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In this work, we suggest a system for chaos-based encryption of electrocardiographic signals. It uses simple electronics organized around a colpitts chaotic oscillator. The system has been designed, implemented and tested. The encrypted signal has been decrypted and compared to the original ECG signal. Experimental results were analysed and proved encouraging.

The need for ECG signal encryption cannot be overemphasized. In many countries, patient records often need to move from expert to expert on one hand. On the other hand, increasingly, portable ECG recorders allowing patients to make their own recording are used. These recordings are then regularly reported to a medical centre for analysis. Recently, in order to reduce the cost and to improve the service, electronic forms of medical records have been sent over networks from the laboratories to medical centres or to doctor’s offices. A form of remote assistance can thus be developed between countries with deficiency of specialists, including underdeveloped countries, and cardiology experts in the world. In all these cases, the ECG signal has to be encrypted to protect privacy.

Since the proof by Percorra et al. [

From the study by Kolumbàn et al. [

The chaotic synchronization techniques which have been published to date are quite sensitive to both noise and distortion in the channel which makes signal recovery very difficult.

Mindful of the fact that synchronisation is very sensitive to noise, some authors have tried a number of techniques excluding any need for synchronization. The first of this type is chaos shift keying (CSK) [_{i}(t), (i = 1, ···N) from one of N chaos generators with different characteristics is transmitted. The main drawback of the CSK is that the threshold level required by the decision circuit depends on the signal to noise ratio (SNR). A spe- cial case of CSK is the chaotic on-off keying (COOK) [

However, the threshold value can be kept constant and the distance can be doubled by applying the differential CSK (DCSK) [

Several different methods have been proposed in the literature to increase the data rate of DCSK, of which one of the most efficient is the quadratic chaos shift keying (QCSK) [

Among several systems proposed, one of the best performances has been achieved by the differential chaos shift keying (DCSK) scheme and its variation utilizing frequency modulation, and that is FM-DCSK.

Schemes based on the use of the chaos synchronization principle, all suffer from some common weakness [

• It is difficult to determine the synchronization time; therefore, the message during the transient period will be lost.

• Noise throughout the transmission significantly affects the intended synchronization. This means the synchronization noise intensity should be small compared to the signal level, or the desired synchronization will not be achieved.

• Technically, it is difficult to implement two well-matched analog chaotic systems, which are required in syn- chronization, and if this is not required (i.e., with certain robustness) then the opponent can also easily achi- eve the same synchronization for attack.

A close look at the two groups of methods reveals some drawbacks. The main drawback of the first group of methods boils down to inaccuracy in synchronization. For the second group it is the fact that the decrypted signal is rather estimated which increases imprecision during recovery of the hidden signal.

In this work, we propose an encryption and decryption method for ECG signal, using simple electronics and whose principles and elements of novelty are described below. Our method is based on four important concepts that are encryption by adding the chaos to information to be hidden, multiplexing, demultiplexing and subtraction. In the literature, some authors have used methods of transmission to non-coherent receiver. We used this principle of non-coherent receiver. However, by multiplexing the signals, we use the same channel to carry the encrypted message and the reference signal. This differs from other non coherent receiver methods proposed in the literature where the coding of the information is done without putting itself on line as it is the case with coherent receiver systems. Our approach also differs from masking method encountered in coherent receiver system. Indeed, with such a system, encryption is also done by addition of course, but it requires the use of another chaotic oscillator at the reception and once synchronized, it serves as a reference for information retrieval. By carrying the reference signal, we bypass the stress of synchronization often difficult to perform when using another chaotic generator at the reception. The system is therefore free from the setbacks inherent to coherent system. Moreover, unlike in the other non-coherent systems presented in the literature where the recovered signal is only estimated, in our case, the decrypted ECG signal is deducted by the encrypted one. This adds to the accuracy of the proposed scheme. It should also be noted that the multiplexed signal is chaotic, composite and therefore cannot be synthesized by any pirate. This adds to the security.

In the next section, we shall describe the general organization of the system. Section III is devoted to experimental setting and result description followed by discussion of these results. This gives way to conclusion and a list of references.

The general organization of the Encryption-Decryption-System (EDS) is given in

In this work, we used the ECG generator that was developed in our laboratory by Tchimnoue et al. [

This unit is organized around two main sub-units which are the chaotic generator and the encrypting and multiplexing subunit.

The chaotic generator is a Colpitts oscillator. It is made of an LC circuit at the collector of NPN bipolar junction transistor, a voltage divider whose elements are two capacitors (C_{1} and C_{2}) connected to a bipolar junction transistor (BJT) output. In this oscillator, the non linear component of the circuit is the BJT Q2N2222. The circuit we used is represented in

Under certain circumstances that are discussed in [

General organization of the EDS

The ECG Generator Unit [17]

The colpitts oscillator used

Let’s assume that U_{1} is the voltage across C_{1} and U_{2} the voltage across C_{2}. Applying Barkhausen criterium to this oscillator, the resonance frequency f_{0} can be computed

Applying Kirchhoff current and voltage laws to the circuit, we have:

where α and β are the BJT parameters:

Let’s introduce some dimensionless variables for convenient numerical analysis:

The first equation of system (2) becomes:

We consider

Posing

we transform Equation (4) into Equation (6).

Similarly, with these changes in variables, the second equation of the system (2) is transformed into equation (7).

with

The third equation becomes:

Finally, the set of Equations (2) is transformed to set of Equations (9)

where (.) denotes the partial derivative. A change of origin led to the set of Equations (10).

The nature of the solution of set of Equations (10) strongly depends on the control parameter μ.

Using fourth order Runge-Kutta to resolve the system (10), we realized that for

•

•

• from

From Equation (5), we can see that μ is a function of the current and the elements of the Colpitts circuits. Deducing the current _{2}, L, C_{1}, C_{2}).

This subunit is made of an adder whose inputs are the ECG signal and the chaotic signal from the Colpitts oscillator. The output of the adder is sent to one output of a 2-to-1 multiplexer while its second input receives once more the chaotic signal from the Colpitts generator. The encrypting and multiplexing subunit is depicted in

The decryption unit is made of a 1-to-2 demultiplexer whose two inputs are connected to the two inputs of a subtractor. The output of the substractor is sent to a low-pass filter whose output yields the decrypted ECG signal.

The encrypting and multiplexing subunit

The decrypting unit

The colpitts oscillator has been well researched in the literature. Its main role is to generate chaotic oscillations that are added to the signal to be hidden. In our experimental setting, the value of the current _{1}(V_{C1}) and C_{2}(V_{C2}) are displayed on the oscilloscope. The value of C_{1} and C_{2} is 470 nF, inductor L value is 2.2 mH while R_{2} value is 36 Ω. The supply voltages are 7 V for U_{0} and −7.5 V for U_{3}. We realized during our experiments that:

For

For

For

We can see that the waveforms change according to the current’s value until the chaotic state is reached as shown below by waveforms V_{C1} and V_{C2} for a current of 7.6 mA (

A usual test for chaos is calculation of Lyapunov exponents. It is common to refer to the largest one as the Maximal Lyapunov exponent (MLE), because it determines a notion of predictability for a dynamical system. The Lyapunov exponents give the average exponential rates of divergence or convergence of nearby orbits in the phase-space. In systems exhibiting exponential orbital divergence, small differences in initial conditions which we may not be able to resolve get magnified rapidly leading to loss of predictability. Such systems are chaotic. In

The signal yielded across resistor R_{6} of the ECG generator (_{1} of the encryption unit (_{2}. At the output S_{0}, the encrypted ECG signal is collected.

Voltage waveforms from V_{C1} and V_{C2}

Phase diagram

Bifurcation diagram

Dynamics of Lyapunov exponents for the oscillator

ECG original signal: the upper signal is the original ECG

Encrypted ECG signal

After encryption, the signal is sent to one input of a 2 to 1 multiplexer while the other input receives the chaotic signal. The output of the multiplexer is S_{1} and is displayed in

The multiplexed signal is sent on the transmission line and gets to the decrypting subunit whose results are given in the next subsection.

The signal enters this unit by a 1-to-2 demultiplexer (DMX) who receives the encrypted ECG. The two outputs of the DMX are sent to the substractor whose output is sent to a low-pass filter in order to retrieve the hidden ECG signal. The result is shown in

Visually, there is a good level of concordance between the original and the decrypted ECG as can be seen from _{11} and capacitor C_{3} of the filter. When R_{11} = 159 Ω and C_{3} = 10nF, the decrypted signal is visually good, but it still contains noise (_{11} = 1 KΩ and C_{3} = 10

Multiplexed signal

The upper signal is the retrieved (decrypted) ECG signal for R_{11} = 1 KΩ and C_{3} = 10 μF while the lower one is the original ECG

The signal is the retrieved (decrypted) ECG for R_{11} = 159 Ω and C_{3} = 10 nF

uF, the quality of decrypted signal is visually very good as we can observe on

We also computed the signal to noise ratio and found 25.50 dB. This value is an indication of the level of corruption of the signal by noise. The noise is therefore about twenty times smaller than the signal carrying the information. The system therefore yields a good margin. The last metric that was computed to numerically evaluate the resemblance is the frequency distortion which a measure of how far the recovered signal has drifted from the original signal frequency-wise. We found a value of 6 × 10^{−4}. This value shows there is really no frequency drift between the two signals.

The three metrics computed permits us to conclude that both visually and numerically, the concordance (resemblance) between the two signals can be termed as good.

During our experiments, for to the value of C_{1} = C_{2} = 470 nF, we observed that when R1 ≤ 300 Ω or R1 ≥ 2000 Ω there is not chaos in our system. With the appropriate values of C_{1}, C_{2} and R_{1}, we also lost chaos when L ≤ 2.1 mH and L ≥ 5 mH.

We noticed that the range of multiplexer/demultiplexer frequency for which the hidden signal is well decrypted is 53.3 Khz to 850 Khz. For frequencies out of this range, we had only noise at the receiver. Furthermore, it was completely impossible to retrieved the hidden signal when the working frequency of the multiplexer was different from the one used by demultiplexer. This aspect enhances the security of our system. The experiment of transmission in this work was tested on a distance of 45 m.

In this paper, we have designed and tested a very simple chaos-based encryption system for a very delicate and common medical signal. The system was designed on the basis of some shortcomings of earlier techniques. The results in terms of mean quadratic error signal to noise ratio and frequency distortion are satisfactory. In future works, we wish to examine the effect of the transmission conditions on the recovered signal, namely non-linear- ity in the propagation line, type and level of noise and then radiofrequency transmission.