WO2008017897A1

WO2008017897A1 - Secure telecommunications systems based on chaotic and interference reduction techniques

Info

Publication number: WO2008017897A1
Application number: PCT/GR2006/000038
Authority: WO
Inventors: Petros Stavroulakis
Original assignee: Petros Stavroulakis
Priority date: 2006-08-08
Filing date: 2006-08-08
Publication date: 2008-02-14

Abstract

This invention refers to secure telecommunications systems which are used for the transmission of analogue as well as digital data/signals derived from any- type of voice, images or video information and which are based in the minimization of the possibility of any outside intrusion with the intention to obtain or damage useful information and thus realizing extremely secure systems .

Description

SECURE TELECOMMUNICATION SYSTEMS BASED ON CHAOTIC AND INTERFERENCE REDUCTION TECHNIQUES

This invention refers to a unique design for secure telecommunication systems by which a third party cannot by intrusion get the information that is intended to be secure and in the same time the quality of service to be preserved without increasing the complexity of the system under consideration. The security provided is a result of the usage of chaotic techniques in combination with interference mitigation mechanisms in all stages of the telecommunication process. The present invention is proposed with the intention to create a secure system for both the analogue and digital cases. For digital systems we recognize two distinct cases. On one hand, the encoding takes place by using the digital chaotic signal as the encoding signal and thus the entire information signal is incorporated in the chaotic signal whereas on the other hand the digital chaotic signal can be used to create the keys for encrypting the information signal. For the analogue case, the chaotic signal is used as the modulating signal of the information signal. Even though the methods described above contribute to the secure design of the telecommunication system under consideration, it has been observed that the chaotic intervention in the original system is considered as additional interference of the multiplicative type and the overall result is to reduce the quality of service offered by reducing the ratio of the power of the received information signal to the power of, interference plus noise. The deterioration can be in such a level so that the received signal can be completely unrecognizable or even cause the link to go down. When the information signal is operationally sensitive, a link interruption can cause much more damage than the benefit provided by the increased security offered by the usage of the chaotic signal. Therefore, the use of just chaotic techniques guarantees maximum security but may cause deterioration in the quality of service and thus we need to think of ways to alleviate this problem. This invention is doing just that.

The theory of chaos is considered one of three sciences of the 20^th century along with Relativity Theory and the Quantum Mechanics. As a philosophical concept, it existed since the antiquity and chaos is everything unpredictable but quickly became obvious that chaos can lead to order and thus be used in a beneficial manner even in the design of super secure telecommunications system without quality of service deterioration and without increase of system complexity.

The solution provided by this invention, in view of the above, consists of the usage of interference mitigation techniques along with chaotic signals. Combination of these two techniques has never been proposed before and exist thus no products which implement this invention. The use of the chaotic signals leads to the expansion of the spectrum of the combined signal and thus we have to work in the realm of the wideband systems and must utilize interference reduction techniques appropriate to this type of systems. The proposed solution by this invention guarantees maximum security and satisfactory performance as far as quality is concerned and thus the overall benefits and usefulness of the system are much larger than any other existing system.

During the decade of the 1960-1970,when most of the wireless Telecommunications systems were developed such as the satellite and other microwave systems, the theory of chaos was a subject of study only for Mathematicians. During the decade of the 80s, when the various encrypted systems were developed in parallel with digital communications, the usage of chaotic digital signals in Cryptography was considered not very advantageous because the conversion of the chaotic signals, which are analogue in nature, into the digital format capable of handling wideband digital information signals, robbed the chaotic signals from their chaotic nature in addition of the fact that the substitution of the existing cryptographic techniques by chaotic techniques which worked satisfactorily for so long was not very attractive at least from the economic point of view. For the new concept to be adopted universally, it had to be extremely advantageous in order to justify the retirement of all the investments made in the conventional systems and that did not seem to be the case. The natural analogue format of chaotic signals which preserves all the chaotic characteristics was not used either, for different reasons, because the chaotic systems of this type even though increase the security aspect, create a negative affect to the system overall performance since the system reacts to the chaotic intervention as if the chaotic signal were additional interference. The development of the Mobile Systems created a new situation which requires the revisiting of the realm of security in wireless systems. Special attention is given to the Code Division Multiple Access ( CDMA) technique because this technique is the most appropriate in introducing and having all of users occupying a single spectrum of the system and thus a lot of users simultaneously share the same frequency band. This situation brought the concept of Chaos to the forefront because as we shall see in the following chaotic signals offer a distinct advantage.

Up to now the use of wideband digital CDMA systems with parallel usage of various cryptographic techniques such as those which incorporate the Public Key methodology created the basis of the present day of affairs as far as the secure Telecommunication systems are concerned. The exchange of keys between transmitter and receiver based on a special algorithm characterizes the level of security of the system. An example of such an algorithm is the famous Diffie-Hellman (DH) algorithm named after its inventors. This method provided a solution to the problem of having to distribute and exchange the keys without the necessity of knowing the individual secret keys of each other (sender-receiver). Other inventions based on the key exchanges such as the RSA algorithm were used in the 80s are still in existence. All cryptographic methods have two disadvantages, however, since, on one hand, when they provide maximum security they are not practical especially for multi-user systems because they utilize and occupy a large part of the processing resources of the telecommunications systems and thus are not efficient when they are applied to systems which are based on low speed data such as Mobile systems. On the other hand when they are simplified, they become vulnerable to external threats and attacks. The only practical solution which also has engineering applications and importance and it is a basic element of this invention is to use a simpler cryptographic method and its reduced security to be more than counterbalanced by the expanded security provided by the application of the chaotic techniques to the process of encryption. It is proven that this type of incorporation of chaotic techniques in the encryption along with the usage of interference reduction techniques without the deterioration of the quality of the offered service and without the disproportionate increase of the system complexity is possible and thus we achieve our goal of designing a maximally secure Telecommunication system but in the same time a practical one. This invention proves that such a design is possible.

Brief Description of the Figures of the Invention

Figure 1 refers to the synchronization of two chaotic systems

Figure 2 refers to the indirect synchronization Figure 3 refers to the self-synchronization or auto-synchronization

Figure 4 refers to a secure Telecommunication system based on Chaos.

Figure 5 refers to a secure system based on synchronized chaotic systems

Figure 6 refers to a secure Telecommunication system based on selfsynchronization of a chaotic system. Figure 7 refers to the secure transmission of information of multi-user systems.

Figure 8 refers to the use of adaptive mechanism for the maximization of signal to interference plus noise ratio.

Figure 9 refers to the two components of the secure system covered by the invention i.e the chaotic and interference reduction components. Advantages and Method of Operation of the invention

This invention is based on four important characteristics of Chaos whose importance was never realized in the context of secure Telecommunication system design.

The first property refers to the comparison of chaotic signals with pseudorandom noise and their similarity.

The second property refers to the fact that periodic signals are not periodic. The third property refers to the sensitivity of the chaotic signal to the initial conditions of the chaotic signal generator.

The fourth property refers to the fact that chaotic signal generators can be synchronized with each other or even selfsynchronized.

The fours properties of chaotic signals are of great importance are analyzed below in view of their usage in the present invention. The first and second property put chaotic signals in the category of signals which can be used in cryptography. The aperiodicity can be considered an advantage for the construction of chaotic signal generators in comparison with pseudorandom noise which has been used up to now for multiuser systems such as CDMA systems. The third property which refers to the sensitivity to the initial conditions, even though a disadvantage in general, in the present case is a big advantage because a small change in the initial condition produces a distinct signal which may refer to a new user. The fourth property refers to the synchronization and self-synchronization of two chaotic generators which finds useful applications in both the analogue and digital cases. The mathematical model of chaotic synchronization can be the basis for proving that at least theoretically two chaotic generators can be synchronized and produce exactly the same signals whereas the same thing can be achieved by self-synchronization. Without this property there would not be possible to detect or demodulate signals at the receiver and thus it could not have been possible to receive the information signal reliably and be obtained by the party to whom it was intended even though along the communication path it could be very secure.

The Mathematical model below is a good description of a three dimensional chaotic system which proves a basic element of this invention which refers to synchronization of chaotic generators.

Xi = σ ( xi - X₂ >

X₂ = i~Xi -X2- Xi X3 X₃ = Xi X₂ - b X3 We observe that the implementation of chaotic generators requires three integrators, three adders, two multipliers and three amplifiers with amplification gains equal to the values σ, b , r. It can be proved that choosing the values σ=10, b=8/3 and r=28 and proper initial conditions , a chaotic signal can be produced suitable for the communication process. A different chaotic system with variables yi , yi , V3 with the same parameters σ, b, r and satisfying the same differential equations as above and with different initial conditions can be proved that it can create a different chaotic signal. Hence it is possible from the same generator to produce a new chaotic signal by appropriately changing the initial conditions and thus represent a new user. If we substitute the variable y2 of the second system by the variable x2 of the first system, the second system is thus driven by x2 and can be proved that we can achieve synchronization. In other words as t-→oo and (yl-xl) -→O and y3 = x3. Mathematically this can be proved as follows. Substitution y2 by x2 yields

O = σ ( yi - y₂ )

73 = yi^X2 - bT3

If we substitute in the above system, ei = xi - yi and β₃ = X₃ - y₃ then the system becomes :

It is easy to show that the eigenvalues of the above system are the negative values -σ και -b , then when t-→oo and ei-→O , β₃-→0 hence xr y₁-→0=> yi = xi και y3→ X₃ . Hence these two systems are completely synchronized since we have set y2=x2.

As explained before this is a very important property and finds direct usage in the information signal recovery/detection as shown in figure 1 by which it is shown that since the chaotic systems are synchronized then y3 = x3 and thus at the receiver we have x3+m-x3 = m, the exact replica of the information signal m. We can with different combination of chaotic systems achieve the same result i.e to obtain the information signal as it is shown in figure 2. For synchronization to be effective, it must be as perfect as possible and thus in cases that is not possible we can use self- synchronization as shown in figure 3. There exist many alternatives to synchronization and self-synchronization and these methods are valid for both analogue and digital systems. The transmission of the information signal as shown above is realized by being carried by the chaotic signal depending on the particular case whether the system is analogue or digital along with the various coding , encryption and modulation techniques that can be used. In the following we shall deal with digital information signal to prove the case as depicted in figure 4.

We observe that when the information signal (+1) is transmitted at that instant the chaotic signal from the chaotic generator (Gl) will be transmitted via the bridge A to the transmitter (3) and through the channel (C), whereas when the symbol is (-1), the electronic switch (S) via the bridge (B)will be transferred to the chaotic generator (G2) and thus the value of that generator will be transmitted with negative sign. At the receiver (4) there exist two self-synchronized generators (G3) and (G4). If the symbol which was sent is (+1), the output of the adder (5), which subtracts the output of the self-synchronized generator (G3) from the received signal .will be zero or almost zero, whereas in this case the output of the adder (5a )will be a signal with large power. Comparing these signals at the output of the comparator (6)we obtain as information symbol (SI) the output of the adder (5) and thus it is accepted that (+1) was the original signal sent e.t.c. We could avoid the use of a second chaotic generator and use a self-synchronized generator which amplifies the chaotic signal of the chaotic generator (Gl) when the transmitted symbol is (-1) of the transmitter by, let's say, 2 and when compared at the receiver, it becomes obvious how the separation can be accomplished by comparing the power of the signals. Chaotic signals due to their unique properties can be used for the secure transmission of both analogue and digital information signals via the methods of modulation and coding and in turn be detected at the receiver. For the case when various cryptographic methods such as the DH and RSA which utilize encryption 'keys" are used, the security provided by these methods determine the security level of the system. The implementation of these systems is shown in figures 5 and 6 . In figure 5 , the digital information signal is coded by using keys generated by the chaotic generator (G5) which has been specially modified to become a proper chaotic key generator. The encoding takes place at the coder (7) and in turn the encoded signal is transmitted by the channel (C). At the receiver (S) where the decoding takes place, there exists an equivalent chaotic key generator which is synchronized with the generator (G5) in order to enable the decoder( 8 )to detect the information signal m exactly and with high degree of reliability. In Figure 6, we repeat the same process and instead of the absolute synchronization of generators( G5) and (G6), we use a self-synchronized generator (G7) at the decoder( 8). We observe , therefore, that the above ideal cases utilize chaotic techniques for the design of extremely secure Telecommunications systems. An ideal case for the use of chaotic signals is that of CDMA systems for which security through coding is their special characteristic even though their interference profile is their weakest point. For these multi-user systems, all users share the same sprectrum at the same time and by necessity each user interferes with each other. If we neglect the problem of interference ,the use of chaotic techniques for CDMA can be proved to have a positive effect to the capacity of the overall system as shown in Figure 7. The digital information signal is modulated at the modulator (9) which converts the digital signal to a modulated analogue signal. In turn this analogue signal is further modulated via the chaotic spreader (10) whereas the spreader's signal is the result of the spreading of the signal of the generator (G6) by the spreading signal of the signal generator (G8) and then sent via the channel (C) to the transmitter (3). At the receiver (4), a synchronized chaotic generator (Go), after a similar process of spreading as before, modulates the filtered signal through filter(l 1) which at the demodulator( 12) a reverse process produces the information signal m at the demodulator (9). As far as the increased vulnerability of the chaotic system to interference is concerned, since the original system treats the chaotic intervention as additional interference, the problem can be effectively faced by the use of any interference reduction techniques such as those which utilize adaptive mechanisms. In figure 8, a method which uses adaptive interference reduction techniques is shown. The whole process is represented by an optimal feedback equalizer since the adaptation is terminated only after the information signal estimation at the receiver becomes equal to the value of the information signal sent by the transmitter. This system which uses adaptive methods to reduce the interference plus noise level at the receiver and thus increase the signal to interference plus noise power ratio could be realized if its input signal becomes the input signal of the demodulator (12) of figure 7. In turn the output of the filter (13) enters the demodulator (12) which produces an estimate of the information symbol m which is reconstructed at the filter (14), the output of which is subtracted from the output of the estimating filter (13). This subtraction if it does not give zero difference, it indicates that the estimation process of the signal in relation to the one that was transmitted has not been terminated and it is continued until the difference becomes zero. When that happens the adaptation process terminates because the true signal in comparison is equal to the estimated one. Since the adaptive procedure is working in parallel with the information signal reception, the mitigation of interference and the reduction of the other system imperfections and nonlinearity effects can be achieved on line through these adaptive techniques in parallel with the usage of chaotic signals. The filter construction of (13) and (14 )in figure 8 is obtained by minimizing the error between the information signal sent and the information signal obtained at the receiver. We observe in figure 8 that when is signal z is zero the adaptation process stops because the error is zero. Adaptive techniques which are based on the minimization of that error, indirectly increase the signal to interference plus noise power ratio. The main goal of interference reduction techniques via adaptive methods is to reduce the interfering effects of any signal including the ones that are used to increase security as in this case the chaotic signals. The main characteristics of adaptive methods used to decrease the effect of interference and any other negative effects caused by other systems imperfections are summarized below.

1) Minimization of the difference between the power of the received signal and the power of that one which was sent. 2) Estimation of the information signal and in turn its subtraction from the total sum of all coexistent signals so that its interfering effects is eliminated.

3) Estimation of the interfering signal power and its subtraction from the final signal plus interference sum so that the result contains the least possible interfering signal.

4) In the case systems with unknown parameters, we can use Neural Networks which via the process of learning can estimate the received signals without the use of the filters used in the figure 8.

When the interfering signal doesn't cause additive effects such as the effect of fading, we use the signals from alternate paths in a diversity manner and through proper estimation techniques, we determine he information signals and repeat the process as explained above. Another procedure which is used especially in mobile systems is based on the adaptive estimation of the interference effects for the mean value system i.e. for the system for which the mean value of its parameter are used. These mean values are determined by using the Rayleigh distribution as the underlying probability distribution. Summarizing, we observe that chaotic systems can be used in the design of secure wireless Telecommunications systems in combination with appropriate adaptive interference reduction mechanism and thus we both achieve our purpose of designing a secure system but also eliminate any interference that the chaotic intervention causes. This way we manage the eliminate the disadvantage that chaotic systems have as far as the degree of quality is concerned of the Telecommunications systems which are using chaotic techniques for expanded security. Figure 9, shows the entire concept of this invention. It is shown that secure Telecommunication systems based on chaotic techniques must be accompanied by sophisticated interference reduction mechanisms in order that besides increased security to preserve quality of service

Claims

1. Secure Telecommunication Systems based on the combination of chaotic techniques with sophisticated interference reduction mechanisms for the maximal protection against any intervention whether it is intended to make the communication link ineffective or identify and detect the information signal which can be any digital or analogue data/signals derived from voice, images and video transmitted using chaotic techniques which result into two different subcategories A and B for the digital case with a resulting common denominator which are characterized by that both techniques create a chaotic system for the hiding and the secure transmission of any nature of information signals via an encrypted communication system since chaos, because of its unique properties, can be used in the transmission of signals by incorporation of these information signals in the chaotic signal where in the subcategory A the information signal is coded using as the coding signal the chaotic signal whereas in the case of analogue information signals, the use of chaotic signals is similar to case A above but instead of using the chaotic signal to encode the information signal, we use the analog chaotic signal directly from the chaotic signal generator to modulate the information signal.

All cases and subcategories above bring to the surface the four properties of chaotic signals used for the design of secure Telecommunications systems where he first property refers to the similarity of chaotic signals to periodic pseudorandom noise .The second property refers to the aperiodicity of chaotic signals and these two properties present considerable advantages in the usage of chaotic signals since the first property is used for coding and encryption whereas the second property in the design of chaotic signal generators specially in the cases where it is necessary for a lot of users to occupy the same spectrum simultaneously. The third property refers to the strong dependence of chaotic signals to the initial conditions which originally was considered as a disadvantage from the general mathematical point of view, whereas in the telecommunication context , as is used here, it is a big advantage especially for the multi-user systems where a small change in the initial condition can create a distinct chaotic signal which can characterize a new user and thus be utilized in user identification whereas the fourth property refers to the synchronization of two systems by having one driving the other to synchronization or self- synchronization or auto synchronization in which a chaotic generator can be synchronized to another chaotic generator essential for the detection or demodulation of the transmitted information signal by using the reverse process of coding /encryption or modulation. The chaotic signal generator consists of integrators, adders, multipliers and amplifiers with gains σ, b, r. Also the variables yl,y2,y3 satisfy the same system of equations as the variables xl,x2,x3 and with the same parameters σ,b, r but with different initial conditions and thus a new chaotic signal is generated to be used for another user. The synchronization of the chaotic systems is then used to detect the information signal m at the receiver depending on the situation at hand and since the synchronization and self-synchronization have to be as close to perfection as possible for the recovery of the information signal, there exist a lot of variations and combinations of synchronization and self- synchronization so in any case the transmission of the information signal is very secure by incorporating the information signal with the chaotic signal so that for example, when digital information m consists of the symbols (+1) and (-1) and the (+1) symbol is transmitted, at that instant the chaotic signal from the chaotic generator (Gl) will be transmitted via the bridge (A) to the transmitter (3) and through the channel (C), whereas when the symbol is (-1), the electronic switch (5) via the bridge (B) will be transferred to the chaotic generator (G2) and thus the value of that generator will be transmitted with negative sign and since at the receiver (4) there exist two self-synchronized generators (G3) and (G4) and if the original symbol sent was (+1), the output of the adder (5), which subtracts the output of the self-synchronized generator (G3) from the received signal will be zero or almost zero, whereas in this case the output of the adder (5a )will be a signal with large power and comparing these signals at the comparator (6) we obtain as information symbol (SI) the output of the comparator (6) and thus it is accepted that (+1) was the original symbol sent and thus identify the transmitted signal. We can avoid the use of the second chaotic generator and use an amplifier which amplifies the chaotic signal of the transmitter only when the symbol is (-1) and when compared at the receiver, it becomes obvious how the separation can be accomplished by comparing the power of the signals. In case of encryption, the digital information symbol is coded at the coder(7)using keys which are generated by the chaotic generator (G5), whereas generator (G6) reproduces the same keys so that decoder (8) recovers with great reliability the information signal m which in turn is modulated in the modulator (9) and the process continues and the chaotic signal from the generator (G8) is used to spread this modulated signal further via the spreader (10) which uses as spreading signal that of the generator (G9) which has already been underwent similar spreading as mat of generator (GS) after the received signal goes through the Filter (li) and then through the demodulator (12) via a reverse process reproduces the information signal m with great reliability. Because of the fact that the adaptation process starts when the information signal m enters the filter (13) of the adaptive unit in order to trigger the interference reduction mechanism and the estimated received signal at the output of filter (13) enters at the demodulator (12) wMch recovers the information signal m and after being reconstructed at the output of filter (14) , it is subtracted from the received signal at the output of the filter (13) and the process stops when the difference becomes zero which means that these two signals are equal. This way we achieve minimization of the interference effects because the algorithms used are based on the minimization of the difference between the power of the received signal and the power of the transmitted signal and thus the maximization of the ratio of powers of the signal to interference plus noise be achieved . When the structure and parameters of the adaptive mechanism are unknown, we use Neural Networks which through learning estimate the received information signal without the use of filters (13) and (14) and in the case that the system undergoes fading and operates in the presence of a severe interference environment ,we can develop adaptive mechanisms based on the mean value of its parameters.

2. Secure telecommunications systems based on the combination of chaotic and interference reduction techniques as it is mentioned in claim 1 and are characterized by that in the subcategory B the information signal is already coded and for the encryption process we use the chaotic signals to produce the keys required.