A new image security system based on cellular automata and chaotic systems

Transcription

1 A new image securiy sysem based on cellular auomaa and chaoic sysems Weinan Wang Jan 2013 Absrac A novel image encrypion scheme based on Cellular Auomaa and chaoic sysem is proposed in his paper. The suggesed scheme firs uilizes he chaoic sequences generaed by Sandard map o scramble he pixel marix of plain image. Then according o crypographic characerisics such as parallel compuaion and pseudorandom aribue, he pixel values of he scrambled image are ransformed. Furhermore, encrypion of differen pixels depends on each oher in order o diffuse he informaion of plain image. Simulaion experimen and securiy analysis imply ha he proposed scheme has a large key space and is sensiive o secre keys and he cipher image has excellen diffusion properies. Hence, he proposed scheme is of high securiy and can resis exhausive aack, sensiive aack and chosen-plainex aack, ec. 1 Inroducion Nowadays wih he rapid developmen of digial communicaion and compuer science, he securiy of images, videos and oher digial producs has aracs more aenion. And image encrypion is differen from ex encrypion due o he properies of high correlaion, daa redundancy, ec. Hence, radiional ciphers such as Daa Encrypion Sandard (DES) and Advanced Encrypion Sandard (AES) canno be effecive candidaes of qualified encrypion mehods [1]. Researchers herefore proposed a variey of cryposysems by combining oher models such as chaos-based algorihms [2-5], cellular-auomaa-based algorihms [6-9] and oher model-based algorihms [10-13]. Chaoic sysems possess he propery of high sensiiviy o iniial values and sysem parameers, pseudoranomiciy and ergodiciy and are widely employed in he fields of image encrypion research [14-15]. Cellular Auomaa are a class of emporally and spaially discree dynamical sysems. Due o he advanages of informaion processing parallelism, ease of realizing and local ineracions [16], hey have been widely used o consruc cryposysem and have been a ho issue in crypography. Wang e. al [2011] proposed a novel encrypion echnique based on rapid dispersion of errors which could generaes sream cipher wih excellen pseudorandom propery. Zhang e. al [2010] presened an encrypion scheme based on improved Cellular Auomaa, which possesses faser encrypion speed and decrypion speed. The main characerisics can be described as follows: 1. The sream cipher can be obained hrough synchronizaion of he cipher-ex; 2. The efficiency of he encrypion algorihm is improved by using Cellular Auomaa. However, some of he proposed encrypion algorihms based on Cellular Auomaa sill have weakness and shorcoming including: 1. In he common encrypion algorihm, rules of sae ransiion and ieraion sep is chosen as secre keys and hence he key space no large enough o resis he exhausive aack; 2. Cipher ex dose no have 1

2 high relaionship wih he plain ex and dispersion of keys errors is slow, hrough which crypanalys can obain he informaion of he plainex by he similariy of he cipher ex; 3. Mos of he CA-based image encrypion algorihms change he pixel values only, which lack enough diffusion and confusion propery. Therefore, i is very necessary o invesigae some pracical secure algorihms o overcome he embarrassing siuaions menioned above. In his paper we propose a novel image encrypion algorihm by combining Cellular Auomaa and chaoic map. The encrypion archiecure is originaed from he permuaion-diffusion process [19]. The sae ransiion rules of Cellular Auomaa are exraced from he chaoic sequences of sandard map. The confusion sage depends on boh he secre keys and he plain image. Numerical simulaions and heoreical analysis verify he superioriy and effeciveness of he suggesed encrypion scheme. The res of he paper is organized as follows. In Secion 2, sandard map and Cellular Auomaa model is described briefly. Secion 3 performs he permuaion sage and diffusion sage o lower he relaionship beween he plain image and cipher image. In Secion 4, algorihm performance and simulaion resuls are repored and analyzed. Finally, Secion 5 ends he paper wih brief conclusions. 2 Preliminaries The sandard map is a kind of chaoic model which possesses diverse dynamical properies and has been analyzed deeply in he field of physics and biochemisry deeply. I can be defined as follows: x i+1 = (x i + K sin(y i )) mod 2π (2.1) y i+1 = (y i + x i+1 ) mod 2π, (2.2) where, x i, y i (0, 2π) and i = 1, 2, 3,..., M N, when K = 131, he sysem is in chaoic sae. Cellular Auomaa is a class of dynamical sysem which consiss of hree pars: cells, local sae ransiion rules, neighborhood, and discree laice srucure. And i can be denoed as: {Q, Z d, N, f}, (2.3) where Q is he cell which denoes he discree laice srucure and d is he dimension of he Cellular Auomaa which represens he neighborhood vecor space; f is he sae ransiion rule according o which each cell can have evoluion. Definiion 2.1. If all he cells of a Cellular Auomaa have he same sae ransiion rule, hen he Cellular Auomaa is called a uniform Cellular Auomaa. Definiion 2.2. If all he cells of a Cellular Auomaa have various sae ransiion rules, hen i is called a hybrid Cellular Auomaa. A wo dimensional Cellular Auomaa can be regarded as a laice marix wih he size of M N. Le be he cener cell, and is neighborhood can be defined as: N(i, j) = (S i 1,j 1, Si,j 1 1, Si+1,j 1, Si,j+1 1 ) (2.4) Hence, he sae of S i,j a he sep is decided by he neighborhood and iself a 1 sep. S i,j = f(s i 1,j 1, Si,j 1 1, Si+1,j 1, Si1,j 1,, Si,j+1 1 ) (2.5) 2

3 Here we propose a novel cryposysem based on he coupling of Cellular Auomaa and chaoic sysem. In he proposed cryposysem, he sae ransiion rules of each cell are decided by he chaoic sequences, which can guaranee he dynamical uniformiy of he wo models. For differen secre keys of sandard map, he cells will have sae evoluion in a differen way. Firsly, we ierae he sandard map and he 2D chaoic sequence {x k, y k } is obained. For each ieraion round, map x k and y k ino he formula m = mod (m, 1). Then a 4 bi sequence (b 1 b 2 b 3 b 4 ) k is generaed by he encrypion characerisic funcion f(x): 00, 0 < m , 0.25 < m 0.5 f(x) = 10, 0.5 < m , 0.75 < m 1 Nex, le r represen he rh round of ieraion and we can obain ha: x k y k, mod (r, 4) = 0 y k x k, mod (r, 4) = 1 B k = x k y k, mod (r, 4) = 2 y k x k, mod (r, 4) = 3 Define each four-bi binary number as rule-deciding number, which decides he sae ransiion rules of each cell. We implemen he 2D von Neumann ype Cellular Auomaa model. For S i,j, we se he evoluion as follows: S i,j +1 = (b 1S i 1,j ) (b 2 S i,j 1 ) (b 3 S i+1,j 3 The proposed encrypion algorihm ) (b 4 S i,j+1 ) (S i,j ) (2.6) The encrypion scheme proposed in his paper is based on he permuaion-diffusion archiecure. Firsly, he chaoic sequences generaed from he sandard map are employed o shuffle he posiion of he pixel in he plain image. Then gray-level ransformaion is performed by he cryposysem consrucion of Cellular Auomaa and sandard map. The encrypion scheme can be described as follows (ake a sandard graylevel image of size M N as an example). The firs sep is o generae keys: wo encrypion keys Key1 and Key2 are generaed from he informaion of he plain image in order o make cipher image more close o he plain image: M/2 Key1 = mod ( Key2 = mod ( i=1 j=1 M i=m/2 j=1 N p ij, 256) (3.1) N p ij, 256), (3.2) where P ij is he pixel value whose posiion is (i, j) in he plain image. The second sep is o ierae he sandard map hen he pseudorandom sequence {x k, y k } are generaed. We scramble he pixel marix from lef o righ, op o boom, by he sandard map: { i = (i + jx k + Key1) mod (M) j = (j + i y k + Key2) mod (N), 3

4 where (i, j) denoes he coordinae of he presen pixels posiion and (i, j ) is he posiion ha he former will exchange wih and hence we can he scrambled marix P. The hird sep is o obain he four-bi random code (b 1 b 2 b 3 b 4 ) k and hen decide he ransiion rules of each cell in he Cellular Auomaa. The las sep is o ake Cellular Auomaa a he ieraion sep, he we perform he gray-level ransformaion: ( ) C(i, j) = mod (P (i, j) + mod (is i,j + js i,j +1 + P (i, j ), 256)), 256, (3.3) where P (i, j) is he pixel value wih he corresponding poin a (i, j); C(i, j) denoes is subsiuion value; P (i, j ) is he pixel value of (i, j ) in he las encrypion round; S i,j is he sae value of he poin (i, j) a sep. 4 Simulaion In he simulaion experimens of he proposed encrypion algorihm, he secre keysare se, and we ake he 2-D von Neumann Cellular Auomaa model as he experimens model. A sandard gray-level image wih he size ofis aken as he plain image. The experimen is simulaed on a PC wih 2GB memory and 2.0 GHz CPU in Inel Core 2 Duo, running on C programming language. The simulaion resuls can be seen in Fig.1. Fig.1(a) is plain image Lena and he cipher image is shown in Fig.1(b). 5 Performance and securiy analysis The hisograms of he plain image and cipher image are shown in Fig.2 (a) and Fig.2 (b), respecively. The wo hisograms have shown ha cipher image is in grea difference from he plain image. In he cipher image, he values of pixels are disribued evenly and conceal he informaion of he plain image well. Furhermore, he cipher image possesses excellen saisical properies. Hence, he proposed encrypion scheme can resis saisical aack effecively. To resis he exhausive aack effecively, he encrypion algorihm should have large enough key space. In he proposed algorihm, he secre keys consis of, x 0, y 0. If he double precision of each key is in he sandard map, ieraion sep can reach infiniy heoreically according o he pracical need. Hence, we can see ha he proposed algorihm has large enough key space, which means i can resis he exhausive aack effecively. To es he key sensiiviy of he proposed encrypion algorihm, we make a sligh change o each secre key and decryp he cipher image: = 200, x 0 = 1, y 0 = ; = 200 x 0 = , y 0 = 0.2; = 201 x 0 = 0.1, y 0 = 0.2. The corresponding decryped images are shown as follows: The decryped image wih he righ keys is in Fig. 3(a) and Fig. 3(b), Fig. 3(c) and Fig. 3(d) are he decryped images wih wrong keys. I is obviously seen even if he keys are changed a lile, he decryped image is quie differen from he plain image. Hence, he proposed algorihm has high sensiiviy o he iniial values of secre keys and can defend sensiive aack effecively. The correlaion coefficiens are used o es he properies of diffusion in he cipher image. In he plain image adjacen pixels in an image have high correlaion and hus a good algorihm is o lower he high correlaion. To es he correlaion beween pixels in he cipher image using he proposed algorihm 4

5 from verical, diagonal and horizonal direcions, 1000 pair pixels are chosen randomly from he plain image and cipher image. The correlaion coefficiens can be calculaed as follows: 6 Conclusion A novel image securiy sysem based on 2D Cellular Auomaa and sandard map is proposed in his paper and has achieved excellen encrypion effec. Chaoic sequences are uilized o decide he sae ransiion rules of each cell o enhance he pseudorandomiciy of he algorihm. Simulaion experimens and securiy analysis indicae ha he proposed algorihm is has large enough key space, and he cipher image shows well disribuion and excellen confusion and diffusion properies. Furhermore, he proposed algorihms can resis sensiive aacks and exhausive aack effecively. References [1] G. Chen, X.Y. Zhao, J. Li, A self - adapive algorihm on image encrypion, Journal of Sofware 16 (2005), no. 2, [2] Shaojiang Deng, Yanping Zhan, Di Xiao, Yanao Li, Analysis and improvemen of a hashbased image encrypion algorihm, Communicaions in Nonlinear Science and Numerical Simulaion 16 (2011), no. 8, [3] Paidar V, Pareek NK, Sud KK, A new subsiuiondiffusion based image cipher using chaoic sandard and logisic maps, Communicaions in Nonlinear Science and Numerical Simulaion 14 (2009), no. 8, [4] Yang Tang, Zidong Wang, Jian-an Fang, Image encrypion using chaoic coupled map laices wih ime-varying delays, Communicaions in Nonlinear Science and Numerical Simulaion 15 (2010), no. 9, [5] Valerij Rozouvan, Modulo image encrypion wih fracal keys, Opics and Lasers in Engineering 47 (2009), no. 9, 1 6. [6] Rong-Jian Chen, Yuan-Hsin Chen, Chao-Shen Chen, and Jui-Lin Lai, Image Encrypion/ Decrypion Sysem Using 2-D Cellular Auomaa, IEEE Tenh Inernaional Symposium on Consumer Elecronics 2006, 1 6. [7] Savvas A. Chazichrisofis, Dimiris A. Mizias, Georgios Ch. Sirakoulis, Yiannis S. Boualis, A novel cellular auomaa based echnique for visual mulimedia conen encrypion, Opics Communicaions 283 (2010), no. 21, [8] Xiaofeng Liao, Shiyue Lai, Qing Zhou, A novel image encrypion algorihm based on selfadapive wave ransmission, Signal Processing 90 (2010), [9] Ling Li, Weinan Wang, Jinjie Li, Jin Jiang, A self-adapive image encrypion scheme based on Logisic map and hyper-chaos sysem, Microelecronics & Compuers 1 (2011), no. 29,

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