Image Encryption using Chaos and Parity based Pixel Modification in Permutation

Transcription

1 Image Encrypton usng Chaos and Party based Pxel Modfcaton n Permutaton T.Gopalakrshnan Assstant Professor Dept. of EEE Dr.Mahalngam college of Engneerng and Technology Pollach, Inda S.Ramakrshnan Professor & Head Dept. of IT Dr.Mahalngam college of Engneerng and Technology Pollach, Inda M.Balakumar PG Scholar Dept. of EEE Dr.Mahalngam college of Engneerng and Technology Pollach, Inda ABSTRACT Ths paper ntroduces a chaos based mage encrypton wth party based pxel value modfcaton n the permutaton stage. The encrypton algorthm conssts of two stages permutatondffuson. Permutaton stage orgnal mage pxels are scrambled and dffuson stage masks the orgnal mage pxel wth the pseudo random bnary sequence. Party based pxel modfcaton n permutaton gves maxmum securty level n mnmum rounds. The D chaotc maps logstc map, sne map and cubc map employed to permute and dffuse mage pxels. Keywords Chaotc map, Image encrypton, Odd or even party, Random bnary sequence, Securty analyss.. INTRODUCTION Cryptosystem has grown over recent years partcularly ganed much attenton for ts potental role n nformaton safety. Chaotc systems have good features such as senstvty to ntal condtons, ergodcty, mxng property and parameters, whch have granted chaotc cryptosystems a promsng alternatve for the tradtonal cryptography algorthms. To attan a great demand for protected mage communcatons through publc channels, a varety of chaos-based mage encrypton schemes have been proposed []-[4]. In 989, Matthews frst proposed the chaos-based encrypton algorthm [2], and Frdrch frst adopted chaotc systems nto mage encrypton n 997 [3]. Frdrch's scheme conssts of substtuton and dffuson n spatal doman. The substtuton s attaned by shufflng all the pxels as a whole usng a 2D chaotc map. The current pxel s moved to calculated new poston usng 2D chaotc map. In the dffuson process, the pxel values are changed consecutvely and the change made to a partcular pxel depends on the accumulated effect of all the prevous pxel values. Ths substtuton dffuson style forms the basc structure for many followng chaos based mage encrypton algorthms. The man characterstcs of these schemes consst of one or several chaotc maps servng the purpose of ether just scramblng the pxels or consequently maskng the resultng shuffled mage. A 2D chaotc map s generalzed to 3D standard map to shuffle the postons of the mage pxels and another chaotc map s used to confuse the relaton between the encrypted and ts orgnal mage n [4]. The smlar dea s used wth the 3D chaotc baker's map at the substtuton stage nstead of the 3D standard map [5].In [6], the 2D cat map s used to shuffle the poston of the mage pxels and the output of a dscretzed Chen's system s used to mask the pxel values. After shortly encrypton scheme n [6] proposed, t s exposed that there are some weak keys present, and the key space of the chaotc baker s and cat maps s not as large as that of the chaotc standard map [7]. Then, the chaotc standard map s used for the confuson or substtuton along wth a new dffuson functon havng hgh dffuson speed based on the quantzed chaotc logstc map and a key stream generator based on the chaotc skew polynomal map. It s also recommended that at least four rounds of the substtuton and dffuson are essental for securty performance. Agan, [8] showed that the dffuson effect n [7] s not necessarly contrbuted solely by the dffuson process. Instead, t s ntroduced n the substtuton stage to acheve securty performance n less number of rounds than the one suggested n [7].The mage encrypton schemes are cryptanalyzed due to weakness n key stream or n ts archtecture. To avod the chosen-plantext attack for every round of mage encrypton the permutaton and dffuson bts needs to be updated. In ths proposed method n the permutaton stage the mage pxels are scrambled and the pxel values are also modfed based on the party of the chaotc map generated pseudo random sequence. In the dffuson stage dfferent random sequence are generated for each round to avod dfferent attacks. The rest of the paper s organzed as follows; secton II explans the proposed encrypton scheme. Secton III shows the expermental analyss and also dfferent vsual effect analyss and n the last secton concluson s gven. 2. PROPOSED METHOD In ths secton a chaotc mage encrypton usng permutatondffuson structure shown n Fg.. In permutaton process the orgnal mage pxels are scrambled n spatal doman and dffuson process the orgnal mage pxel bts are masked wth the randomly generated bnary sequence. The man am of the encrypton algorthm should resst the cpher mage from varous attacks and also the speed of the algorthm s one of the mportant constrants n the real tme processes. In ths proposed method chaotc maps are used to generate the pseudo random sequence to permute and dffuse the mage pxels. In the permutaton process orgnal mage pxels locatons are modfed and also the pxels values are modfed. Logstc map Eq. s one of the popular chaotc maps n the chaos based mage encrypton algorthm and t s gven by followng relaton, 30

2 Rounds Orgnal mage Permutaton process Party based pxel value modfcaton Dffuson process Cpher mage Secret key to logstc map Dffuson keys z n rzn( zn) () where r s the parameter and t ranges from 0 to 4. When r s greater than the 3.57 t possesses the chaotc behavor. Permutaton process the logstc map whch s used to generate the random sequence wth non-repeated values. The outcome of the map s (0.2, 0.9, 0.3, 0.8, 0.7, 0., 0.5, 0.6) and sorted sequence s n random (6,, 3, 7, 8, 5, 4, 2). Usng ths random sequence the orgnal mage pxels are altered and also by usng Eq. 2 random ntegers are generated. rand seq x 32 _ ( ()*2 )mod 256 (2) The generated random ntegers are converted n to bnary of 8 bts each and based on the s party the scrambled pxel bts are shfted usng Eq. 3. The party of the random values s determned by the number of s present n the bnary form of the random value and the number of bt shftng determned by number of s present n the random value. If the random nteger value of s party s odd then the pxel bts shft towards rght and f the s party s even, then the pxel bts are shfted towards left sde. The shftng s performed sequentally up to all pxels gets over. odd rght shft even,, left shft party _ output (3) Ths smple pxel value changes drectly the encrypton technque n the reducton of number of rounds requred to acheve the maxmum securty. In the dffuson process random bnary sequence s generated as shown n Fg. 2. The dffuson keys are fed as ntal condton for the sne map Eq. 4 and cubc map Eq. 5; t s terated for the length of the bnary sequence of the shuffled mage pxel bts. xn asn( xn) (4) 2 y n byn ( yn ) (5) Fg : Proposed Encrypton Structure where a and b are the control parameters of the sne and cubc map s n the range of [0,] and [0,3]. Both maps possess chaotc behavor n the range of sne map 0.76 to 0.99 and for cubc map 2.59 to 3. K K Sne map Cubc map cmp Fg 2: Random Bnary Sequence Generator Random bnary sequence K s the dffuson keys for round the frst two keys are fed as ntal condton for sne and cubc map. For second round other two keys act as an ntal condton to both maps. The sne and cubc map values are compared (cmp) and f sne s greater than cubc value the random bnary value s 0 otherwse t produces. Ths sequence s generated up to total length of shuffled mage pxel bts. Ths random bnary sequence generator produces the dfferent sequence for every round though the cphered mage at every round s dfferent from prevous one. Employng of two chaotc systems mproves the chaotc behavor and randomness of the random bnary sequence. The generated random bnary sequence s masked wth mage bnary sequence and produces the bnary cpher mage. Then the bnary sequence s converted to nteger sequence to produce the cpher mage. 2. Encrypton Algorthm The chaotc based spatal doman encrypton technques should resst the dfferent cryptanalyss attacks and also dfferental attacks and statstcal attacks. The effectve permutaton-dffuson gves effcent cpher mage. Step: Orgnal mage pxels are scrambled based on the random sequence generated by logstc map. Step2: Based on party of the random nteger sequence the shuffled mage pxel bts are shfted ether rght sde or left sde. 3

3 Step3: Random bnary sequence s generated as shown n Fg. 2. The generated sequence s manpulated wth the shuffled mage pxel bts. Step4: The bnary sequence s converted nto nteger sequence to produce the cpher mage. Ths process s repeated for two rounds. 2.2 Decrypton Algorthm Decrypton s the reverse of the encrypton process. It s a symmetrc key encrypton algorthm n whch the same keys are used n the retreval process. The use of chaos provdes the lossless encrypton and decrypton. 3. EXPERIMENTAL ANALYSIS To demonstrate the cpher mage securty and the encrypton archtecture performance analyss are performed lke statstcal analyss, dfferental analyss, and entropy analyss. The smulated resultant outputs are shown n Fg. 3. The Lena gray scale mage s encrypted usng ths encrypton algorthm. Fgure 3 shows the cphered mage for two rounds. The pxel ntensty value modfcaton n permutaton process mproves the encrypton qualty n mnmum rounds. The proposed encrypton algorthm n the frst round attans encrypton crtera s NPCR, UACI, Correlaton coeffcent and t s performed for maxmum two rounds to produce complex computatons. 3. Secret Key and Key Space Analyss The symmetrc keys are used n the both encrypton and decrypton sde. The use of chaotc map and ts man and very effectve property of beng senstve to ntal condton provdes good securty to encrypton algorthm. The secret keys are gven n floatng numbers, The MATLAB can perform up to 4 bts maxmum length (.e) 0 4. Sne and cubc map parameters a, b, four dffuson keys and logstc map parameter r and ts ntal condton. The total key space s 084 and t s greater than the mnmum requred level of key space to avod brute force attack. 3.2 Key Senstvty Analyss The mage s encrypted wth ntal set of dffuson keys and the four dffuson keys are slghtly modfed the resultant mage and ts hstogram s shown n the Fg.3.The hstogram varaton shows that the encrypton algorthm s very senstve to ts ntal condton (.e) symmetrc encrypton keys. The slght varaton n the key gves drastc varaton n ts cpher mage. 3.3 Hstogram Analyss A hstogram of an mage shows how pxels are dstrbuted n that mage. The graph shows the pxel values n x-axs and number of occurrence n y-axs. The hstogram of several encrypted and orgnal mages of wdely dfferent content are calculated and analyzed. It s clear that the hstograms of encrypted mages are flat and has no clue about the orgnal hstogram of the mage. The results of hstogram analyss are n Fgure 3 (a) and 3(b) shows the orgnal and encrypted mages of sze 256x256 Fg. 3 (e) and Fg. 3 (f) shows the orgnal and encrypted mages hstograms respectvely. From these results Fg. 3 (f) s completely flat and has no clue about the hstograms of Fg 3 (a). 3.4 Correlaton Coeffcent Analyss The notceable characterstc of vsually meanngful mages s redundancy. There are hgh correlatons between pxels and ther adjacent pxels at horzontal, vertcal and dagonal drectons. The mage encrypton algorthm ams to break these pxel correlatons n the orgnal mages wth lttle or no correlatons. Ths analyss shows the correlaton between the randomly selected pars of both orgnal mage and cpher mage. Ths analyss carred out by followng the procedures, Randomly 5,000 pars horzontally, vertcally and dagonally adjacent. The correlaton s calculated by the followng equatons, r xy E x E(x) y E(y) (6) D(x) D(y) s E(x) x (7) s s D(x) x E 2 (x) (8) s where x and y are the gray level values of the two adjacent pxels n the mage, E(x) and D(x) are the mean and standard devaton of the correspondng gray level values. rxy s the correlaton between the adjacent pxels. If the correlaton coeffcent value s means the mage s orgnal and the correlaton between the adjacent pxels s not broken. If the value s - means that the mage s the exact negatve of the orgnal mage. The Table shows the correlaton coeffcents of the orgnal and encrypted mages when compared wth wong k et al. algorthm n horzontal, vertcal and dagonal drecton. The orgnal mage values are nearly equal to because the correlaton between the adjacent pxels s hgh. The encrypted mage values are approxmately 0. Fgure 4 shows the horzontal drecton correlaton plot. Fgure 5 shows vertcal drecton correlaton plot and Fgure 6 shows dagonal correlaton plots of orgnal and encrypted mage. Table. Correlaton coeffcents Drecton Orgnal mage Proposed Wong k [8] Horzontal Vertcal Dagonal Dfferental Attack In order to avod dfferental attack, a mnor change of orgnal mage should cause a substantal change n the cpher mage. The common measures used to measure ths senstvty are NPCR (Number of pxel change rate) and UACI (unfed average changng ntensty) proposed by NIST. They are gven by the followng equatons, NPCR UACI W H D (, j), j 00% W H c (, j) c (, j) (9) 00% (0) 2, j

4 where C and C2 are the cpher mages whose orgnal mages have a slght dfference n one pxel. Fg 3:a) Orgnal mage b) Encrypted mage wth ntal key c) Encrypted mage wth modfed key d) Dfference between two encrypted mages e) Hstogram of orgnal mage f) Hstogram of Encrypted mage wth ntal key g) Hstogram of Encrypted mage wth modfed key h) Hstogram of Dfference between two encrypted mage C (, j) denotes the poston of pxel n C.W and H are wdth and heght of the cpher mage. D(, j) s determned as,f C(, j)=c2(, j) otherwse D(, j)=0. The resultng NPCR and UACI values are tabulated n Table 2. NPCR s greater than or equal to and UACI s greater than or equal to From Table 3 t clearly shows that the proposed method has NPCR and UACI values average of and and also compared wth wong k et al. method. For the securty purpose maxmum 2 rounds of the proposed algorthm performed. The NPCR of our scheme can reach 99.6% n the frst round. That ndcate the cryptosystem s very senstve to even a -bt modfcaton. The Table III shows the NPCR and UACI for dfferent mages. For varous mages the proposed method satsfes the NPCR and UACI crtera. Table 2. NPCR and UACI analyss Proposed Wong k [8] Round NPCR UACI NPCR UACI Randomness Test The randomness test s performed to check the encrypted mage randomness. Ths test s performed usng sp test sute developed by NIST [2]. The Table 4 shows that the encrypted mage has the randomness qualty and t succeeds n the all above tabulated tests. Table 4. Randomness test Statstcal test P value Result Frequency Success Block frequency Success Runs Success Bnary Matrx Rank.0000 Success Cumulatve sums Success 3.7 Informaton Entropy Analyss The entropy of a message source can be measured by, Table 3. NPCR and UACI analyss of varous mages Images NPCR UACI Lena Baboon House Camera man Boat Barbara M H ( m) p( m ) log () pm ( ) 0 where m s total number of symbols, p(m) represents the probablty of occurrence of symbol m, and log denotes the base 2 logarthm so that the entropy s expressed n bts. The entropy can be used for evaluatng the randomness of an mage. If an entropy score of an mage s close to the maxmum entropy value t shows the excellent random property. Table 5 shows the nformaton entropy comparson of proposed and Wong et al. algorthm. For a gray scale mage wth a data range of 0 to 255, ts maxmum entropy s 8. The cpher mage entropy value s nearly equal to 8 bts. Hence the proposed algorthm s robust aganst entropy attacks. Table 6 shows the entropes of varous mages. The entropy 33

5 determnes the randomness of the encrypted mage. In our algorthm the entropy value s approxmately (entropy=7.9972) equal to 8. Fg 6: Dagonal Drecton Correlaton Plot Table 5. Entropy comparson Fg 4: Horzontal Drecton Correlaton Plot Lena Image Entropy Wong et al. method Proposed method Table 6. Entropy analyss Fg 5: Vertcal Drecton Correlaton Plot Images Entropy Lena Baboon House Peppers Camera man Boat CONCLUSION In ths paper, permutaton process scrambles the mage pxels and also party based smple pxel modfcaton ntroduced n the permutaton stage. Ths party based shufflng proves that the encrypton algorthm needs only very less number of rounds (Rounds=2) to acheve hghly uncorrelated cpher mage. Employng dfferent chaotc maps n the encrypton algorthm ncreases the randomness of the cpher mage that can be proved by NIST tests. In the dffuson process the random bnary values are masked wth the permuted mage pxel bts. The dffuson bt updaton n each round provdes dfferent cphered mage for every round of encrypton ths process can resst the chosen plantext attack. Manly, encrypted mages of the proposed encrypton algorthm are random, non- repeated and unpredctable, even usng same set 34

6 of keys and the same orgnal mage. The algorthm can also wthstand varous dfferent attacks such as statstcal, dfferental and securty. Further extenson of ths work s ntroducng compresson and employment of multdmensonal chaotc maps whch gve more securty. The compresson provdes small bandwdth for large mage data transmsson through network. 5. REFERENCES [] G. Alvarez, S. L, Some basc cryptographc requrements for chaos based cryptosystems, Internatonal Journal of Bfurcaton and Chaos, vol. 6, pp , [2] R. Matthews, On the dervaton of a chaotc encrypton algorthm, Cryptologa, vol. 3, pp , 989. [3] J. Frdrch, Symmetrc cphers based on twodmensonal chaotc maps, Internatonal Journal of Bfurcaton and Chaos, vol. 8, pp , 998. [4] G.R. Chen, Y. B. Mao, C. K. Chu, Asymmetrc mage encrypton scheme based on 3D chaotc standard maps, Chaos Soltons and Fractals, vol. 2, pp , [5] Y. B. Mao, G. R. Chen, S. Lan, A novel fast mage encrypton scheme based on 3D chaotc baker maps, Internatonal Journal of Bfurcaton and Chaos, vol. 4, pp , [6] Z. H. Guan, F. Huang, W Guan, Chaos based mage encrypton algorthm, Physcs Letters A, vol. 346, pp , [7] S. Lan, J. Sun, Z. Wang, A block cpher based on a sutable use of chaotc standard map, Chaos Soltons and Fractals, vol. 26, pp. 7 29, [8] K. W. Wong, B. S. H. Kwok, W. S. Law, A fast mage encrypton scheme based on chaotc standard map, Physcs Letters A, vol. 372, pp , [9] R. Rhouma, E. Solak, S. Belghth, Cryptanalyss of a new substtuton dffuson based mage cpher, Communcatons n Nonlnear Scence and Numercal Smulaton, vol. 5, pp , 200. [0] C. L, S. L, K. T. Lo, Breakng a modfed substtuton dffuson mage cpher based on chaotc standard and logstc maps, Communcatons n Nonlnear Scence and Numercal Smulaton, vol. 6, pp , 20. [] Ahmed A. Abd El-Latf, L L, Nng Wang, Q Han, Xamu Nu, A new approach to chaotc mage encrypton based on quantum chaotc system, explotng color spaces, Sgnal Processng, vol. 93 pp , 203. [2] The NIST webste. jshome.html. [3] Yang Lu, Xaojun Tong, Shcheng Hu, A famly of new complex number chaotc maps based mage encrypton algorthm, Sgnal Processng: Image Communcaton, vol. 28, pp , 203. [4] Ycong Zhou, Long Bao, C.L. Phlp Chen, Image encrypton usng a new parametrc swtchng chaotc system, Sgnal Processng, Vol. 93, pp ,