Medical Image Encryption Based on Pixel. Arrangement and Random Permutation for. Transmission Security. Koredianto Usman" 3,4 Hiroshi Juzojil Isao ...
Medical Image Encryption Based on Pixel Arrangement and Random Permutation for Transmission Security Koredianto Usman" 3,4 Hiroshi Juzojil Isao Nakajimal Soegijardjo Soegidjoko2 Mohamad Ramdhani3 Toshihiro Hori4
Seiji Igi4
'Tokai University, School of Medicine, Japan 2Sekolah Teknik Elektro dan Informatika, Institut Teknologi Bandung, Indonesia 3Teknik Elektro, Sekolah Tinggi Teknologi Telkom, Indonesia 4National Institute of Communication and Information Technology, Japan Abstract - This paper describes the result of our investigation on the utilization Pixels Arrangement and Random Permutation to encrypt medical image for transmission security. The objective of this scheme is to obtain a high speed
Transform based encryption such as Fourier transforms and discrete cosine transform offers an attractive option since in can also provide compression capability in addition to encryption [10, 12]. However, transform based encryption such as Fourier transform required a higher computation power and special treatment to deal with non integer values or complex
computation process and high security. Among other algorithms such as transform method and traditional method, pixels arrangement and permutation provide simple and quick processes; it particularly does not need any mathematical manipulation. This feature is especially very useful for medical image where the image can be very big. We tested the algorithm using gray-scale images. The scheme shows a good randomness and quick computation process. We closed the paper by discussing the strength and limitation of this for practical for example in telemedicine.
values Chaotic encryption recently receive more attention for image
watermarking for its security and quick computation, especially those based on chaotic mapping such as Baker Map. J. Fridrich in [4] and [5] introduced the general discretized Baker Map concept to obtain a chaotic characteristic for encryption. Other improvements on Fridrich's works can be found in [3], [8], and [11]. The main constraint of these schemes
Index Terms - Random permutation, Pixel arrangement, Baker
is key selection and image dimension that preferred to be square. Random permutation encryption, for example, was investigated by Mitra, et al [1]. The proposed scheme consists
Map, encryption, chaos mapping, medical image.
I.
INTRODUCTION
of a sequence combination of bit permutation, pixel permutation, and block permutation. The strength of this The current trend of medical image transmission trough algorithm is its simple structure and low computation the wire network and wireless network is more and more requirement. However this scheme required a big key size for increasing. Telemedicine and e-health especially, have a each bits, pixels, and blocks permutation, which might be basic need of data transmission. The growth of traffic introduce flexibility problem in practical application. volume and network infrastructure is especially very rapid In this paper, we use pixels arrangement, which can be in recent years. However, the security problems during considered as a simple chaotic mapping and row and column transmission also increase. There is a basic need to secure permutations as a modification of Mitra's work in [1]. This the data during transmission. Medical data such as image, work can be considered as another variation of chaotic voice and video, as a basis of remote medical diagnose in mapping encryption and permutation encryption. The goals of telemedicine and e-Health is an important application that this combination are to achieve speed encryption time and has to be protected against security threats during maintain high security. The random permutation as described transmission such as unwanted disclosure and modification for example in [9] became a main security factor in this paper. from unauthorized access during transmission. The presentation of this paper is organized as follows: Section EXISTING IMAGE ENCRYPTION ALGORITHMS II discuss concept of pixel arrangement, and random we discuss the scheme of proposed Conventional encryption methods such as DES, 3DES, and permutation. In Section III, 'l ecyto loih o eia IDEA are considered not suitable for bulky data such as of the proposed scheme, andmgsadeprmn Section IV describes . . process. digital image.. because of long computation One. ~~~~~~~~~~~results .'. further research and of timepad ncrytionon te oter hnd, ffer a smple direction extension this scheme. implementation but need key as big as the image itself. I
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1
II. RANDOM PERMUTATION AND PIXEL ARRANGEMENT
correlations of pixels those are not at the boundary of subimages are not changed. To overcome such situation, we can repeat permutation process several times using different partition width of Pi (or Q') for each iteration. Alternatively we can set the iteration interval equal to one. That is N1 N2 ..= NN= 1 for column permutation, and M1 = M2 MM = 1 for row permutation. Again, if we use the latter approach, not every possible random permutation is good to break the correlation [1]. However if we repeat the permutation process several times, the correlation of neighboring pixels will be low in the result for any chosen random permutation. If we combine the row permutation and column permutation in sequence, and we repeat the process several times, we can successfully produce an image that has small correlation between the neighbor pixels. There is still some unexpected result of the combined row and column permutation scheme alone for encryption. In fact, the statistical property of any row or column after permutation is the same to the original row or column before permutation. This statistical phenomenon can be seen as the vertical a horizontal pattern in the result (see Fig.2). This pattern might give hints to the attacker to crack the encrypted image. We propose a simple pixel arrangement before the permutation process to mitigate this problem.
The perception of an image is developed by the strong correlation of the neighborhood pixels in the image. Therefore, in order to break such perception, most of the algorithm decorrelates those neighboring pixels, either by moving the pixels to other positions or/and changing the value of those pixels according to a certain rule. Random permutation breaks the neighboring pixels correlation by moving position of a pixel to other position. A one-to-one pixel permutation is necessary for encryption so that the decryption process is possible. For our medical image encryption purpose, we suggest a simple row or column random permutation to gain high computation speed.
=
COLUMN PERMUTATION AND ROW PERMUTATION. Consider a rectangular digital image X that has M pixels in row and N pixels in column. We divided the column of the image into P intervals, N1, N2, ..., NP. The value of N1 to NP is any positive integer number. The sum of the intervals should again equal to N.
N1 + N2±
...
+ NP =N
(1)
The image X then divided into sub-images according to this intervals to produce M x N,, M x N2, ... M x Np subimages. After these partition process, the sub-images is the randomly permutated to produce the modified image Y. The row permutation is defined in similar way. The row of the images is divided in to Q intervals, M1, M2, ..., MQ. The sum of all M1 is equal toM. l1 ± Al2 ± . . . ± MQ = M.
A
(a)
=
B
Fig.2: Sequence of random row and column permutation in two round iterations. A. Original Image. B. Result Image. The vertical and horizontal
lines in the result image may give hints to attack the system
(2)
PIXELS ARRANGEMENT Pixels arrangement is reordering the pixels' position
We will have M1 x N, M2 x N, ... MQ x N sub-images. Again we can apply a random permutation on those subimages to produce as modified image Z. Fig. 1 illustrates the
processes.
=
according to a certain rule. In fact, row or column permutation as discussed before, can be considered as pixels arrangement as well. To enable the decryption process, the pixels arrangement should be a one-to-one mapping function :: ::::::.X.. : ::: (bijective mapping). A good pixels arrangement for image encryption also will help us to decorrelate the neighbor pixels. Baker Map, Cat Map and Henon Map, for example, are considered to be good cryptographic pixels mapping. P3 P4 PI P2 However, here we will consider the very simple pixels PI P2 P3 P4 arrangement. We expect a very low processing power when Ql ' ' ' ' ' ' ' ' '1 Q4 this scheme is applied in the implementation. Q2 ] -Ql 1lX 10t..s..ANY,E,March [7]. Kwok-Wo Wong, Bernie Sin-Huang, Wing-Shing Law, "A Fast Image Encryption Scheme based on Chaotic Standard Map" [8] Mazleena Salleh , Suhariah Ihrahim , Ismail Fauzi lsnin, "Enhanced Chaotic Image Encryption Algorithm", Proceedings of the 2003 International Symposium on Circuits and Systems, 2003. [9] Shakir M.Hussain, Naim M.Ajlouni, "Key Based Random Permutation (KBRP)", Journal of Computer Science 2 (5): 419421, 2006 [10] Shiguo Lian, Jinsheng Sun, Zhiquan Wang, "A Novel Image Encryption Scheme Based-on JPEG Encoding", Proceedings of the Eighth International Conference on Information Visualisation (IV'04), IEEE Computer Society, 2004. [1].
~~~~Encrypted C
c
~~~~~y
D
Encrypted D
v
-
Fig.5: Medical images encryption examples. Left image is the original file and right image is the encrypted result. Ten round of iteration is applied for each image. A. Microbiology (Source: Public Health Image Library, phil.cdc.gov) B. Radiology (Source: www.radiology.co.uk) C. Left Ventricular Thrombus, Ultrasonography (Source: Phillips, www3.medical.philips.com) D. Electrocardiography (Source: ECG Library,
www.ecglibrary.com)
Table I: Processing time of encryption and decryption of sample images.. Image
l l size Size | |(MxN)
AveraeEncryption Average cond) Time (second)
IB
l00 500 x446
C
400 x 568
0.706
0.600
D
434 x 823
1.333
1.309
IA B
475 x 700
475
700
446
[11]
Average Decryption Time (Second)
1l231 1.231 0l849 0.849
A
1.093
0.562 0.562
[12]
Yaobin Mao, Guanrong Chen, Shiguo Lian, "A Novel Fast Image Encryption Scheme Based on 3D Chaotic Baker Maps",
International Journal on Bifurcation and Chaos, Vol.14, No.10,
p.3613-3624, 2004.
Yi Xin, Ran Tao, and Yue Wang, "Image Encryption Based on a Novel Reality-Preserving Fractional Fourier Transform", Proceedings of the First International Conference on Innovative Computing, Information and Control (ICICIC'06), IEEE, 2006
Short Biography of the first author:
Koredianto Usman was born in Sumatera Selatan Indonesia October 2, 1975. His obtained his bachelor from Electrical Engineering Bandung Institute of Technology, Indonesia, 1999, and master degree from Munich Institute of
IV. DISCUSSION AND CONCLUSION
We propose an encryption scheme for medical images to produce a high computation speed and high security. A
Technology, Germany in 2001. He is now a researcher on Telecommunication aspect of Telemedicine at Nakajima Laboratory, School of Medicine, Tokai
Unvriy
random permutation precede by a simple pixels arrangement will fulfill the high computation speed, and a long permutation key as inherited from the big image size will
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