WO2020237265A1

WO2020237265A1 - Method for generating and distributing cryptographic or steganographic keys

Info

Publication number: WO2020237265A1
Application number: PCT/AT2019/060183
Authority: WO
Inventors: Ernst Piller; Stefan Bernhard SCHUBERT
Original assignee: Fachhochschule St. Pölten GmbH
Priority date: 2019-05-31
Filing date: 2019-05-31
Publication date: 2020-12-03

Abstract

A method for generating and distributing cryptographic or steganographic keys for use in cryptography or steganography involves two terminals (1) performing a telecommunication (5) and measuring radio channel properties of this telecommunication (5). A respective IT system (3) is connected to a respective terminal (1), wherein each of the two IT systems (3) sends its connected terminal (1) data, some or all of which are transmitted to the other terminal (1) by means of the telecommunication (5). The measured radio channel properties on the two IT systems (3) are processed further such that random, identical keys are produced in the two IT systems (3) separately. According to the invention, the telecommunication (5) takes place via at least one satellite (2). As a result, the radio channel properties change much more quickly, which means that successive measurements are certain to produce different results. One satellite (2) is preferably mobile.

Description

PROCEDURE FOR THE GENERATION AND DISTRIBUTION OF CRYPTOGRAPHIC OR STEGANOGRAPHIC KEYS

Technisches GebietTechnical area

The invention relates to a method for the generation and distribution of cryptographic or steganographic keys for use in cryptography or steganography, in which two terminals carry out a telecommunication and measure radio channel properties of this telecommunication, with one IT system being connected to one terminal in each case Each of the two IT systems sends its connected end device data that is partially or fully transmitted to the other end device by means of telecommunication, with the measured radio channel properties being further processed on both IT systems in such a way that random, identical keys are separated in both IT systems arise.

Stand der TechnikState of the art

Such keys are used for data encryption, data hiding and data integrity checking. Their generation is based on the reciprocity of the high-frequency radio transmission and takes place by measuring radio channel properties of the radio transmission.

Highly secure cryptography and steganography are becoming increasingly important in the age of digitization and globalization. However, the currently used asymmetric cryptography is no longer suitable to guarantee a sufficiently high level of security over the long term. In the current methods based on number theory, e.g. With the Diffie-Hellman procedure, hybrid key distribution procedures and digital signature procedures (e.g. RSA, DSA, ECDSA), today security is determined by unprovable security assumptions. Above all, however, these methods can no longer be used with quantum computers for security reasons. Therefore, attempts are being made to switch increasingly to physical methods and post-quantum systems. However, quantum cryptography as a possible physical method for generating and distributing cryptographic / steganographic keys, which can guarantee the desired security, is expensive and cannot be used in many areas.

Worldwide quantum computer-secure generation and distribution of cryptographic keys, hereinafter referred to as key distribution, was previously reserved for quantum cryptography using physical methods. But with quantum cryptography, end-to-end global key distribution suitable for the masses is not in sight. Since data encryption has to be end-to-end secure, a very large number of communication partners occur when used worldwide, which cannot be economically implemented with quantum cryptography.

For around ten years now, research has been working successfully with a new physical process, key distribution based on the measurement of radio channel properties of direct high-frequency radio transmission. It is based on the reciprocity of radio transmission. This means that with high-frequency radio transmission in both directions with simultaneous measurements on both sides (transmitter and receiver), similar measurement results are achieved. These similar values are the basis for determining a common cryptographic key in further important processing steps. In the prior art, the measurements usually measure the signal strength and occasionally the phase angle.

Basically, the two communication partners use the characteristics of a wireless transmission channel in order to establish a secure connection. The unpredictable conditions are used as a common source of entropy and make for strong cryptographic / steganographic keys. (Note: a "strong" key is long enough to withstand brute force attacks and is evenly distributed over the entire key space required.) Furthermore, the channel conditions do not change suddenly, but steadily over time Measurements on both sides achieved similar measurement results. These similar values are the basis to form a common cryptographic / steganographic key. The theoretical and practical results, which were carried out in the context of telecommunications over short distances (less than 20 km), show that a passive attacker comes to measured values that do not correlate with the values of the partners, unless they are in the immediate vicinity to one of the two is located. This is the basic fact needed to make this method useful.

The entire methodology can be broken down into four sub-steps. These are channel sampling, quantization, error correction, and strengthening confidentiality.

The pattern of the main signal and delayed echoes is random and only the same on both receiver sides, which means that random data can be generated that cannot be eavesdropped by an attacker (who measures other values) unless his antenna is in the immediate vicinity ("immediate" means: within a fraction of a wavelength) to the "regular" antenna, which can of course be seen immediately. From this, through further important processing steps, highly secure cryptographic keys can be generated and distributed.

It is important, however, that the original measured values can assume many different results. There are at least 10 ³⁰ possibilities for a 100-bit long key. If you measure the phase angle with an accuracy of 2 °, for example, there are only 180 possibilities, which is far too few. In practice, the phase angle is therefore often measured (for example 15 times) in succession until you have enough "random numbers". However, this system only works satisfactorily if the result changes rapidly over time, otherwise the same (or at least a very similar) angle is always measured. If, for example, a busy road is nearby, the phase angle will change very quickly due to the constantly changing reflections on the vehicles. People walking around can also cause these readings to change. However, it becomes problematic if there are no changes in the environment of the two communication partners.

Darstellung der ErfindungPresentation of the invention

It is the object of the present invention to provide a remedy here.

According to the invention, this object is achieved in that the telecommunication takes place via at least one satellite.

Satellites are always in motion. A geostationary satellite also moves at around 1 km per day, i.e. at around 1 cm / s. Communication with geostationary satellites usually takes place at 15 GHz, i.e. a wavelength of 2 cm. I.e. the phase angle can change by 18 ° within just 100 ms. With several measurements one after the other, one always gets very different results, which is of course ideal for generating large amounts of random numbers. The situation is even better for moving satellites with orbits in the LEO (see below), which move at a speed of over 7 m / ms. Communication with satellites in the LEO is usually in the L-band, i.e. with frequencies of around 1.5 GHz, which corresponds to a wavelength of around 0.2 m. This means that the phase angle changes by around 12 ° in 1 µs.

The method according to the invention thus provides a suitable solution for the highly secure generation and distribution of cryptographic or steganographic keys, the security of which does not come from the complexity of mathematical problems, but from the nature and location of satellites. It is based on a method that is based on the measurement and post-processing of radio channel properties of a telecommunication via satellite with the help of end devices and as a result determines a cryptographic / steganographic key on both communication sides (end devices), which guarantees the necessary entropy for such keys.

In the method according to the invention, radio signals are measured in both terminals which, in the case of a reciprocal channel, only occur in identical form in both terminals - and not in others, e.g. devices in the vicinity - and correlate with the distance to the endpoints depending on the wavelength of the signal used. The set of measured values of the radio channel properties is random and only the same for both terminals, which means that random data can be generated for the generation of cryptographic / steganographic keys that cannot be eavesdropped by an attacker. From this random data (set of measured values of the radio channel properties), which are mostly slightly different despite the reciprocity, an identical, random value is then determined on the two sides that are communicating with each other. This involves "sampling the data", quantization, channel modeling, preprocessing, error bit elimination and error correction. Data from the data transmission are also taken into account. This then results in the random, identical, cryptographic / steganographic key on both sides. The required entropy of the key, which is very important for the security of the key, arises, among other things, from a suitable integration of many measured values into one value. The randomness of the respective radio measured values is important here, which primarily dictates the nature and position of the satellite in the form of "dynamics" and can vary greatly. In the case of the terminals, the method according to the invention only provides specifications to the extent that these devices can be used to measure the radio channel properties with the required accuracy and that the same devices are located on both communication sides so that reciprocity can be achieved.

The satellite key distribution according to the invention, which is based on the above-mentioned state of the art and represents a new technology, now enables the generation and distribution of quantum computer-secure cryptographic keys by measuring properties of a communication via satellite: This physical method is also possible worldwide. It builds on the skills and special properties of satellite communication such as reciprocity, phase difference (phase angle), signal strength, signal polarization, satellite orbit, spread spectrum, environmental influences, etc. The dynamics required for the required randomness and length of the cryptographic key are determined by the dynamics of the earth's atmosphere (especially the troposphere, stratosphere, ionosphere), the movement of the satellites, in particular the inaccuracy of the current position of moving satellites related to the very high measurement accuracy required (Millimeter range), as well as mathematical methods from post-quantum cryptography. This means that the satellite key distribution is a combination of mathematical methods (methods of post-quantum cryptography) and physical methods, so that an attacker has to break both.

The satellites can be geostationary (e.g. Eutelsat, orbit 35,786 km) or satellites in motion with orbits in LEO (Low Earth Orbit, less than 2,000 km above the earth's surface). Satellites in the LEO move so fast that both communication partners can only get the same result with greater effort. However, it is preferred that a satellite be movable.

A particular advantage here is that the inaccuracy of the orbit of satellites, which in principle is naturally known, is much too great to be able to draw conclusions about radio channel properties based on the known data. The exact position at the relevant point in time can only be obtained by measuring the phase shift (phase angle) or the transit time of the signals.

For worldwide use, the satellites must also pass on the signals to one another (distribute), e.g. in that a satellite forwards the signals to certain other satellites at a certain transmission frequency or at certain times or this re-transmission takes place in connection with so-called ground stations, which relay the signals from one satellite to other satellites. It should be noted, however, that normally only a maximum of one non-geostationary satellite is possible in a signal path, because otherwise the two signals cannot find the two non-geostationary satellites in the same position, because while the signal is traveling from one non-geostationary satellite to another , the position of the satellites is already changing significantly.

With this relay-like forwarding of the signals, it must of course be ensured that the signals are forwarded immediately after receipt without significantly disturbing the reciprocity.

In general, it is possible for the satellites to perform their "mirror function" (transparent transponder) only at certain times and / or at certain transmission frequencies, so that terminals can only communicate with the respective satellite at these time slots. The desired times and / or transmission frequencies can be reported beforehand from the terminals on earth to the satellites, so that each terminal on earth can only do this to a very limited extent, number per time unit, with very short time units in the single-digit millisecond and microsecond range. The satellites should not report back the times and transmission frequencies, otherwise an attacker could find out.

The satellite communication is preferably started on both sides in such a way that the signals from the two terminals arrive at the mobile satellite at the same time. The more precisely this simultaneity is fulfilled, the more precisely the position of the satellite is the same for the two transmissions, and the better the reciprocity of the transmission path is given.

However, the satellite orbit is often not known precisely enough to calculate by how much time difference the signals have to be sent away from the two terminals differently in order for them to arrive at the satellite at the same time. If at least one terminal itself receives the signals sent to the satellite again, it can measure the time difference between these two signals (its own signal and the signal of the other terminal) very precisely. This time difference does not change on the way from the satellite to the receiving device and therefore corresponds to the time difference with which the signals arrived at the satellite differently. If the next communication is started differently by this time difference compared to the theoretical calculation, the signals should arrive at the satellite at the same time. For this purpose, the detected error can be transmitted to the other end device - usually via a different channel, e.g. classic internet - to be announced.

The radio channel property (s) measured in the two terminals can represent the amplitude of the signal, the phase angle of the signal, the transit time of the signal and / or the polarization of the signal.

The radio channel property can be measured as the sum of the two phase angles of the transmitted and received signal, or the radio channel property can be the change in the phase shift between the transmitted and the received signal between different measurements. Both results are almost identical for both devices:

Let us denote the phase angle of the vibrations sent by the two terminals A and B with φ _{A, S} and φ _{B, S.} While the signal traverses the radio link, the phase angle changes by Δφ, i.e. the signal received from A has the phase angle φ _{A, E} = φ _{B, S} + Δφ, and the signal received from B has the phase angle φ _{B, E} = φ _{A, S} + Δφ. Because of the reciprocity of the radio channel, Δφ is (almost) the same in both cases. The sum φ _{A, S} + φ _{A, E} is therefore equal to the sum φ _{B, S} + φ _{B, E.}

The disadvantage here is that an in-phase reference signal is necessary to determine the phase position for both terminals. If this is not available, the change in phase shift between the transmitted and the received signal can be used for various measurements. Let us assume that there are three measurements, with the change in phase position being different each time due to the changing signal path, namely
(Δφ) ₁ , (Δφ) ₂ and (Δφ) ₃ .
The terminal A then measures i during the measurement
φ _{A, S} ‑φ _{A, E} = φ _{A, S} ‑φ _{B, S} - (Δφ) _i ,
the terminal B measures analogously
φ _{B, S} ‑φ _{B, E} = φ _{B, S} ‑φ _{A, S} - (Δφ) _i . If you now form the difference between the first and the second measurement, for example, then both terminal A and terminal B get (Δφ) ₂ - (Δφ) ₁ as a result, which can then be used as a random number.

When "phase position" is spoken of in relation to the present invention, it does not have to be the phase position of the carrier frequency. It is of course possible to modulate a lower frequency signal (e.g. in the MHz range) onto the carrier frequency and to use the phase position of this modulated signal. This reduces the demands on the necessary measurement accuracy, which can be particularly advantageous when using mobile satellites.

When communicating via satellites, the measured radio channel properties will be more difficult to reproduce than with a direct radio link. The following evaluation is therefore preferred:
The measurement results are summarized on both communication sides, and from this, with the help of a KDF function, an identical key is determined on both sides without any further mutual communication, whereby the KDF function is defined as follows:
a) n measured values are interpreted as coordinates of a point in n-dimensional space;
b) the n-dimensional space is subdivided by (n-1) -dimensional areas into fields to which numbers are assigned;
c) the field in which it lies is determined for each point in n-dimensional space;
d) the key is generated based on the numbers of the fields of the points.

In this way, measurement inaccuracies only have an effect if they result in a point being assigned to an incorrect field. For the case n = 2 the following situation arises:
a) 2 measured values are taken as coordinates of a point in the plane;
b) the plane is subdivided by straight lines (possibly also by curved curves) into fields to which numbers are assigned;
c) the field in which it lies is determined for each point in the plane;
d) the key is generated based on the numbers of the fields of the points.

In order to make it more difficult for an attacker to find the key, provision can also be made for the generated key to be linked to an authentication secret of both partners XOR before it becomes the final common key.

Even if this is comparatively seldom the case, it is still possible for a point measured by the two terminals to be assigned to different fields. In this case, a hash value can be generated either from the generated key or from the sequence of determined field numbers in both remote stations, which is transmitted from one remote station to the other, with the key if the hash values of the self-determined and the hash value of the partner match is recognized as a shared key and the key is discarded if the hash values do not match. Since the data cannot be inferred from a hash value, the hash value can be transmitted via an insecure channel without an attacker being able to gain any advantage from spying on the hash value.

In the case of hash values that do not match, according to preferred embodiments of the present invention, the following two procedures are available: one reduces the number of (n-1) -dimensional surfaces (with n = 2 that is the straight line) and the method is repeated with a correspondingly reduced number of fields, or a counterpart searches for points that are in the immediate vicinity of an (n-1) -dimensional surface (with n = 2, a straight line) and moves these points individually and in any combination into the neighboring field, determined then each time the hash value and compares it with the hash value of the remote station. If they match, a common key is found. These two procedures can of course also be combined: one first shifts the "critical" points and only if this does not lead to success, one reduces the number of (n-1) -dimensional surfaces.

The satellite communication signals are preferably "spread" by the terminal using the spread spectrum method prior to transmission. This means that any receiver can only measure the signals if the associated spreading code is known; so the signals themselves are hidden.

In communications engineering, frequency spreading (spread spectrum) describes a process in which a narrow-band signal is converted into a signal with a larger bandwidth than is necessary for the transmission of information. The entire satellite communication of all participants is obscured by the spread spectrum method. The spreading code required for this is determined in the previous steps in the form of a random number and encrypted or distributed between the two communication partners using the Diffie-Hellman method. The spreading code is secret - only the two communication partners know it.

Kurze Beschreibung der ZeichnungenBrief description of the drawings

The present invention is explained in more detail using the following exemplary embodiment. Fig. 1 shows the basic arrangement; Fig. 2 shows the measured values which are taken as points in a plane; 3 shows the same measured values, the subdivision of the plane having been reduced; 4 again shows these measured values, with another possible subdivision of the plane being shown.

Weg(e) zur Ausführung der ErfindungWay (s) for carrying out the invention

The terminal 1 (see Fig. 1) is a transmitting / receiving station for satellite radio, which can measure the required radio channel properties with an accuracy sufficient for the method according to the patent. The IT system 3 is a device that exchanges data with a terminal 1 and processes data, in particular measured values from radio channel properties, of the terminal 1 in such a way that a key with the required randomness and length is determined at the end.

The method according to the invention consists in that two terminals 1, each connected to an IT system 3, exchange data via satellite (s) 2 with the help of telecommunication 5 via satellite radio and measure one or more radio channel properties with sufficient accuracy. The measured radio channel properties are the amplitude of the signal and / or the phase shift of the signal and / or the transit time of the signal. Each of the two IT systems 3 sends their connected terminal 1 data. Part of this data is measurement signals. The measurement signals are short sinusoidal oscillations at different frequencies and can generate so-called Channel State Information (CSI). The telecommunication 5 between the terminals 1 via satellite (s) 2 can take place via the L-band in the frequency range between 1616 MHz and 1626.5 MHz with a mixture of frequency and time multiplexing. The measured signals are sampled in both terminals 1, adapted in time to the signals by a fixed or variable measuring rate. Depending on the amount of measured values, the data determined therefrom are extracted by measuring the step response (CIR). The quantization of the measured values that are determined in both terminals 1 takes place in the IT system 3 by means of n-bit quantization based on a comparison with one or more threshold values, as will be described below with reference to FIGS. 2 to 4.

Hash functions that are used in cryptography are designed in such a way that they deliver a completely different output with a small change in the input. These hash functions cannot be used to derive a key from a physical system. The phase angle measured in satellite cryptography is reciprocal. However, this does not mean that the phase angle is the same on both sides. Each sample can differ, for example participant A measures 63 ° and participant B measures 53 °. The search for a hash value is here to look for similarity in data records and to produce the same hash value even with small changes. Standard error correction systems, however, cannot be used to adjust the data, as they would firstly reveal parts of the key and secondly produce more data than the key, since these are designed to correct some places, but not all.

So we want to derive the same key on two sides with similar but not the same data. In the best case, the communication between both participants should be zero in order to rule out a man-in-the-middle attack. This complicates the adjustment for both communication partners. In order to eliminate these problems, the following procedure is proposed according to the invention:

1) A byte string, which was generated from the individual measured values of a satellite communication, is obtained on both sides. This contains the phase angle of the signal in degrees for each measurement. Basically, however, any type of byte string that is to be compared can be used (e.g. wave pattern of an MP3 file)
Byte ring = byte (0), byte (1) …… byte (n)

Example byte string from communication partner A:
63, 89, 76, 287, 94, 81, 189, 103, 13, 273, 350, 355, 300, 196, 75, 233, 114, 357, 194, 229.
Example byte string from communication partner B:
53, 76, 81, 276, 98, 77, 194, 103, 15, 277, 357, 359, 285, 191, 86, 230, 114, 354, 192, 234

2) Two-dimensional points are formed from these byte strings, where the odd byte forms the x coordinate and the subsequent even byte value the y coordinate:
Communication partner A therefore forms the following points:
(63 | 89), (76 | 287), (94 | 81), (189 | 103), (13 | 273), (350 | 355), (300 | 196), (75 | 233), (114 | 357), (194 | 229).
And communication partner B forms the following points:
(53 | 76), (81 | 276), (98 | 77), (194 | 103), (15 | 277), (357 | 359), (285 | 191), (86 | 230), (114 | 354), (192 | 234).

3) These points are then projected into a plane on the respective receiving device A and B. This is only carried out on the respective side A and B, since A and B do not know the received data of the respective other side.

This is shown graphically in FIG. The points of A are shown as triangles, the points of B as rhombuses. Note that A ONLY knows the triangles and B ONLY the rhombuses.

Now there are two different modes in the implementation.

4) Let us first consider the "Square mode". The level is divided into "buckets" by dividing it into squares of equal size. In Fig. 2, a grid is shown with 60 ° side length of the squares. The resolution depends of course on how big the expected differences between the measured values at A and B are. If the agreement is very good, can also be started with a side length of 2 °.

The squares are numbered consecutively. Then it is "clustered" i.e. the square in which each point is located is determined, resulting in a sequence of numbers. A hash value is generated from this number sequence at A and B, and these hash values are compared. If the number is different for even one square, the handshake is unsuccessful. In this example, the first points of A and B are in different squares. Even if all other points are in the same square, the hash value is different.

Therefore the squares are enlarged, in the example the side length is doubled to 120 ° (see Fig. 3). Now all points are in the same square, the sequence of numbers is identical for A and B, so the hash values are the same. This means that A and B have found a common, identical random number.

If the hash value still does not match after the first enlargement of the squares, the squares would be enlarged even further. You should only enlarge the squares as little as possible, because the number of possible random numbers decreases with the increase in the size of the squares.

5) In the second mode, the space created in this way is intersected with one or more random straight lines. Fig. 4 shows the space with ten points and six straight lines. The intersection lines create 18 different "buckets" in which the points are located. Here you can see that due to the different coordinates, some points are in different positions, but still fall into the same bucket.

6) The bit pattern for key generation is then calculated in such a way that the cross product for each intersection line is formed from each point, and it is calculated whether the point lies above (bit 1) or below (bit 0) an intersection line. Code example in Python using a lambda function (where p represents the point and a / b the starting points of the respective straight line):
Points A / B: P0…. Pn
Straight line A / B: Gab0…. Gabn
isabove = lambda p, a, b: np.cross (pa, ba) <0

As a result, each point is compared with each line and a corresponding bit pattern is generated (e.g. 2 straight lines, point X is above straight line 1 but below 2 -> 10)

This is repeated for every point for every straight line (pseudocode):

For b in points A / B:
For a, b in straight lines A / B:
isabove = lambda p, a, b: np.cross (pa, ba) <0

This now results in a long bit pattern on both sides, which will be the same if the measured values do not deviate too much. How sensitive the algorithm reacts to deviations is determined by 1) the number of intersection lines and 2) the deviation of the physical properties. There is a certain likelihood that a point will fall into another "bucket", and this depends on the parameters listed.

7) After a bit pattern has been calculated on both sides, communication must take place (on an insecure channel 8) in which the two bit patterns are compared. This is done using a hash handshake. The bit pattern is fed into a cryptographic hash function (SHA-2 or SHA-3) as input on both sides and thus produces the output hash. This hash is now compared via a classic channel 8. If the value is the same on both sides, the bit pattern on both sides can be used for the final key calculation (see below). At best, a man-in-the-middel can only see whether or not he has produced the same bit sequence. It gives him no information about the bit pattern of A and B as long as the hash function is secure. If the hash values do not match, new physical data is generated again and the process starts over. Alternatively, the process can also be repeated with fewer straight lines.

In a further step, the entropy of the key can be improved in both IT systems 3 as follows.

1) The entire procedure specified above is carried out several times (n times) and the first provisional key formed is XOR (Exclusive OR) with the mirrored second provisional key formed and XOR (Exclusive OR) with the non-mirrored third provisional key formed and with the The mirrored fourth provisional key XOR (Exclusive OR) etc. is linked and the result of this forms the final key for use in cryptography or steganography. This reduces possible weaknesses in the randomness of the key.

2) A second provisional key is determined via another transmission channel 8 without satellite 2 with the help of an ECDH (Elliptic Curve Diffie-Hellman) or a "Diffie-Hellman with supersingular isogenic curves" and this second provisional key and the provisional key from the previous one Further processing of the data (first provisional key) is linked with an XOR (Exclusive OR) and the result of this forms the final key for use in cryptography or steganography.

The previous n determined keys can always be stored in both IT systems 3, and the provisionally determined key can be compared individually with all these stored keys and only if at least m bit positions differ per comparison, i.e. the Hamming distance of all in the IT system 3 stored key and the provisional key is m or larger, the provisional key can become the final key. The two parameters n and m can be transmitted in both IT systems by telecommunication 5 or via another transmission channel 8 without satellite 2 or can be specified in advance. This reduces further possible weaknesses in the randomness of the key.

The satellites must be able to automatically transmit the received signals directly to one or more other satellites without significantly disturbing the reciprocity, e.g. in that a satellite transmits the signals to certain others at a certain transmission frequency and geostationary ones are also integrated here so that global key distribution is also possible right from the start. I.e. the antennas are set up so that the signals can also be passed on to other satellites.

If satellite-to-satellite communication is not possible or useful, ground stations have to take over this task. A ground station works like a transparent transponder on a satellite, i.e. it "mirrors" the signals from one satellite to one or more other satellites without significantly disrupting the reciprocity.

Claims

Method for the generation and distribution of cryptographic or steganographic keys for use in cryptography or steganography, in which two terminals (1) carry out a telecommunication (5) and measure radio channel properties of this telecommunication (5), each with an IT system (3) each connected to a terminal (1), wherein each of the two IT systems (3) sends its connected end device (1) data that is partially or fully transmitted to the other end device (1) by means of telecommunications (5), with the measured radio channel properties on both IT systems (3) are further processed in such a way that random, identical keys are generated separately in both IT systems (3), characterized in that the telecommunication (5) takes place via at least one satellite (2).
Method according to Claim 1, characterized in that a satellite (2) is movable.
Method according to Claim 1 or 2, characterized in that the satellites (2) transmit the data only at certain times and / or at certain transmission frequencies and the terminals announce these times and frequencies to the satellites in advance without the satellites confirming these data.
Method according to claim 2 and optionally 3, characterized in that the satellite communication is started on both sides in such a way that the signals from the two terminals (1) arrive at the mobile satellite (2) at the same time.
Method according to Claim 4, characterized in that at least one terminal (1) itself also receives the signals sent to the satellite (2) again, determines the time difference between the two signals therefrom and takes the result into account for the next communication.
Method according to one of Claims 1 to 5, characterized in that the radio channel property (s) measured in the two terminals (1) include the amplitude of the signal, the phase angle of the signal, the transit time of the signal and / or the polarization of the signal represents.
Method according to Claim 6, characterized in that the sum of the two phase angles of the transmitted and received signals is measured as the radio channel property.
Method according to Claim 6, characterized in that the radio channel property is the change in the phase shift between the transmitted and the received signal between different measurements.
Method according to one of Claims 1 to 8, characterized in that the measurement results are combined on both communication sides and the key is determined therefrom with the aid of a function KDF, the function KDF being defined as follows:

a) n measured values are interpreted as coordinates of a point in n-dimensional space;

b) the n-dimensional space is subdivided by (n-1) -dimensional areas into fields to which numbers are assigned;

c) the field in which it lies is determined for each point in n-dimensional space;

d) the key is generated based on the numbers of the fields of the points.
Method according to Claim 9, characterized in that the generated key is linked to an authentication secret of both partners XOR before it becomes the final common key.
Method according to claim 9 or 10, characterized in that a hash value is generated either from the generated key or from the sequence of the determined field numbers in both remote stations, which is transmitted from one remote station to the other that if the hash values of the self-determined match and the hash value is recognized by the partner as the key as a shared key and that the key is discarded if the hash values do not match.
Method according to Claim 11, characterized in that in the event of inconsistent hash values, the number of (n-1) -dimensional areas is reduced and the method is repeated with a correspondingly reduced number of fields.
Method according to Claim 11, characterized in that, in the event of non-matching hash values, a remote station searches for points that are in the immediate vicinity of an (n-1) -dimensional area and moves these points individually and in any combination into the adjacent field and then each time the hash value is determined and compared with the hash value of the remote station.
Method according to one of Claims 1 to 13, characterized in that the terminal device "spreads" the signals of the satellite communication with the aid of the spread spectrum method before transmission.