你的心跳可能成為您的密碼 Your heartbeat could be your password

1. Ching-Kun Chen 你的心跳可能成為您的密碼 Your heartbeat could be your password Department of Electrical Engineering National Chung Hsing University Taichung, Taiwan, R.O.C. April 30, 2013

2. Outline • Introduction • Chaos and Quantifying Chaotic Behavior • Phase space reconstruction • Lyapunov Exponent • Chaotic Functions • ECG-Based Biometric Recognition • Synchronization of Two Identical Lorenz Systems • System Design and Secure Information Transmission • Experimental Results and Discussion • Conclusions and Feature Work

3. Introduction • Motivation • As multimedia and network technologies continue to develop, digital • information is increasingly applied in real-world applications. • However, digitized information is easy to copy, making information • security increasingly crucial in the communication process. • Cryptography is one of basic methodologies for information security. Since • 1990s, many researchers have noticed that there exists a close relationship • between chaos and cryptography. Recently, chaos theory gradually plays • an active role in cryptography consistently.

4. Introduction • Motivation • Biometric based authentication system provides better security solutions • than conventional. But some biological parameters that are used as biometric • don’t provide the robustness against falsified credentials such as voice can • be copied through microphone, fingerprint can be collected on silicon • surface and iris can be copied on contact lenses. ECG doesn’t have these • problems and it’s unique in every individual. • Human heart is a supremely complex biological system. There are no model • that account for all of cardiac electrical activity. Researchers in the field of • chaotic dynamical system theory have used several features, including • correlation dimension (D2), Lyapunov exponents ( ), approximate entropy, • etc. These key features have can explain ECG’s behavior for diagnostic • purposes.

5. Literature Survey • Chaos-related research Chaos Transmission ECG Encryption

6. Literature Survey - Chaotic Encryption • Pareek et al. proposed an image encryption scheme which utilizes two • chaotic logistic maps and an external key of 80 bits. (2006) • Kwok et al. proposed a fast chaos-based image cryptosystem with the • architecture of a stream cipher. (2007) • Behina et al. proposed a novel algorithm for image encryption based on • mixture of chaotic maps, using one dimensional chaotic map and their • coupling to obtain high level security. (2008) • Zhu et al. proposed a chaos-based symmetric image encryption scheme • using a bit-level permutation. (2012)

7. Literature Survey - Chaotic ECG Signal • Babloyantz et al. showed the human heart is not a simple oscillator, the • heart behavior exhibits a chaotic behavior. (1988) • Casaleggio et al.applied lyapunov exponents to analysis and estimation • of ECG signals from MIT-BIH database. (1995, 1997) • Owis et al.present a study of features based on the nonlinear dynamical • ECG signals for arrhythmia detection and classification. (2002) • Al-Fahoum et al. used simple reconstructed phase space approach for • ECG arrhythmia classification. (2006)

8. Literature Survey - ChaoticTransmission • The application of chaotic synchronization to secret communication was • suggested by Pecora and Carroll. (1990, 1991) • A successful experimental realization of signal masking and recovery • was first made using electric circuits by Cuomo. (1993) • Control of chaos techniques have also been used for the transmission of • messages by means of chaotic signals. There are several control • techniques used to synchronize chaotic systems, such as fuzzy control, • delayed neural networks, impulsive control, and linear error feedback • control. The chaotic signals can be used to mask information waveforms or serve as modulating waveforms.

9. Chaos and Quantifying Chaotic Behavior

10. Description of Methods • Phase space reconstruction Packard et al. (1980)proposed phase space reconstruction that is a standard procedure while analyzing chaotic systems which shows the trajectory of the system in time. Phase space in d dimensions display a number of points of the system, where each point is given by where n is the moment in time of a system variable, with denoting the sampling period and T being the period between two consecutive measurement for constructing the phase plot. The trajectory in d dimensional space is a set of k consecutive points and where is the starting time of observation.

11. Phase space reconstruction Description of Methods Fig. 2 Attractors of an ECG form encryption person Fig. 1 ECG Signals

12. Description of Methods • Correlation dimension - by Grassber & Procaccia (1983) Reconstructed time series Calculating correlation integral

13. Description of Methods Lyapunov exponents are defined as the long time average exponential rates of divergence of nearby states. If a system has at least one positive Lyapunov exponent, than the system is chaotic. The larger the positive exponent, the more chaotic the system becomes. In general Lyapunov exponents are arranged such that , where and correspond to the most rapidly expanding and contracting principal axes, respectively. Therefore, may be regarded as an estimator of the dominant chaotic behavior of a system. • Lyapunov Exponent

14. Lyapunov Exponent Description of Methods The largest Lyapunov exponent is treated as a measure of the ECG signal using the wolf algorithm. The process of determination is listed as follows: 1. Compute the separation doof nearby two points in the reconstructed phase space orbit. 2. Come next both points as they move a short distance along the orbit. Calculate the new separation d1. 3. If becomes dotoo large, keep one of the points and choose an appropriate replacement for other point. 4. Repeat Steps 1-3 after propagations, the largest Lyapunov exponent should be calculated via . where

15. Chaotic Logisitic Map Chaotic Functions The logistic map is a polynomial mapping of second order which chaotic behavior for different parameters proposed by the biologist Robert May. where n=0,1,2,…, A is a (positive) bifurcation parameter. . Fig 5. Bifurcation diagram for the logistic map Fig 6. Lyapunov exponents of the logistic map

16. Property of logistic map with different bifurcation parameter with L0=0.1 (a) A=2.7 (c) A=3.8 (b) A=3.1

17. Chaotic Henon Map Chaotic Functions The Henon map is a 2-D iterated map with chaotic solutions proposed by Mchel Henon (1976). where a and b are (positive) bifurcation parameters . Fig 3. Attractors for the Henon map with a=1.4;b=0.3 Fig 4. Bifurcation diagram for the Henon map, b=0.3

18. Chaotic Functions • The Lorenz system – by Edward Lorenz(1963) system parameters： a=10; b=28; c=8/3 Initial values： x0=-7.69; y0=-15.61; z0=90.39

19. Characteristics of Chaotic Systems • They are aperiodic. • They exhibit sensitive dependence on initial conditions • and unpredictable in the long term. • They are governed by one or more control parameters, • a small change in which can cause the chaos to • appear or disappear. • Their governing equations are nonlinear.

20. ECG-Based Biometric Recognition

21. Normal 12-Lead ECG Augmented-leads Standard-leads Chest-leads

22. ECG Waveform from electrical activities of heart • P wave • Atrium • Depolarization • QRS wave • Ventricular • Depolarization • T wave • Repolarization

23. A novel handheld device ET-600

24. ECG-Based Biometric Recognition Comparison of related works with the proposed method Method Fiducial Detection No. of Tested Subjects Recognition Rate* Data Source Electrode Orientation Biel et al.[20] PCA Yes 20 MIT-BIH Standard Leads (I,II,III) Shen et al.[33] Templ. Matching+DBNN Yes 20 MIT-BIH standard Lead I Israel et al.[22] LDA Yes 29 Collected from lab. Standard 12-leads Agrafioti et al[26]. LDA+PCA No 56 MIT-BIH/PTB Standard Lead II Wang et al.[25] AC/DCT+KNN No 13 MIT-BIH/PTB Standard 12-leads Chan et al.[24] Wavelet Distance No 50 Collected from lab. standard Lead I Khalil et al.[35] High-order Legendre Polynomials No 10 Collected from lab. standard Lead I Fatemian et al.[38] Wavelet+LDA No 14 MIT-BIH/PTB Standard 12-leads Chiu et al.[21] Wavelet Distance No 35 MIT-BIH standard Lead I Loong et al.[36] LPC+WPD No 15 Collected from lab. standard Lead I Coutinho et al.[39] Cross Parsing+MDL No 19 Collected from lab. standard Lead I Silva et al.[37] FSE Yes 26 Collected from lab. Standard Lead I Our research [28-30] Chaos Theory+ BPNN No 19 Collected from lab. Lead I (two contact points) [*]value claimed in the paper

25. Classification of ECG-Based Biometric Techniques • Direct Time-Domain Feature Extraction • Intervals (PQ, PR, QT intervals ) • Durations (P, QRS, T durations) • Amplitudes (P, QRS, T amplitudes) • Slope (ST slope) • Segment (ST segment) • Frequency-Domain Feature Extraction • Wavelet Decomposition • Fourier Transform • Discrete Cosine Transform • Chaos Feature Extraction • Lyapunov Exponents • Correlation Dimension

26. Age, height and weight of 19 subjects joining the experiment

27. Distribution of the 19 subjects’ characteristics and their Centroids

28. Distribution of the 19 subjects’ characteristics and their Centroids

29. Distribution of the 19 subjects’ characteristics and their Centroids

30. Distribution of the 19 subjects’ characteristics and their Centroids

31. Synchronization of two identical Lorenz systems

32. Linear Coupled Feedback Synchronization Control where di＞0(i=1,2,3) are coupling coefficients； ei(t)are error states,ei(t) →0(t→∞, i = x, y, z)

33. Chaotic phase trajectories for two Lorenz system

34. Simulations of Synchronization Control of Lorenz System with ECG Signal

35. Hardware Implementation of the Lorenz-based Oscillator Component list of Lorenz-Based chaotic masking communication circuits

36. Lorenz-Based chaotic masking communication circuit

37. Hardware Implementation of the Lorenz-based Oscillator (a)x-y plane (b)x-z plane (c)y-z plane Phase portraits of Lorenz oscillator

38. Synchronization of Lorenz-Based Circuits (a) numerical plot (b) experimentally obtained The synchronization of the driver signal x1 and response signal x2

39. Synchronization of Lorenz-Based Circuits with ECG Signal (a) numerical plot (b) experimentally obtained Channel 1: private key ECG_signal, Channel 2: transmitted chaotic signal ECG_masking, Channel 3: recovered private key ECG_signal in the response system

40. The testing scene of self-developed ECG acquisition system with Lorenz-based circuits

41. System Design and Secure Information Transmission

42. Concept of Cryptography • Classical cryptography - Caesar displacement • Plaintext：THE QUICK BROWN FOX JUMPS OVER THE LAZY DOG • Ciphertext：WKH TXLFN EURZQ IRA MXPSV RYHU WKH ODCB GRJ

43. Concept of Cryptography • Modern cryptography • When K1=K2, the system is called symmetric encryption system. • When K1K2, the system is called asymmetric encryption system, where K1 is called public key and K2 is called secret key.

44. Information encryption and decryption schemes

45. Structure of the secure information transmission

46. Experimental Results and Discussion

47. Experimental Parameters TABLE III Parameters of chaotic function for Encryption and Decryption TABLE I Computed of ECG Signals for Different Persons TABLE IV Parameters of chaotic functionfor Decryption TABLE II Different Kinds of Images

48. Simulation Results -8 bits grayscale Fig 5. Encryption and Decryption for case 1 (a) original image. (b) histograms of original image. (c) encrypted image. (d) histograms of encrypted image. (e) wrong decrypted image. (f) correct decrypted image.

49. Simulation Results - 8 bits indexed Fig 6. Encryption and Decryption for case 2 (a) original image. (b) histograms of original image. (c) encrypted image. (d) histograms of encrypted image. (e) wrong decrypted image. (f) correct decrypted image.

50. Simulation Results - 24 bits GRB Fig 7. Encryption and Decryption for case 3 (a) original image. (b)(c)(d) The histograms of red, green and blue channels of original image respectively. (e) The encrypted image. (f)(g)(h) The histograms of red, green and blue channels of encrypted image respectively. (i) wrong decrypted image. (j) correct decrypted image.