digital medical image cryptosystem based on in nite ... · tor image. the security keys are initial...

46 INTERNATIONNAL JOURNAL OF APPLIED BIOMEDICAL ENGINEERING VOL.5, NO.1 2012

Digital Medical Image Cryptosystem Basedon Infinite-Dimensional Chaotic Delay

Differential Equation For SecureTelemedication Applications

Sarun Maksuanpan 1 and Wimol San-Um 1 ,

ABSTRACT

Digital medical image cryptosystem based oninfinite-dimensional multi-scroll chaotic Delay Differ-ential Equation (DDE) for secure telemedication ap-plications is presented. The proposed cryptographytechnique realizes XOR operations between separatedplanes of binary gray-scale image and a shuffled multi-scroll DDE chaotic attractor image. The securitykeys are initial condition and time constant in DDErepresented by 56-floting-point number. Simulationresults are performed in MATLAB. Nonlinear dy-namics of DDE are described in terms of equilibriumpoints, time-domain waveforms, and 3-scroll attrac-tor in phase-space domain. Encryption and decryp-tion performances of three gray-scale human bodyComputerized Axial Tomography (CAT) scan imageswith 256256 pixels are evaluated through pixel den-sity histograms, 2-dimensional power spectral den-sity, key space analysis, correlation coefficients, andkey sensitivity. Demonstrations of wrong-key de-crypted image are also included. The proposed tech-nique offers a potential alternative to simple-but-highly-secured image storage and transmissions intelemedication applications.

Keywords: Medical image cryptosystem, Delay dif-ferential equation, Chaos-based encryption.

1. INTRODUCTION

Recent advances in communication technologieshave led to great demand for secured image trans-missions through internet networks for a variety ofparticular applications such as in medical, industrialand military imaging systems. The secured imagetransmissions greatly require reliable, fast and robustsecurity systems, and can be achieved through cryp-tography, which is a technique of information privacyprotection under hostile conditions [1]. Of particularinterest in telemedication in which distributed medi-cation resources can be achieved anyplace, real-time

Manuscript received on July 29, 2012 ; revised on October15, 2012.1 The authors are with Intelligent Electronic Systems Re-

search Laboratory Faculty of Engineering, Thai-Nichi Instituteof Technology Pattanakarn, Suanluang, Bangkok, Thailand,10250. Tel: (+662)763-2600 Ext.2926. Fax: (+662) 763-2700,E-mail: [email protected]

telemammography examinations and digital medicalimages will be diagnosed by distributed medical ex-perts[2]. Consequently, medical treatment processesthat deal with patients confidential data are supposedto strictly and only be accessible to authorized per-sons. Most recent telemedication technologies trans-port and storage medical images such as magneticresonance images (MRIs) and computed tomography(CT) through Picture Archiving and CommunicationSystems (PACS) as well as Digital Imaging and Com-munications in Medicine (DICOM) [3], leading to theneed for cryptosystems that protect the confidential-ity in terms of legal and ethical reasons.

Typically, image cryptography may be classifiedinto two categories, i.e. (1) pixel value substitu-tion which focuses on the change in pixel values sothat original pixel information cannot be read, and(2) pixel location scrambling which focuses on thechange in pixel position. Conventional encryption al-gorithms for such cryptography, for example, DataEncryption Standard (DES), International Data En-cryption Algorithm (IDEA), Advanced EncryptionStandard (AES), and RSA algorithm may not ap-plicable in real-time image encryption due to largecomputational time and high computing power, espe-cially for the images with large data capacity and highcorrelation among pixels [4]. Recently, the utilizationof chaotic systems has extensively been suggested asone of a potential alternative cryptography in securedimage transmissions. As compared with those of con-ventional encryption algorithms, chaos-based encryp-tions are sensitive to initial conditions and parame-ters whilst conventional algorithms are sensitive todesignated keys. Furthermore, chaos-based encryp-tions spread the initial region over the entire phasespace, but cryptographic algorithms shuffle and dif-fuse data by rounds of encryption [5]. Therefore, thesecurity of chaos-based encryptions is defined on realnumbers through mathematical models of nonlineardynamics while conventional encryption operationsare defined on finite sets. Such chaos-based encryp-tion aspects consequently offer high flexibility in en-cryption design processes and acceptable privacy dueto vast numbers of chaotic system variants and nu-merous possible encryption keys.

Chaos-based encryption algorithms are performedin two stages, i.e. the confusion stage that permutes

Sarun Maksuanpan and Wimol San-Um 47

the image pixels and the diffusion stage that spreadsout pixels over the entire space. Most existing chaos-based encryptions based on such two-stage operationsemploy both initial conditions and control parame-ters of 1-D, 2-D, and 3-D chaotic maps such as Bakermap [6,7], Arnold cat map [8,9], and Standard map[10, 11] for secret key generations. Furthermore, thecombinations of two or three different maps have beensuggested [12, 13] in order to achieve higher securitylevels. Despite the fact that such maps offer satis-factory security levels, iterations of maps require spe-cific conditions of chaotic behaviors through a narrowregion of parameters and initial conditions. Conse-quently, the use of iteration maps has become typicalfor most of proposed ciphers and complicated tech-niques in pixel confusion and diffusion are ultimatelyrequired.

The DDE has emerged in mathematical models ofnatural systems whose time evolution depends ex-plicitly on a past state, and can be described byan infinite-dimensional system that can exhibit com-plex chaotic behaviors with a relatively simple first-order differential equation. Existing DDEs includethe prominent Mackey-Glass DDE [14] which mod-els the production of white blood cells and the IkedaDDE [15] which models a passive optical resonatorsystem. In recent years, further chaotic DDEs [16-17]based on the Mackey-Glass DDE have been reportedthrough the use of piecewise-linear nonlinearities cor-responding to a complex two-scroll and multi-scrollattractors. In addition, the simplest DDE with a si-nusoidal nonlinearity [18] based on the Ikeda DDEhas also been presented.

This paper introduces a new digital medical imagecryptosystem based on infinite-dimensional multi-scroll chaotic Delay Differential Equation (DDE) forsecure telemedication applications is presented. Theproposed cryptography technique realizes a XOR op-eration between separated planes of binary gray-scaleimage and a shuffled multi-scroll DDE chaotic attrac-tor image. The security keys are initial condition andtime constant in DDE represented by 56-floting-pointnumber. Nonlinear dynamics of DDE will be de-scribed in terms of equilibrium points, time-domainwaveforms, and 3-scroll attractor in phase-space do-main. Encryption and decryption security perfor-mances of three gray-scale human body CAT scan im-ages with 256256 pixels are evaluated through densityhistograms, 2-dimensional power spectral density, keyspace analysis, image correlation coefficients, and keysensitivity.

2. REALIZATIONS OF MULTI-SCROLLCHAOTIC DELAY DIFFERENTIAL EQUA-TION

The first-order multi-scroll chaotic DDE is ex-pressed in a simple first-order differential equationas follows [18];

x = −axτ + bFn (xτ ) (1)

where a and b are unity, and the nonlinear termFn (xτ ) is a piecewise-linear nonlinear function de-scribed as

Fnxτ =n∑

m=1

(sgn(xτ − (2m− 1)) (2)

+(sgn(xτ + (2m− 1)))

where n and m are positive integers. The nonlinearfunction in (2) particularly exhibits a stair-shape pos-itive slope, and offers 2n+1 scroll chaotic attractorswith complex dynamic behaviors depending on thesetting of the delay time τ . In this paper, the caseof three scroll with n=1 is realized. Consequently,the resulting DDE obtained from (1) and (2) can beexpressed as

x = −axτ + sgn(xτ − 1) + sgn(xτ + 1) (3)

The DDE in (3) possesses three equilibrium points at-2,0,2 and the corresponding characteristic equationof its linearized form, i.e. =0, can be obtained by thepartial derivative with respect to x as follows;

−1 + δ(x− 1) + δ(x+ 1) (4)

where δ() is a Dirac delta function. The eigenval-ues evaluated at each fixed point are all equal at -1,which are negative real values, indicating that thethree equilibrium points are all stable nodes whenτ = 0. In the case where τ > 0, the characteristicequation of DDE generally has infinitely many rootswhile the number of characteristic roots of ODEs co-incides with the dimension of the system. Therefore,the DDE in (3) can be approximated by an infinite-dimensional system of ODEs as

x0 = −xN + sgn(xN − 1) + sgn(xN + 1) (5)

xi =N(xi−1 − xi)

τ

where 1 < i < N and the values of N approachesinfinity. The equation xi advances N discrete-timelags of x0 over the interval t − τ to τ . It can beconsidered that the term sgn(xN − 1) + sgn(xN + 1in (5) provides five constants in a set of k, i.e. k ={−2,−1, 0, 1, 2}, at any values of N.

The eigenvalues of (5) for the flow in the vicin-ity of the stable equilibrium for N approaches infinityare given by the solutions of λ = −exp (−λτ), whichcan be expressed in terms of the Lambert function Was λ = −W (−τ) /τ . The resulting eigenvalues arealways in the form of a pair of complex conjugates,indicating that the equilibria are saddle focus pointswhen the DDE exhibit chaotic behaviors. It can beconsidered that the values of the delay time τ sets thechaotic behaviors with a specific topology of attrac-tors based on the nonlinearity. Therefore, the use ofDDE as a resource of complex attractor images canbe employed for image encryption with a high degreeof complexity can be achieved through an infinite di-mension of the DDE systems.


Fig.1:: Proposed encryption and detection al-gorithms using XOR operation between separatedplanes of binary gray-scale image and a shuffled multi-scroll DDE chaotic attractor image.

3. PROPOSED MECHANISMS OF IMAGEENCRYPTION ALGORITHM

The proposed cryptography technique attempts toachieve simple-but-highly-secured image encryptionand decryption algorithms in a category of chaos-based cryptosystems. Fig. 1 shows the proposed en-cryption and detection algorithms. In the encryptionprocess, the original gray-scale image is initially con-verted into binary matrix in which each pixel is rep-resented by 8-bit binary numbers. For example, thepixel p(1,1) contains the binary number a0-a7. Eachpixel will then be separated into eight planes corre-sponding to binary bits a0 to a7. It can be consid-ered that such eight planes are all represented in ma-trix forms with a single binary number in each pixel,which is ready for further Excusive-OR (XOR) oper-ations. Meanwhile, the chaotic DDE attractor imageis generated from Eqn. (2). This image is uniquesince chaos is sensitive to initial conditions, i.e. anextremely small change in the initial conditions or inthe time constant will result in largely chaotic be-haviors. Therefore, the setting of initial conditions,time constants, and simulation time of DDE equationcan be exploited as security keys in both encryptionand decryption processes. It is seen in Fig.1 that thechaotic DDE attractor image in a matrix form is shuf-fled prior to XOR operations. As a particular case,this paper divides the chaotic DDE attractor imageinto sixteen sections before shuffling. It should benoted that the attractor image can also be shuffledwith more divided sections if desired.

The XOR operations diffuse the shuffled DDEchaotic image and the eight binary images in parallel

process. The XOR operation yields bit ”1” if the twoinput bits are different, but yields bits ”0” if the twoinputs are similar. The results from such XOR opera-tions are eight matrices with single binary number ineach pixel. All the eight matrices are combined into asingle 8-bit matrix in which each pixel is representedby [b0-b7]. As a result, the encrypted image can beachieved. The decryption process also follows the en-cryption process in backward algorithms as long asthe security keys are known.

4. SIMULATION RESULTS

Experimental results have been performed in acomputeraid design tool MATLAB. Nonlinear dy-namics of DDE were initially simulated. As forverification of effectiveness of the proposed encryp-tion and decryption algorithms security performanceswere subsequently evaluated. Three examples of dig-ital medical images have been selected from [20-22]which are CT scan images of human brain, spine andheel with the 256× 256 image size.

4.1 Multi-Scroll DDE Dynamical Behaviors

Fig. 2 shows the bifurcation diagram of the timeconstant τ where chaotic regions are indicated bydense area. The highly chaotic region appears fromτ=1.73 and are boundlessly sustained over all rangeof time approaches infinity. In order to guaran-tee chaotic behaviors of the DDE, the values of τmust be any real numbers greater than 1.73. Ini-tial conditions are not crucial and can be selectedfrom any numbers in the basin of attractors ex-cept the equilibrium points. Fig.3 illustrates chaoticattractor images and corresponding time domainwaveforms within 0.2 ms. Four different cases ofτ and x(0) were selected arbitrarily, including (a)=1.821357 and x(0)=0.000001, (b) τ=2.239473 andx(0)=0.000002, (c) τ=2.671521 and x(0)=0.000003,and (d) τ=3.000001 and x(0)=0.000004. It is ap-parent in Fig. 3 that the time domain waveforms arechaotic and the chaotic attractors resemble the three-scroll topology as described in Equ. (2) and (3). Suchfour cases show distinctive chaotic regimes in terms ofdynamical behaviors. In other words, the increase inthe values of τ provides more randomness in time-domain and more complicated attractor images in

Fig.2:: The bifurcation diagram of the time constantτ where chaotic region is indicated by a dense area,initializing from approximately τ > 1.5.


Fig.3:: Chaotic attractor images and time do-main waveforms for four different cases ofand x(0)within 0.2ms, including (a) τ= 1.821357 and x(0)= 0.000001, (b) τ= 2.239473 and x(0) = 0.000002,(c) τ= 2.671521 and x(0) = 0.000003, and (d) τ=3.000001 and x(0) = 0.000004.

phase-space domain. It can also be considered thatsuch chaotic attractor images are unique determinedby two particular parameters, i.e. time constant andinitial condition, which will be used as security keysin this paper.

4.2 Multi-Scroll DDE Dynamical Behaviors

The security keys of the proposed encryption anddecryption algorithms are represented by floating-point numbers, i.e. S×2E where S is a significandand E is an exponent, throughout encryption anddecryption processes. In this work, the secret key aregiven by

τ = 3.0012946528743651987234688167 (6)

x (0) = 0.0000012654982346587193581368 (7)

It can be seen that the secret keys are represented by28 digits of a floating-point number ( 7.2058×1016),resulting in 56 uncertain digits, which is a minimumrequirement of the 56-bit data encryption standard(DES) algorithm [23]. It should be noted that the keyspace can be designated longer while chaos from themulti-scroll DDE is robust, but the longer key spacerequire longer time for simulations. With the secret

keys determined in (6) and (7), the proposed digitalmedical image encryption and decryption algorithmis certainly protected from the brute-force attack.

4.3 Histograms and 2D Power Spectral Anal-ysis

The image histogram is a graph that illustrates thenumber of pixels in an image at different intensityvalues. In particular, the histogram of an 8-bit grayscale image has 256 different intensity levels, graphi-cally displaying 256 numbers with distribution of pix-els amongst these gray scale values. In addition, the2D power spectrum can be obtained through a Dis-crete Fourier Transform (DFT) analysis and the algo-rithm is given by [24] where x and y are a coordinatespair of an image, M and N are the size of image, f(x,y)is the image value at the pixel (x,y). Fig. 4 (a) to (d)shows the histograms and the 2D power spectrumtests of the brain image, the encrypted brain image,decrypted brain image, and the decrypted brain im-age with wrong keys, respectively. Fig. 5 (a) to (d)shows the histograms and the 2D power spectrumtests ofthe spine image, the encrypted spine image,decrypted spine image, andthe decrypted spine imagewith wrong keys, respectively. In addition, Fig. 6 (a)to (d) shows the histograms and the 2D power spec-trum tests of the heel image, the encrypted heel im-age, decrypted heel image, and the decrypted heelimage with wrong keys, respectively.

It can be seen from Figs. 4 to 6 that the intensi-ties of all original images in the histogram are con-tributed with different values in a particular shapeand the power spectrum is not flat having a peak ofintensity in the middle. The encrypted image has aflat histogram and power spectrum, indicating thatthe intensity values are equally contributed over allthe intensity range and the original images are com-pletely diffused and invisible. One can notice thatthe histograms of all original are relatively flat withsome spikes due to the characteristics of medical im-ages that generally contain black colors more thanthe white colors. The decrypted images with rightkeys provide similar characteristics of the original im-ages while the decrypted images with wrong keys arestill diffused and the original images cannot be seen.These results qualitatively guarantee that the imageis secured.

4.4 Correlation and Key Sensitivity Analysis

In order to quantify the encryption performanceand key sensitivity analysis, correlation between im-age pairs, which is a measure of relationships betweentwo pixels intensities of two images, of the three real-ized images have been analyzed. The covariance (Cv)and the correlation coefficient (γxy) can be obtainedas follows [25];


(a)

(b)

(c)

(d)

Fig.4:: Histograms and 2D power spectrum tests;(a) Brain image, (b) Encrypted Brain image, (c) De-crypted Brain image, (d) Decrypted Brain image withwrong keys.

Cv (x, y) =1

N

N∑i=1

(xi − E (x)) (yi − E (y)) (8)

γxy =cov (x, y)√D(x)

√D(y)

(9)

where the functions E(x) and D(x) are expressed as

E(x) =1

N

N∑i=1

xi (10)

E(x) =1

N

N∑i=1

(xi − E(x))2 (11)

and the variables x and y are grey-scale values ofpixels in corresponding pixels in different images ortwo adjacent pixels in the same image. Typically, the

(a)

(b)

(c)

(d)

Fig.5:: Histograms and 2D power spectrum tests;(a) Spine image, (b) Encrypted Spine image, (c) De-crypted Spine image, (d) Decrypted Spine image withwrong keys.

values of γxy are in the region [- 1, 1]. The values ofγxy in the region (-1,0) and (0,1) respectively indicatepositive and negative relationships, while the largernumber close to 1 or -1 have stronger relationships.Two images are identical if γxy are precisely equal to1 and -1. Using a random selection of 2,048 pairs ofpixels, Figs. (7), (8), and (9) show correlation of hor-izontally, vertically, and diagonally adjacent pixels oforiginal and encrypted brain image, original and en-crypted spine image, and original and encrypted heelimage, respectively. It can qualitatively be consid-ered from Figs. (7), (8), and (9) that the adjacentpixels of all encrypted images are highly uncorrelatedas depicted by scatters plots of correlations.

For the quantitative measures, Table 1 summarizescorrelation coefficients of 2,048 pixels of each imagepair. First, the correlations between all original andencrypted images with correct keys are equal to unity,indicating that the images are completely decrypted.The original and encrypted brain, spine, and heel im-ages respectively have the correlation coefficients of-0.0038, -0.0025, and -0.0119, indicating that the im-ages are uncorrelated as the values are closely equal


(a)

(b)

(c)

(d)

Fig.6:: Histograms and 2D power spectrum tests; (a)Heel image, (b) Encrypted Heel image, (c) DecryptedHeel image, (d) Decrypted Heel image with wrongkeys.

(a) Correlation of adjacent pixels of original brain image

(b) Correlation of adjacent pixels of encrypted brain image

Fig.7:: Correlation of horizontally, vertically, anddiagonally adjacent pixels of (a) original brain image,and (b) the encrypted brain image

(a) Correlation of adjacent pixels of original heel image

(b) Correlation of adjacent pixels of encrypted heel image

Fig.8:: Correlation of horizontally, vertically, anddiagonally adjacent pixels of (a) original Heel image,and (b) the encrypted Heel image

(a) Correlation of adjacent pixels of original spine image

(b) Correlation of adjacent pixels of encrypted spine image

Fig.9:: Correlation of horizontally, vertically, anddiagonally adjacent pixels of (a) original Spine image,and (b) the encrypted Spine image

to zero. In other words, the encrypted images aresecured. In order to analyze key sensitivity, two dif-ferent cases of wrong keys were also investigated. Thekey set 1 and set 2 were the changes in the lease sig-nificant number and the most significant number ofthe given key in (6). The results shows that the cor-relation coefficients of all three images are still closelyequal to zero, indicating that the images are protectedeven an extremely small changes of the security keys.

5. CONCLUSIONS

Since great demand for secured image storage andtransmissions through internet networks have beenincreasing, especially for Telemedication applicationin which distributed medication resources can beachieved anyplace. This paper has presented the dig-ital medical image cryptosystem based on infinite-


Table 1:: Summary of correlation coefficients of2,048 pixels of each image pair.

TestImage 1 Image 2 γxyImages

Original Original 1(1) Original Encrypted -0.0038

Brain Original Decrypted with correct keys 1Image Original Decrypted with wrong keys Set 1 0.0121

Original Decrypted with wrong keys Set 2 -0.0046Original Original 1

(2) Original Encrypted -0.0025Spine Original Decrypted with correct keys 1Image Original Decrypted with wrong keys Set 1 0.0049

Original Decrypted with wrong keys Set 2 -0.0070Original Original 1

(3) Original Encrypted -0.0119Heel Original Decrypted with correct keys 1Image Original Decrypted with wrong keys Set 1 0.0055

Original Decrypted with wrong keys Set 2 -0.0026

dimensional multi-scroll chaotic DDE. The proposedcryptography technique realizes a XOR operation be-tween separated planes of binary gray-scale imageand a shuffled multi-scroll DDE chaotic attractor im-age. The security keys have been assigned throughinitial condition and time constant in DDE repre-sented by 56-floating-point number. Nonlinear dy-namics of DDE have been described in terms of equi-librium points, time-domain waveforms, and 3-scrollattractor in phase-space domain. Encryption and de-cryption security performances of three gray-scale hu-man body CAT scan images with 256×256 pixels areevaluated through density histograms, 2-dimensionalpower spectral density, key space analysis, image cor-relation coefficients, and key sensitivity. Demonstra-tions of wrong-key decrypted image are also included.The proposed technique has offered a potential al-ternative to simple-but-highly-secured image storageand transmissions in telemedication applications.

6. ACKNOWLEDGEMENT

The authors are grateful to Thai-Nichi Institute ofTechnology for research fund supports. The authorswould also like to thank Assist. Prof. Dr.AdisornLeelasantitham for his useful suggestions.

References

[1] R. Norcen, M. Podesser, A. Pommer, H.-P.Schmidt, A. Uhl, “Confidential storage and trans-mission of medical image data.,” Computers inBiology and Medicine, Vol. 33, pp. 277-292, 2003.

[2] [2] G. Alvareza, S. Lib, L. Hernandeza, “Anal-ysis of security problems in a medical imageencryption system.,” Computers in Biology andMedicine, Vol. 37, pp. 424–427, 2007.

[3] S. S. Maniccam, N. G. Bourbakis, “Lossless imagecompression and encryption using SCAN.,” Pat-tern Recognition, Vol. 34, pp. 1229–1245, 2001.

[4] M. Philip, “An Enhanced Chaotic Image Encryp-

tion.,” International Journal of Computer Sci-ence, Vol. 1, No. 5, 2011.

[5] G. H. Karimian, B. Rashidi, A. farmani, “A HighSpeed and Low Power Image Encryption with128- bit AES Algorithm.,” , International Journalof Computer and Electrical Engineering, Vol. 4,No. 3, 2012.

[6] X. Tong, M. Cui, “Image encryption scheme basedon 3D baker with dynamical compound chaoticsequence cipher generator.,” Signal Processing,Vol. 89, pp. 480-491, 2009.

[7] J. W. Yoon, H. Kim, “An image encryptionscheme with a pseudorandom permutation basedon chaotic maps.,” Commun Nonlinear Sci Num-ber Simulation, Vol. 15, pp. 3998-4006, 2010.

[8] X. Ma, C. Fu, W. Lei, S. Li, “A NovelChaos-based Image Encryption Scheme with anImproved Permutation Process.,” InternationalJournal of Advancements in Computing Technol-ogy, Vol. 3, No. 5, 2001.

[9] K. Wang, W. Pei, L. Zou, A. Song, Z. He, “On thesecurity of 3D Cat map based symmetric imageencryption scheme.,” Physics Letters A, Vol. 343,pp. 432–439, 2005.

[10] K. Wong, B. S. Kwok, W. Law, “A Fast ImageEncryption Scheme based on Chaotic StandardMap.,” Physics Letters A, Vol. 372, pp. 2645–2652, 2008.

[11] S. Lian, J. Sun, Z. Wang, “A block cipher basedon a suitable use of the chaotic standard map.,”Chaos, Solitons and Fractals, Vol. 26, pp. 117–129, 2005.

[12] K. Gupta, S. Silakari, “New Approach for FastColor Image Encryption Using Chaotic Map.,”Journal of Information Security, Vol. 26, pp. 139–150, 2011.

[13] F. Huang, Y. Feng, “Security analysis of im-age encryption based on two-dimensional chaoticmaps and improved algorithm.,” Front. Electr.Electron. Eng. China, Vol. 4, No. 1, pp. 5–9, 2009.

[14] M. C. Mackey, L. Glass, “Oscillation andchaos in physiological control systems, Science.,”Vol. 197, pp. 287–289, 1977.

[15] K. Ikeda, K. Matsumoto, “High-dimensionalchaotic behavior in systems with time-delayedfeedback.,” J.Phys. Nonlinear Phenom, Vol. 29,pp. 223–235, 1987.

[16] H. Lu, Z. He, “Chaotic behavior in firstrst-order autonomous continuous-time systems withdelay.,” IEEE Trans. Circuits Syst. I Fund. Th.Appl., Vol. 43, pp. 700–702, 1996.

[17] A. Tamasevicius, G. Mykolaitis, S. Bumeliene,“Delayed feedback chaotic oscillator with im-proved spectral characteristics.,” Electron.Lett.,Vol. 42, pp. 736–737, 2006.

[18] JC.Sprott, “A simple chaotic delay differentialequation.,” J. Physics Lett. , Vol. 366, pp. 397–402, 2007.

[19] W. San-Um, B. Srisuchinwong, “A Simple Multi-


Scroll Chaotic Delay Differential Equation.,”Electrical Engineering/Electronics, Computer,Telecommunications and Information Technology(ECTI) Association of Thailand. , pp. 137–140,2011.

[20] Online: www.mrithailand.com/images/services/ortho014.jpg.

[21] Online: www.mrtip.com/exam gifs/brain mritransversal t2 001.jpg

[22] Online:www.cedars-sinai.edu/MedicalProfessionals/ImagingCenter/Neuroradiology / Images/MRI-Spine-9238.jpg

[23] Q. Gong-bin, J. Qing-feng, Q. Shui-sheng, “Anew image encryption scheme based on DES algo-rithm and Chua’s circuit.,” Imaging Systems andTechniques. , pp. 168–172, 2009.

[24] Z. Peng, T. B. Kirk, “Two-dimensional fastFourier transform and power spectrum for wearparticle analysis.,” Tribology International. ,Vol. 30, Issue. 8, pp. 583–590, 1997.

[25] N. K. Pareek, V. Patidar, K. K. Sud, “Image en-cryption using chaotic logistic map.,” Image andVision Computing. , Vol. 24, Issue. 9, pp. 926–934, 2006.

Mr.Sarun Maksuanpan was bornin Samutsakorn Province, Thailand in1991. He is a 4th-year student pur-suing B.Eng. in Computer Engineer-ing from Computer Engineering Depart-ment, Faculty of Engineering, Thai-Nichi Institute of Technology (TNI).Currently, he is also a research assistantat Intelligent Electronic Research Lab-oratory. His research interests includeinformation security systems, cryptosys-tems, artificial neural networks, and dig-

ital image processing.

Wimol San-Um was born in NanProvince, Thailand in 1981. He receivedB.Eng. Degree in Electrical Engineer-ing and M.Sc. Degree in Telecommuni-cations in 2003 and 2006, respectively,from Sirindhorn International Instituteof Technology (SIIT), Thammasat Uni-versity in Thailand. In 2007, he wasa research student at University of Ap-plied Science Ravensburg-Weingarten inGermany. He received Ph.D. in mixed-signal very large-scaled integrated cir-

cuit designs in 2010 from the Department of Electronic andPhotonic System Engineering, Kochi University of Technology(KUT) in Japan. He is currently with Computer EngineeringDepartment, Faculty of Engineering, Thai-Nichi Institute ofTechnology (TNI). He is also the head of Intelligent ElectronicSystems (IES) Research Laboratory. His areas of research in-terests are artificial neural networks, control automations, dig-ital image processing, secure communications, and nonlineardynamics of chaotic circuits and systems.

digital medical image cryptosystem based on in nite ... · tor image. the security keys are initial...

Documents