The 2014 Biomedical Engineering International Conference (BMEiCON-2014)
A Lossless Physical-Layer Encryption Scheme in medical Picture Archiving and Communication Systems using Highly-Robust Chaotic Signals Wimol San-Urn and Natthorn Chuayphan
Intelligent Electronic Systems (IES) Research Laboratory Faculty of Engineering, Thai-Nichi Institute of Technology (TNI) 177111 Patthanakarn 37, Suanlaung, Bangkok, Thailand, 10250. Tel :( +66-2)-763-2600 E-mail:
[email protected] Abstract- this paper reviews some major techniques related to the security issues in Picture Archiving and Communications System (PACS) of medical images. Three conventional techniques including watermarking, digital signature and encryptions are studied.
The
encryption
scheme using
highly-robust
chaotic
signals is also proposed as a new lossless physical-layer that improves security in medical images in PACS. The dynamical system utilizing signum function is employed to generate chaotic signals with smooth bifurcation, i.e. no appearance of periodic windows. Nonlinear dynamics of the chaotic maps were initially investigated Lyapunov
in
terms
exponent
dimensional
of
Cobweb
spectrum,
parameter
map,
bifurcation
spaces.
chaotic
attractor,
diagram,
Encryption
and
2-
qualitative
performances are evaluated through pixel density histograms, 2dimensional power spectral density, key space analysis, key sensitivity, vertical, horizontal, and diagonal correlation plots.
Encryption quantitative performances are evaluated through correlation coefficients, NPCR and UACI. Demonstrations of wrong-key decrypted image are also included.
Keywords-
Encryption
Scheme,
Picture
Archiving
and
Communication Systems, Highly-Robust Chaotic Signals.
I.
INTRODUCTION
Picture Archiving and Communications System (PACS) is typically an integrated image management system for archiving and distributing medical image in an environment, which is generally over hospital internal networks and is protected by a firewall from outside intruders for teleradiology and other telehealth applications [1-3]. Nonetheless, most conventional internet security methods may not sufficient to guarantee that medical image can be compromised during data transmissions due to intruders or even information loss of the system itself Typically, the secured image transmissions greatly require reliable, fast and robust security systems. Security is the protection of an organization or property from attacks, involving three aspects, i.e. security attack, security mechanism and security service. Such security especially in medical images can be achieved through three possible techniques, involving watermarking, digital signature and encryptions [4]. First, a "digital watermarking" is a technique which allows an individual to ass hidden copyright notices or other verification message to digital audio, video or image signals and documents. However, the major problem of digital water 978-1-4799-6801-5/14/$31.00 ©2014 IEEE
marking technique is the non-robustness against different types of image manipulations or attacks. In addition, these techniques are relatively complicated to implement ini real-time operation. Second, a "digital signature", which is based on the concept of public key encryption, provides a public key known to every one and a private or secret key known only to the recipient of the message. Nevertheless, problems of the digital signature involve technological compatibility; the legal issues are the major concerns with respect to finger prints. Last, an "Encryption", i.e. cryptography, which is a technique of information privacy protection under hostile conditions [1]. The plain text is converted into the cipher text and finally encode to the plain text again at the receiver. It is seems to be that the image cryptography the the most powerful tool for medical image in PACS environments as it provides high degree of security comparing to other two previous techniques. Image cryptography may be classified into two categories, i.e. (1) pixel value substitution which focuses on the change in pixel values so that original pixel information cannot be read, and (2) pixel location scrambling which focuses on the change in pixel position. Conventional cryptography such as Data Encryption Standard (DES), International Data Encryption Algorithm (IDEA), Advanced Encryption Standard (AES), and RSA algorithm may not be applicable in real-time image encryption due to large computational time and high computing power, especially for the images with large data capacity and high correlation among pixels [5]. Recently, the utilization of chaotic systems has extensively been suggested as one of a potential alternative cryptography in secured image transmissions. As compared to those of conventional encryption algorithms, chaos-based encryptions are sensitive to initial conditions and parameters whilst conventional algorithms are sensitive to designated keys. Furthermore, chaos-based encryptions spread the initial region over the entire phase space, but cryptographic algorithms shuffle and diffuse data by rounds of encryption [6]. Therefore, the security of chaos-based encryptions is defined on real numbers through mathematical models of nonlinear dynamics while conventional encryption operations are defined on finite sets. Such chaos-based encryption aspects consequently offer high flexibility in encryption design processes and acceptable privacy due to vast numbers of
TABLE I.
= 6 �
'E O.B
Test Methods
Mono-bit Frequency Block Runs Longest Run of Ones Block Binary Matrix Rank Discrete Fourier Transform Non-overlapping Template Matching Overlapping Template Matching Universal Statistical Linear Complexity Serial Approximate Entropy Cumulative Sums Random Excursions Random Excursions Variant
'" �
=
� 0.6
-
... = '"
� 0.4
.,Q
8
=
Z 0.2 0 0
0.5
,-..
�
d ....
= � = =
�
TABLE I SUMMARY OF NIST TEST RESULTS OF 1,000,000
BITS GENERATED FROM THE PROPOSED CHAOTIC MAPS.
o -1
I>
° which falls in the region [0,1]. Consequently, the bifurcation parameter a is limited to the region [0, 2]. Fig. l shows the plots of the bifurcation diagram and the LE spectrum of parameters a over the parameter space [0, 2]. Apparently, parameter a has an influence on chaotic dynamics in both bifurcation and LE values, but not larger than 2. Fig.2 shows the resulting chaotic waveform in time-domain over 500 iterations. It can be seen that both amplitude and frequency of the waveform are random. For standard randomness test, the National Institute of Standards and Technology (NIST) has provided a statistical tests suite in order to evaluate the randomness of binary sequences. This paper generates chaotic signals for 1,000,000 iterations and simply proceed a digitization at 0.5, i.e. bit "1" for any values that greater than 0.5 and bit "0" for any values that smaller than 0.5. Subsequently, the NIST test suite from a special publication 800-22revla was realized using a typical 1,000,000 random bits. The test suite attempts to extract the presence of a pattern that indicates non-randomness of the sequences through probability methods described in terms of p value. For each test methods, the p-value indicates the strength of evidence against perfect randomness hypothesis, i.e. a p value greater than a typical confidence level of 0.01 implies that the sequence is considered to be random with a confidence level of 99%. Table 1 summaries NIST test results, indicating that the generated sequences from both cases of chaotic maps pass all standard 15 tests. As a result of the NIST tests, the randomness of proposed chaotic maps is sufficient for use in encryption process.
RED Component Image
GREEN Component Image
BLUE Component Image
Rl Binary Image
G1 Binary Image
Bl Binary Image
Diffused RED Component Image
Encrypted Image (Size: mxn)
Fig. 4. Proposed bit-plane separation digital image encryption scheme for using absolute-value chaotic map.
III.
PROPOSED BIT-PLANE SEPARATION IMAGE ENCRYPTION
SC HEME Fig.5 depicts the proposed bit-plane separation digital image encryption scheme for using absolute-value chaotic map. Four major procedures are performed for the overall encryption scheme. First, the original image is prepared for diffusion. The original color image with mXn image size is initially converted into three sets of sub-images with Red, Green, and Blue components containing pixels in scale levels. Each sub-image will subsequently be converted into binary matrix in which each pixel is represented by 8-bit binary numbers. Each pixel will then be separated into eight planes corresponding to binary bits. As a result, there are 24 sets of bit plane images represented in matrix forms with a single binary number in each pixel, which is ready for further Excusive-OR (XOR) operations. Second, the input security keys from users which is represented in a floating real number with the condition that the parameter a ([1,2] while the parameter b can be any number, but should not too large. The initial condition is also considered as a key, but it is not crucial as long as initial conditions are in attractor basin. These keys are used to generate the chaotic sequence for random bit generation. The random bits are consequently reshaped into 24 sets of mXn binary image.
decrypted image, and decrypted image with wrong keys. The original image is Lena image with 256x256 image size. The intensities of all original images in the histogram are contributed with different values in a particular shape and the power spectrum is not flat having a peak of intensity in the middle. The encrypted image has a flat histogram and power spectrum, indicating that the intensity values are equally contributed over all the intensity range and the original images are completely diffused and invisible. The decrypted images with right keys provide similar characteristics of the original images while the decrypted images with wrong keys are still diffused and the original images cannot be seen. These results qualitatively guarantee that the image is secured. B.
Correlation Coefficient Analysis
In order to quantify the encryption performance and key sensitivity analysis, correlation between image pairs, which is a measure of relationships between two pixels intensities of two images, of the three realized images have been analyzed. The covariance Cv and the correlation coefficient Yxy can be obtained as follows [17];
Last, the XOR operations diffuse the generated chaotic bit and the 24 binary images in parallel process. The XOR operation yields bit "1" if the two input bits are different, but yields bits "0" if the two inputs are similar. The results obtained from such XOR operations are 24 matrices with single binary number in each pixel. All the 24 matrices are combined into three RGB matrices of a single 8-bit matrix. As a result, the encrypted image can be achieved. The decryption process also follows the encryption process in a backward algorithms as long as the security keys are known. IV.
EXPERlMENTALRESULTS
Simulation results have been performed in MATLAB. The secret key in the form Sx2E where S is a significant and E is an exponent. The keys is represented by 56-bit data (�7.2057x1016) which is satisfied the minimum requirement of the encryption standard (DES) algorithm [15].
Fig. 5. Histograms and 2D power spectrums of original image, encrypted image, decrypted image,and decrypted image with wrong keys.
A. Image Histogram and Power Spectral Density The image histogram illustrates the number of pixels in an image at different intensity values. Each Red (R), Green (G), and Blue (B) sub-image has 256 different grey intensity levels, graphically displaying 256 numbers with distribution of pixels amongst these grayscale values. Moreover, the 2-D power spectrum that shows the power of image intensity can be obtained through a Discrete Fourier Transform (DFT) analysis and the algorithm is given by [16] M-J N-J
F(u,v) L L!(x,y)exp(-j(2;r/ M)ux)exp(-j(2;r/ N)vy) =
x=o
(7)
y=o
where x and y are a coordinates pair of an image, m and n are the size of image, fix, y) is the image value at the pixel (x, y). Fig.6 shows the histograms of three R, G, B components and 2D power spectrums of original image, encrypted image,
Fig. 6. Image correlation tests in original and encrypted images, including horizontally,vertically, and diagonally adjacent pixels.
CvCx,y)
=
1 "N �i =J (Xi - E(X))(Yi - E( y ))
N
(8)
cov(x, y)
r
=
----;=���
;g;
�D(x)�D(y)
(9)
where the functions E(x) and D(x) are expressed as E(x)
=
� "N X and N L,,'�l
I
D(x)
1
"N
(x,. - E(x)) N L,,'�l
= -
2
(10)
and the variables x and y are grey-scale values of pixels in corresponding pixels in different images or two adjacent pixels in the same image. Typically, the value ofyxy is in the region [ I, 1]. In other words, the values ofyxy in the region (-1,0) and (0,1) respectively indicate positive and negative relationships, while the larger number close to 1 or -1 have stronger relationships. Fig.7 shows image correlation tests in original and encrypted images, including horizontally, vertically, and diagonally adjacent pixels. The adjacent pixels of all encrypted images are highly uncorrelated as depicted by scatters plots of correlations. For the quantitative measures, the correlations between pairs of original images and corresponding encrypted images through the computation of correlation coefficient TABLE IL
Correlations Of Colors CRR CRG CRE CGR CGG CGB CBR CBG CBB
COMPARISONS OF CORRELATION COEFFICIENTS OF LENA IMAGE AT DIFFERENT SIZES.
evaluated through pixel density histograms, 2-dimensional power spectral density, key space analysis, key sensitivity, and correlation plots. Quantitative performances are evaluated using correlation coefficients, NPCR and UACI. Both correct and wrong key decryptions are also demonstrated. The proposed cryptosystem offers a potential alternative to private data protection systems. ACKNO WLEDGEMENTS
The authors are grateful to Thai-Nichi Institute of Technology for research grant supports. The authors would also like to thank Mr.Patinya Ketthong for his useful suggestions. REFERENCES [1] [2]
[3]
[4]
[5]
Lena Image Sizes 256x256
512x512
1024xl024
0.00312 0.00298 -0.00406 0.00195 -0.00061 0.00267 -0.00052 0.00061 -0.00419
-0.00306 -0.00325 -0.00099 -0.00421 -0.00211 -0.00153 -0.00367 -0.00060 -0.00108
0.00181 -0.00081 0.00033 0.00113 -0.00056 -0.00053 0.00077 0.00008 -0.00063
between ROB components of the original images and corresponding encrypted images have been analyzed. Table 2 summarizes correlation coefficients each image pair. It can be seen in Table 2 that the correlation coefficients are very small closing to zero, indicating that each pair of images are completely independent of each other.
[6]
[7]
[8]
[9]
[10] [II]
[12]
[13]
V.
CONCLUSION
The digital image encryption based on nonlinear dynamics of an absolute-value chaotic map has been presented. The proposed absolute-value chaotic map provides a robust chaos property that has smooth bifurcation without periodic window in order to increase high-entropy randomness for encryption scheme. Digital image diffusion is performed by bit-plane separations prior to XOR operations. Security keys are realized through the floating number of initial conditions and two control parameters. Experiments have been performed in MATLAB using standard colour images. Nonlinear dynamics of the absolute-value chaotic maps are investigated in terms of Lyapunov exponent spectrum, bifurcation diagram, and 2dimensional parameter spaces. Qualitative performances are
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