Department of Mathematics, Shantou University, Shantou, Guangdong, , China.

Transcription

1 205 Internatonal Conference on Computer Scence and Communcaton Engneerng (CSCE 205) ISN: A Novel Color Image Encrypton Scheme ased on Permutaton-substtuton Archtecture Ru-Song Ye,a, Mng Ye, Xao-Yun Sh, Wen-Hao Ye, Ya-Fang L Department of Mathematcs, Shantou Unversty, Shantou, Guangdong, 55063, Chna a rsye@stu.edu.cn Keywords: Skew tent map, Permutaton, Substtuton, Image encrypton. Abstract. A novel color mage encrypton scheme wth permutaton-substtuton archtecture s proposed. One round of permutaton and one round of substtuton acheve desrable results. he color plan-mage szed H W s converted to 2D matrx wth sze H 3W and then dvded nto two equal parts P, P 2. he 2D skew tent map s appled to generate pseudo-random sequences for the permutaton and substtuton processes mplemented row-by-row/column-by-column nstead of pxel-by-pxel to ncrease the encrypton rate. he permutaton s performed between P, P 2 and the substtuton s executed wthn the permuted mage. he securty and performance of the proposed scheme have been analyzed as well. All the expermental results show that the proposed scheme s secure and effectve for practcal applcaton. Introducton hanks to the fantastc features of chaotc systems, such as hgh senstvty to ntal condtons and control parameters, ergodcty, pseudo-randomness etc., chaos-based mage encrypton schemes are extensvely studed and developed recently. On one hand, tradtonal encrypton algorthms, such as DES, AES, are typcally desgned for textual nformaton and are not sutable for mage encrypton due to the ntrnsc natures of mages lke hgh redundancy and hgh correlaton among pxels []. On the other hand, the good chaotc natures agree wth the fundamental requrements such as confuson and dffuson n cryptography, and therefore chaotc systems provde a potental canddate for constructng cryptosystems [2-4]. Snce Frdrch frstly presented the fundamental permutaton-dffuson archtecture of chaos-based mage encrypton n 998, a great number of chaos-based mage encrypton algorthms wth such permutaton-dffuson archtecture have been proposed [2-6]. However Wang et al. found that the typcal permutaton-dffuson archtecture wth fxed parameters has one fatal drawback, that s, the two processes wll become ndependent f the plan-mage s a homogeneous one wth dentcal pxel gray value [7]. As a matter of fact, some mage encrypton algorthms wth permutaton-dffuson archtecture have been broken by chosen-plantext or known-plantext attacks [8,9]. In ths paper, we present an mage encrypton scheme wth permutaton-substtuton mechansm nstead of permutaton-dffuson mechansm. Permutaton-substtuton mechansm has been shown to be one effectve mechansm for constructng cphers [6]. he mage encrypton scheme proposed here conssts of two stages: one permutaton and one substtuton. hey are performed between the RG,, components of color mage. he color plan-mage szed H W s converted to a 2D matrx wth sze H 3W and then s dvded nto two parts 22

2 P, P 2 wth the same sze H.5W. o acheve desrable key senstvty and plantext senstvty, the permutaton stage s desgned to be dependent on plan-mage. As a result, the proposed mage scheme owns good resstance to known-plantext and chosen-plantext attacks. he substtuton stage s performed row by row and column by column to mprove the encrypton rate. he substtuton acheves good dffuson effect and shows good resstance aganst dfferental analyss as well. he securty and performance analyss of the proposed mage encrypton are carred out thoroughly. All the expermental results show that the proposed mage encrypton scheme s hghly secure and demonstrates excellent performance. he Proposed Image Encrypton Scheme Read a color plan-mage PI expressed by a 3D matrx wth sze HW 3. We assume that the three color components are denoted by 2D matrx RGrespectvely.,, hen convert PI to a 2D matrx P wth sze H 3W by the way P [ R, G, ]. P s then dvded nto two parts P, P 2, whose szes are the same H.5W. For the sake of smplcty, we assume that W s even and let W.5W, max( H, W). he converson and dvson s shown n Fg.. Fg.. he converson and dvson of color plan-mage. he proposed mage encrypton scheme s composed of one permutaton process and one substtuton process. he entre mage encrypton scheme s outlned as follows. Step. Generaton of pseudo-random gray value vectors IVR, IVC. Wth cpher keys x0, y 0, aband, N, we terate the 2D skew tent map for N tmes and reect the transent ponts{( xk, yk) : k 0,,, N }. he values of ( xn, y N) are saved and the 2D skew tent map wth new ntal values ( xn, yn) to yeld IVR, IVC. We stll wrte ( xn, yn) as ( x0, y 0). x x / p, f x [0, p], IVR floor x*256, IVC floor y*256,,,, y ( x ) / ( p), f x ( p,], where floor( x) returns the largest nteger not larger than x. runcate the frst H elements of IVC and transpose t to get one column vector IVC wth H elements. runcate the frst W elements of IVR to get one row vector IVR wth W elements. Step 2. Generaton of pseudo-random gray value vectors SVR, SVC. We stll denote ( x, y ) as ( x0, y 0) for smplcty. x x / p, f x [0, p], SVR floor x *256, SVC floor y *256,,,. y ( x ) / ( p), f x ( p,], Step 3. Perform the permutaton stage. Calculate the number of teratons to skp before startng the permutaton by N P P W P PH W mod Startng,, 3 2,,

3 wth the ntal condtons ( xn, y N) obtaned n Step, we terate the 2D skew tent map for N tmes and save the new values ( xn, y ) N as ( x 0, y 0). For to, do the followng loop x x / p, f x [0, p], PR floor x* H, PC floor y* W. y ( x ) / ( p), f x ( p,], he vectors PR, PC are then employed to perform the permutaton between P and P 2 row-by-row and column-by-column va the followng loop and get one permuted mage G. For to H, exchange the PR( ) -th row of P 2 wth the -th row of P ; For to W, exchange the PC( ) -th column of P 2 wth the -th column of P. Step 4. Substtute the 2D matrx G row-by-row and column-by-column. he executon for the substtuton s defned by G(,:) G(,:) IVRSVR(); G(,:) G(,:) G(,:) SVR( ), 2,, H, G(:,) G(:,) IVCSVC(); G(:, ) G(:, ) G(:, ) SVC( ), 2,, W, where represents the btwse XOR operaton, and G(,:), G(:, ) denote the th row and th column of G. he resulted cpher-mage for plan-mage Lena s shown n Fg. 2(b). (a) (b) (c) (d) (e) (f) (g) (h) Note: (a) plan-mage Lena; (b) cpher-mage; (c),(d),(e): hstograms for RGcomponents,, of Lena; (f),(g),(h): hstograms for RGcomponents,, of cpher-mage. Fg. 2. he encrypted results. Performance Analyss Hstogram analyss Hstogram analyss s a vsual test whch shows the pxel dstrbuton over the avalable ntensty levels. For a 24-bt color mage, three hstograms can be drawn for each 8-bt red, green and blue channel. Encrypt the color mage Lena one round wth cpher keys ( x, y, a, b, N ) to be (0.20, 0.44, 0.23, 0.57, 933), and then plot the hstograms of plan-mage

4 and cpher-mage as shown n Fg. 2. One can conclude from the hstograms of the cpher-mage that they are farly unform and sgnfcantly dfferent from the correspondng hstograms of the plan-mage. Correlaton coeffcent analyss It s common sense that for one nature mage wth defnte vsual contents, each pxel s hghly correlated wth ts adacent pxels ether n horzontal, vertcal or dagonal drecton. An deal encrypton cryptosystem should produce cpher-mages wth less correlaton n the adacent pxels. We select 6000 pars of two adacent pxels randomly from an mage cov( x y) and then calculate the correlaton coeffcent of the selected pars by Cr, ( ) ( ( ))( ( )) cov xy x E x y E y 2 where, Ex ( ) x Dx ( ) ( x Ex ( )) D( x) D( y) x y form the -th par of horzontally, vertcally or dagonally adacent pxels. he correlaton coeffcents of horzontally, vertcally, dagonally adacent pxels for plan-mage Lena and ts cpher-mage are gven n able. It s clear from able that the proposed mage encrypton scheme sgnfcantly reduces the correlaton between the adacent pxels of the plan-mage. Informaton entropy analyss Informaton entropy measures the dsorder and randomness of nformaton sequence [0]. Regardng mage, t can be used to measure the unformty of mage hstograms. he entropy L H ( m ) of a message source m can be calculated by Hm ( ) pm ( )log( pm ( )) (bts), where L s the total number of symbols m, pm ( ) represents the probablty of occurrence of symbol m and log denotes the base 2 logarthm so that the entropy s expressed n bts. For a 24-bt color mage, the nformaton entropy for each color channel (Red, Green and lue) s gven as RG / / RG / / H ( m) P ( RI )log 2 (bts). RG / / P ( RI ) 0 ab.. Correlaton coeffcents between adacent pxels of plan and cpher mage. Correlaton between adacent pxels Red Green lue Horzontal Plan-mage Cpher-mage Vertcal Plan-mage Cpher-mage Dagonal Plan-mage Cpher-mage We have calculated the nformaton entropy for plan- mage Lena and ts cpher mage. he results are shown n able 2. he value of nformaton entropy for the cpher-mage s very-very close to the expected value of truly random mage,.e., 8bts. Hence the proposed encrypton scheme s extremely robust aganst entropy attacks. 25

5 ab. 2. Informaton entropy analyss. Red Green lue Plan-mage Lena Cpher-mage Dfferental attack analyss Dfferental cryptanalyss s the study of how dfferences n a plantext can affect the resultant dfferences n the cphertext wth the same cpher key. If one slght dfference n the plan-mage wll cause sgnfcant, random and unpredctable changes n the cpher-mage, then the encrypton scheme wll resst dfferental analyss attack effcently. wo most common measures NPCR (number of pxel change rate) and UACI (unfed average changng ntensty) are used to test the robustness of mage cryptosystems aganst the dfferental R/ G/ R/ G/ cryptanalyss. If C and C represent the R, G, channels for two cpher-mages, then NPCR for each color channel s defned by H W RG / / D, R/ G/ R/ G/ f / / / /, C RG RG, D, R/ G/ R/ G/ W H f, C, NPCR 00%, 0, C,, C. H W RG / / RG / / C, C, UACI 00%. L W H 2 RG RG / / UACI s calculated by / / We have performed the dfferental analyss by calculatng NPCR and UACI on plan-mage Lena. he analyss has been done by randomly choosng 500 pxels n plan-mage, and changng all three color ntensty values by one unt at the selectve pxel. he averages of 500 NPCR values and 500 UACI values thus obtaned for all three color components are gven n able 3. It s clear that the NPCR and UACI values are very close to the expected values, thus the proposed mage encrypton technque shows good senstvty to plantext and hence nvulnerable to dfferental attacks. ab. 3. Dfference analyss of plan-mage Lena. Average NPCR (%) Average UACI (%) Red Green lue Red Green lue Lena Key senstvty analyss A good mage encrypton scheme should be extremely senstve to cpher keys, whch s an essental feature for any good cryptosystem n the sense that t can effectvely prevent nvaders decryptng orgnal data. If one uses two slghtly dfferent keys to encrypt the same plan-mage, then two cpher-mages should possess neglgble correlaton. he plan-mage s respectvely encrypted wth one master cpher key and fve other cpher keys whch have only a mnor dfference n any one of fve parts of master cpher key. Sx cpher keys are used to encrypt mage Lena. Master cpher key s MKEY(0.20,0.44,0.23,0.57,933) ; fve slghtly dfferent 26

6 4 4 keys are SKEY(0.20-0, 0.44, 0.23, 0.57, 933), SKEY2(0.20, , 0.23, 0.57, 933), SKEY3(0.20, , , 0.657, 933), SKEY4(0.20, 0.44, 0.23, , 933), SKEY5(0.20,0.44,0.23,0.57,933+). We then calculate the 2D correlaton coeffcents between the varous color channels of the cpher-mage by MKEY and fve other cpher-mages by SKEY,,SKEY5. he results are provded n able 4. All the correlaton coeffcents are very small or practcally zero ndcatng that all the cpher-mages are hghly dfferent. ab. 4. Key senstvty tests. Correlaton coeffcents between the cpher-mages obtaned usng MKEY and SKEY SKEY2 SKEY3 SKEY4 SKEY5 Crr Crg Crb Cgr Cgg Cgb Cbr Cbg Cbb Acknowledgement hs research s supported by the Challenge Promoton Plan of Shantou Unversty. References []D.R. Stnson, Cryptography: heory and Practce. oca Raton: CRC Press, 995. [2]J. Frdrch, Symmetrc cphers based on two-dmensonal chaotc maps, Internatonal Journal of furcaton and Chaos, 8 (998), [3]R. Ye, A novel chaos-based mage encrypton scheme wth an effcent permutaton-dffuson mechansm, Opt. Commun., 284 (20), [4]L. Kocarev, Chaos-based cryptography: a bref overvew, IEEE Crcuts and Systems Magazne, (200), 6-2. [5]R. Ye, A novel mage encrypton scheme based on generalzed mult-sawtooth maps, Fundamenta Informatcae, 33 (204), [6]Vnod Patdar, N.K. Pareek, G. Puroht, K.K. Sud, A robust and secure chaotc standard map based pseudorandom permutaton-substtuton scheme for mage encrypton, Optcs Commun., 284 (20), [7]Y. Wang, K.W. Wong, X.F. Lao,. Xang, G.R. Chen, A chaos-based mage encrypton algorthm wth varable control parameters. Chaos, Soltons and Fractals, 4 (2009),

7 [8]S.J. L, C.Q. L, G.R. Chen, N.G. ourbaks, K.. Lo, A general quanttatve cryptanalyss of permutaton-only multmeda cphers aganst plan-mage attacks. Sgnal Process. Image Commun., 23 (2009), [9]X. Wang, G. He, Cryptanalyss on a novel mage encrypton method based on total shufflng scheme. Opt. Commun., 284 (20), [0]C.E. Shannon, Communcaton theory of secrecy system. ell Syst. ech. J, 28 (949),