (see relation (6));
— methods of cross-correlation analysis;
— methods of optimal reception;
— other methods.
To determine the magnitude of the interference signal Ep when calculating the actual “signal/interference” ratio, two types of interference signal can be used:
1) Interference signal measured directly at the location of the potential interception receiver.
2) A signal of some hypothetical interference, determined taking into account the possible application of the above-mentioned methods of reducing interference, as well as the value of the information to be protected, the nature of the signal transmitting the information, the operating features and a number of other practical conditions.
For various options for operating a product that processes information, the values of these hypothetical interference are determined by a number of current regulatory documents.
Let us move on to examining the magnitude of the informative signal at the point of potential interception Ec.
The nature of this signal was defined above. The value of the electromagnetic field strength of the source at the point under consideration at a distance r from the source is determined by the dependence:
Ec = Eo F(r), (9)
where:
Eo is the value of the electromagnetic field strength at the location of the radiation source;
F(r) is the functional dependence of the decrease in the electromagnetic field of the source at a distance r from it.
Taking into account formula (9), the above-mentioned protection criterion (8) will take the following form:
Eo F(r)/Eп < d, (10)
From the analysis of this relationship and the above consideration of the quantities included in it, we can conclude that in order to analyze the security of information processed by any product from leakage due to side electromagnetic radiation, it is necessary to have at one's disposal the law of decrease of the electromagnetic field depending on the distance F(r).
Referring again to the reasoning given at the beginning of this work about the nature of the decrease of the field from an electrical device with a complex structure, we can note the following facts:
1) The law of decrease of the electromagnetic field is different for different sources. Moreover, this statement is true even for identical devices from the point of view of production. This difference, in turn, is due to physical differences in the parameters of the element base of the device itself, the possibility of using elements in similar devices that differ from each other in secondary parameters that do not affect the operability of the product, differences in the relative positions of the articulated elements (for example, when installing individual boards in a connector on a computer motherboard, or when connecting individual units of the product using flexible cables). It is obvious that the nature of the radiation from the product can change over time.
2) The law of decrease of the field in space depends on a number of external factors. The presence of foreign bodies in the space surrounding the radiation source causes the manifestation of such phenomena as:
— shielding;
— re-radiation;
— diffraction.
From the above, we can conclude that the theoretical calculation of the law of field decay from a radiation source, which is an electrical device that processes information, is not possible in practice.
In order to solve this problem, it seems appropriate to conduct practical experimental studies in order to study the law of field decay from various sources under various operating conditions with a set of statistics and their subsequent processing and systematization.
Results of practical studies
A practical experiment was conducted in order to study the law of electromagnetic field decay under real conditions.
An IBM PC/AT type personal computer was studied as a radiation source. It was located on the second floor of the building, the plan of which is shown in diagram 1.
Diagram 1. Location of signal pickup points Ti
The typical design building consists of two blocks connected by a passage. The object under study was located in the first block. The block is three-story, panel-and-block, the height of each floor, taking into account the interfloor ceilings, is 4 m. The rooms of the building contain work desks, as well as control and measuring equipment. The information processed on the PC was a test program, during the operation of which the system unit and monitor were involved in a cyclic mode. The PC was located on the work desk at a distance of 1 m from the window. In the figure, the location of the radiation source under study is marked with the letter «I».
Measurements of the electromagnetic field strength were carried out at various distances from the radiation source. In the figure, the symbols Ti indicate the measurement points. The studies were conducted in four directions.
Direction 1 – towards points T2, T8, T10, T11, T13, T14, T15.
Direction 2 – towards points T3, T4, T5, T7.
Direction 3 – towards the gym shown in the figure.
Direction 4 – towards the window, to the street.
The intensity of the electromagnetic field created by the source under study was recorded using a set of calibrated antennas connected to the input of the measuring receiver. A selective microvoltmeter of the SMV-8 type was used as a measuring receiver.
Signal measurements were carried out at the following frequencies:
— 30 MHz (frequency K1);
— 50 MHz (frequency K2);
— 100 MHz (frequency K3);
— 130 MHz (frequency K4);
— 150 MHz (frequency K5);
— 185 MHz (frequency K6);
— 230 MHz (frequency K7);
— 300 MHz (frequency K8).
The field decay coefficient was calculated using the formula:
K = Lg(Ed/Eo), (11)
where:
K is the decay coefficient of the electromagnetic field generated by the radiation source under study;
Eo – electromagnetic field strength measured at a distance of 0.5 m from the source;
Ed – electromagnetic field strength measured at a distance d from the radiation source.
The results of the experimental studies are shown in the graphs (Fig. 1-8).
The graphs of the field decrease at different frequencies are shown in different colors and designated by the corresponding symbols Ki.
For comparison, each of the figures shows the field decrease curves corresponding to the linear (n=1), quadratic (n=2) and cubic (n=3) laws.
Fig. 1. Attenuation coefficient of the PEMIN field from the monitor in direction 1 (logarithmic scale).
Fig. 2. Attenuation coefficient of the PEMIN field from the system unit in direction 1 (logarithmic scale).
Fig. 3. Attenuation coefficient of the PEMIN field from the monitor in direction 2 (logarithmic scale).
Fig. 4. Attenuation coefficient of the PEMIN field from the system unit in direction 2 (logarithmic scale).
Fig. 5. Attenuation coefficient of the PEMIN field from the monitor in direction 3 (logarithmic scale).
Fig. 6. Attenuation coefficient of the PEMIN field from the system unit in direction 3 (logarithmic scale).
Fig. 7. Attenuation coefficient of the PEMIN field from the monitor in direction 4 (logarithmic scale).
Fig. 8. Attenuation coefficient of the PEMIN field from the system unit in direction 4 (logarithmic scale).
Analyzing the presented results, the following can be noted:
First.The law of field decrease from the source under study obviously cannot be described by some simple dependencies at the entire distance from the source. It is possible to note some separate sections that are close in appearance to a certain law described by a mathematical formula.
Second.In directions from the source that are freer from foreign objects (for example, in direction 2 — towards the street), the field decrease is more monotonous in nature without sharp surges.
Third.Comparing the results of the studies obtained for different devices (monitor and system unit), it can be noted that the curves of the electromagnetic field decrease are generally similar in appearance, which indicates the impact of external objects on the propagation process. At the same time, analyzing the graphs provided, it should be noted that there are certain differences due to the physical differences in the devices under study.
Fourth.In some cases, such as at some frequencies in directions 1, 3 and 4 from the source, the electromagnetic field signal measured at some distance from the source exceeds the signal level measured in its immediate vicinity. This phenomenon is observed at distances of up to 7–8 m from the source, and in direction 3 at a frequency of 185 MHz, the measured signal exceeds the original at a distance of up to 54 m.
Fifth.Field decay graphs in most cases are not monotonically decreasing. In almost every direction there are sections of local increase in the field attenuation coefficient. These phenomena are caused by reasons that have already been discussed in the initial part of this work.
Not taking into account the above-mentioned phenomena, it is possible to significantly complicate the assessment of the security of information processed by a particular technical means. In some cases, this can lead to erroneous conclusions about the security of information, which in turn can lead to its leakage through the leakage channel we are considering.
For the purpose of a more in-depth study of the problem considered in this paper, it is advisable to conduct practical research in the following areas:
1) Conducting research on the law of decrease of the electromagnetic field from various sources processing information. The results of the research should be systematized for similar products operating in certain modes.
2) Conducting practical measurement work for various operating conditions of products that process information. For example, the operation of a product in urban conditions in terms of the decrease in the electromagnetic field differs significantly from its operation in field conditions.
3) Collecting statistical data, mathematically processing it, and issuing methodological recommendations on the use of patterns of decrease in the electromagnetic field from sources that process information. Moreover, these methodological recommendations should be differentiated depending on the operating conditions.
Thus, summing up the above, we can note the following:
- the paper considers issues related to the study of the law of decrease of the electromagnetic field from the source processing the information subject to protection, as well as issues of protection of this information from its leakage due to side electromagnetic radiation;
- the law of decrease of the electromagnetic field in real conditions is complex and in most cases cannot be described with sufficient reliability by mathematical formulas;
- the nature of the field decrease is influenced by a number of factors, such as the individual characteristics of the product that is the source of signal radiation, the characteristics of the electrical signal that is the information carrier, the operating conditions of the product;
- it is advisable to conduct practical studies of the law of decrease of the electromagnetic field from various sources for various operating conditions with a set of statistics and the subsequent issuance of methodological recommendations.