Combination of 2D chaotic Encryption and Turbo Coding for Secure Image Transmission

Transcription

1 IJCSS Internatonal Journal of Computer Scence and etwor Securty, VOL.0 o., ovember Combnaton of D chaotc Encrypton and Turbo Codng for Secure Image Transmsson M. A. El-Isandaran, Saad M. Darwsh, Saad M. Abuguba Insttute of Graduate Studes and Research Unversty of Alexandra Egypt Summary Robust and secure transmsson strategy for hgh-qualty mage through wreless networs s consdered a great challenge. However, majorty of encrypted mage transmsson schemes do not consder well the effect of bt errors occurrng durng transmsson and ths ssue s consdered a problem that should be handled by an effcent codng scheme. In ths paper, a modfed wreless mage transmsson scheme that combnes chaotc encrypton and turbo codng technque nto one processng step s proposed. In the proposed scheme, selectve encrypton algorthm based on two-dmensonal chaotc map s utlzed for data securty. Furthermore, error correcton technque based on turbo codng s employed as channel codng for data communcaton n order to solve the problem of channel s lmted bandwdth and throughput. Smulaton results show that the proposed scheme acheves hgh degree of robustness aganst channel mparments and wde varetes of attacs. In addton, t mproves mage qualty wth acceptable data rates. Keyword Error correcton code, Image transmsson, DWT, Image encrypton. Introducton The wreless communcaton medum, as opposed to the wred counterparts, s nosy and open to ntruders. Hence, addtonal level of error protecton and securty s requred to mae the wreless networ as relable and secure as the wred networ. The ssue of usng cryptographcally secure cphers n wreless nosy channel s that the very same property that gves cphers ther cryptographc strength maes them senstve to channel errors. Ths senstvty causes retransmssons thus reducng the overall throughput. To mprove the throughput n nosy envronments, channel codng s performed after encrypton. Unfortunately, performng both encrypton and codng separately can potentally prove to be too computatonally ntensve for many wreless end devces (e.g., personal data assstants (PDA), moble phones). In fact, as both encrypton and codng can be performed at the ln layer, a sngle operaton whch does both encrypton and error correcton would be preferable [,]. Error control codes (ECC) are mportant ssue n wreless transmsson, and are used to protect data from channel errors. ECC codes wor by addng redundancy to data transmsson to retreve the data n the recever sde. In the lterature, ECC can be classfed nto two categores: convolutonal codes and lnear bloc codes [3]. Convolutonal codes process the nformaton on a bt-by-bt bass and ths s used n stream cpher [4]. Lnear codes process the nformaton on a bloc-by-bloc bass and ths s used n bloc cpher,.e. lnear code operates on a fxed bloc length of data at a tme. The man weaness of lnear bloc code s that a sngle bt flp n the encrypted data can cause a complete decrypton falure. Ths senstvty causes retransmssons thus droppng the overall throughput (avalanche effect) []. Generally, the encrypton can be appled n specal doman or n frequency doman. Spatal doman schemes are manly related to the poston of the pxels n the mage. Encrypton n spatal doman does not satsfy the securty applcaton because they cannot survve most mage processng attacs and geometrc attacs []. In the other hand, frequency doman schemes deal wth the dgtal transformaton of the mage and therefore can resst the mage processng attacs [5]. An example of frequency transform s wavelet transforms, whch have several propertes that mae them good canddates. Frst, the approxmaton coeffcents provde a good low-resoluton estmate of the mage, whle mnmzng alasng artefacts resultng from the reducton n resoluton. Second, the wavelet coeffcents are localzed, so a corrupton of a coeffcent through channel errors has only local effect on the mage [6]. Tradtonally, error correcton and encrypton n communcaton networs have been addressed ndependently such as n Refs.[7-8]. Several researchers have studed the trade-off between encrypton and error correcton by tryng to combne these functonaltes n one unt. For nstance, Glgoros et al. [9] proposed technque for jont error correcton and encrypton, ths technque acheves both securty and error correcton but the decodng procedure s extremely complcated and cannot be used n a wreless envronment because t needs more computaton tme. Another wor of Cam et al. [0] that combne the advanced encrypton standard (AES) and turbo codng nto sngle processng step n order to reduce the processng tme. However, the wor of Asm et al. [] compared between Manuscrpt receved ovember 5, 00 Manuscrpt revsed ovember 0, 00

2 80 IJCSS Internatonal Journal of Computer Scence and etwor Securty, VOL.0 o., ovember 00 AES and chaotc based encrypton. Ther results show that chaotc encrypton scheme s less computatonally ntensve compared to AES, and provdes the same level of securty. The man contrbuton of ths paper s to buld a secure and relable mage transmsson scheme that combne turbo codng based on error correcton code and D chaotc map based encrypton functonalty nto one sngle step n order to reduce the overall processng cost. The advantages of our scheme are achevng better securty by utlzng D chaotc map nstead of D chaotc map used by [] and mprovng the throughput of an mage transmsson system by usng turbo codng. The systematc bloc dagram of the proposed scheme s shown n Fgure, and the followng subsectons brefly outlne each step. Dscrete wavelet transform (DWT) s becomng popular n many mage/vdeo applcatons due to ts multresoluton representaton feature. The basc dea of the DWT for a D mage s descrbed as llustrated n Fgure. Wth the pyramd-structured wavelet transform, the orgnal mage wll encounter dfferent combnatons of a low-pass flter and a hgh-pass flter and then based on the convoluton wth these flters to generate the low-low (LL), low-hgh (LH), hgh-low (HL) and hgh-hgh (HH) sub-bands [3]. Fgure. D forward wavelet transform The most of the prevous wors for DWT [4,5] notced that wth only LL4, a large amount of mage nformaton can be extracted, but encryptng only LL4 may reveal hgher frequency nformaton such as edge components and t can be used to nfer useful nformaton. The expermental results of Seo et al. [4] showed that the encrypton of all the sub-bands n level 4 and HH3 from level 3 gve us the ablty to reduce the computaton tme to mplement the encrypton and therefore preserve wreless energy. The proposed scheme utlzes the same technque n order to meet the requrement of computatonal tme. 3. Cryptographc of Chaotc Map Fgure. Bloc dagram of the proposed scheme. The rest of ths paper s organzed as follows. Secton II, descrbes the DWT data selecton brefly. Secton III, dscuses the selectve mage encrypton based on two dmensonal chaotc maps. An effcent error correcton scheme s presented n secton IV. Secton V dscusses the combnaton of chaotc encrypton and turbo codng. The smulaton results are gven n secton VI and fnally n Secton VII, the concluson.. Partal Data Selecton of DWT Ths secton dscusses the methodcal procedure of the proposed mage encrypton as well as decrypton process usng two chaotc logstc maps []. The basc logstc-map s formulated as: X n + = μ X n ( X n ) () where μ represents the parameter of chaotc map. To satsfy the best encrypton,.e. chaotc sequence s unpredctable, μ must les between 3.569< μ < 4.0 [6]. Consequently the chaotc encrypton and decrypton provdes guaranteed hgh securty. The encrypton usng chaotc sequence produced by -D logstc system as depcted n Fgure 3 s nown to be wea n securty, snce t cannot resst nown/chosen-

3 IJCSS Internatonal Journal of Computer Scence and etwor Securty, VOL.0 o., ovember 00 8 plantext attacs. More nformaton about the mplementaton of -D chaotc map can be found n [7,8]. In order to deal wth the problem of the prevous scheme, the proposed scheme utlzes -D chaotc logstc map as drawn n Fgure 4. Mathematcally, the -D chaotc map s defned as follows: xn+ = 4μxn ( xn ) + γyn () yn+ = 4μ yn ( yn ) + γxn (, ) where x y n n represent mage pxels, γ s smple coupled term and μ, μ are control parameters of chaotc system. See [3] for further detals. P( s = s', u =, y, y, y + )/ P( y ) + u L( u ) = log[ ] (3) P( s = s', u = 0, y, y, y )/ P( y ) u + where and are the summaton over the entre + u u possble transton branch par ( s, s ) at tme K gven nput u =, and nput u = 0 respectvely. At the recever sde, the followng equaton s used to estmate the lost nformaton due to channel errors. P( y / u = ) P( u = ) L ( u ) = log + log (4) P( y / u = 0) P( u = 0) For more detals about turbo codng and decodng, readers can refer to [9]. Fgure 3: D Chaotc mage encrypton 5. Cryptcodng: Combnaton of -D Chaotc Encrypton and Turbo Codng Fgure 5 shows the proposed combnaton between -D chaotc encrypton and turbo codng, whch s mplemented n a synchronous way to mprove both the securty and throughput. The algorthm of the combnaton s as follows: Fgure 4: D chaotc mage encrypton 4. Turbo Channel Codng Error correctve codng s used to enhance the effcency and accuracy of transmtted nformaton. In ths wor, turbo codes are used as channel codng for data communcaton over wreless channels wth burst errors. Turbo-codes consst of partcular concatenaton of two recursve systematc codes lned together by non-unform nterleavng [4]. Formally, the redundancy nformaton for turbo coder s computed as follows: Fgure 5: Combnaton of encrypton and turbo codng Algorthm : at the sender sde. For each row (R) of the selected sub bands Encr(Map,R)= E // encrypton step usng chaotc map.

4 8 IJCSS Internatonal Journal of Computer Scence and etwor Securty, VOL.0 o., ovember 00 T.coder (E) =TC // encodng step usng turbo coder n whch the cpher row s encoded End for. For each column (C) of the TC Encr (Map, C) = E // encrypton step usng chaotc map. T.coder (E) =TC // encodng step usng turbo coder n whch the cpher column s encoded End for encrypton procedure s hghly ey senstve and large enough to resst brute force attac. Algorthm : at the recever sde. For each column (C) of the TC Decr (Map, C) = D // decrypton step usng chaotc map. T.decoder (D) =TD // decodng step usng turbo coder n whch the plan-mage column s decoded End for. For each row (R) of the TD Decr (Map, R) = D // decrypton step usng chaotc map. T.decoder (D) =TD // decodng step usng turbo decoder n whch the Plan-mage row s decoded End for 6. Smulaton Results 6. Key Space Analyss Key space sze s the total number of dfferent eys that can be used n the encrypton. For a secure mage encrypton, the ey space should be large enough to mae brute force attacs nfeasble [0]. The proposed cpher has dfferent combnatons of large set of parameters (eys). An mage cpher wth such a long ey space s suffcent for relable practcal use. Fgure 6 clearly shows that the decrypton wth a slghtly dfferent ey fals completely and hence the proposed 6. Statstcal Analyss Fgure 6: Key space analyss It s well nown that many cphers have been successfully analyzed wth the help of statstcal analyss and several statstcal attacs have been devsed on them. Therefore, an deal cpher should be robust aganst any statstcal attac. To prove the robustness of the proposed cpher, we have performed statstcal analyss by calculatng the hstograms as well as the correlatons of two adjacent pxels n the planmage/cpher-mage. 6.. Hstogram of Encrypted Images To prevent the leaage of nformaton to an opponent, t s also advantageous f the cpher-mage bears lttle or no statstcal smlarty to the planmage. An mage hstogram llustrates how pxels n an mage are dstrbuted by graphng the number of pxels at each ntensty level. We have calculated and analyzed the hstograms of several encrypted mages as well as ts orgnal mages that have wdely dfferent content. One typcal example among them s shown n Fg.7 (b). The hstogram of a plan-mage Fg.7 (a) (Pepper mage of sze 56x56 pxels) contans large spes. From Fg. 7(d), t s clear that the hstogram of the encrypted mage s farly unform and sgnfcantly dfferent from the respectve hstograms of the orgnal mage and hence does not provde any clue to employ any statstcal attac on the proposed mage encrypton procedure.

5 IJCSS Internatonal Journal of Computer Scence and etwor Securty, VOL.0 o., ovember Fgure 7 (a) Orgnal mage Fgure 7 (c) Encrypted mage Fgure 7 (b) Hstogram of orgnal mage Fgure 7(d) Hstogram of encrypted mage here s the number of mage pxels. Fgure 8 and 9 demonstrate the correlaton dstrbuton of two horzontally adjacent pxels n plan-mage/cpher-mage (Baboon mage of sze 56x56) for the modfed cpher. The correlaton coeffcents are and -0.0 respectvely for both plan-mage/cpher-mages, whch are far apart. Smlar results for dagonal and vertcal drectons were obtaned as shown n Table. It s clear that there s neglgble correlaton between the two adjacent pxels n the cphermage. However, the two adjacent pxels n the plan-text are hghly correlated. Table : Correlaton coeffcent of two adjacent pxels n orgnal and Encrypted mage Drecton Plan -mage Cpher-mage Horzontal Vertcal Dagonal Fgure 7: Hstogram analyss 6.. Correlaton of Adjacent Pxels In addton to the hstogram analyss, we have also analyzed the correlaton between two vertcally adjacent pxels, two horzontally adjacent pxels and two dagonally adjacent pxels n plan-mage/cpher-mage respectvely. The procedure s as follows: Frst, randomly select 000 pars of two adjacent pxels from an mage. Then, calculate ther correlaton coeffcent usng the followng two formulas: cov( x, y) = E( x E( x))( y E( y)), r = xy cov( x, y ), D( x ) D( y ) where x and y are grey-scale values of two adjacent pxels n the mage. In numercal computatons, the followng dscrete formulas were used: (5) Fgure 8: Horzontal adjacent pxels Correlaton n plan-mage = = E ( x ) x (6) ( ) = ( ( )), = Dx x Ex (7) cov( x, y ) = ( x E ( x ))( y E ( y )), = (8) Fgure 9: Horzontally adjacent pxels Correlaton n cphermage

6 84 IJCSS Internatonal Journal of Computer Scence and etwor Securty, VOL.0 o., ovember Informaton Entropy Analyss Informaton entropy s the mathematcal theory of data communcaton and storage founded n 949 by C.E. Shannon []. Modern nformaton theory s concerned wth error- correcton, data compresson, cryptography, communcatons systems, and related topcs. To calculate the entropy H (m) of a source m, we have: H ( m ) = P ( m )log bts = 0 P ( m ) (9) P represents the probablty of symbol m and the entropy s expressed n bts.. Actually, gven that a practcal nformaton source seldom generates random messages, n general ts entropy value s smaller than the deal one. However, when the messages are encrypted, ther entropy should deally be 8. If the output of such a cpher emts symbols wth entropy less than 8, there exsts certan degree of predctablty, whch threatens ts securty. It can be noted form Table that the entropy of the encrypted mages (n average usng 50 mages) the proposed scheme are very near to 8 compared the mage encrypton scheme presented n []. Table : Entropes of the encrypted mages Encrypton algorthm Entropy Value (average) Modfed AES [] 7.90 Proposed scheme Dfferental Attac Two common measures, PCR and UACI [3-5], are used to test the nfluence of changng a sngle pxel n the orgnal mage on the whole mage encrypted by the proposed scheme. PCR stands for the number of pxels change rate whle pxel of plan mage are changed. Unfed Average Changng Intensty (UACI) measures the average ntensty of dfference between the plan mage and cpher mage. For calculaton of PCR and UACI, let us assume two cphered mages C and C whose correspondng plan mages have only one-pxel dfference. Defne a bpolar array, D, wth the same sze as mages C and C. Then, D(,j) s determned by C(,j) and C(,j), namely, f C(,j) = C(,j) then D(,j) = ; otherwse, D(,j) = 0. PCR and UACI are defned through the followng formulas: D (, j ), j PCR = 00%, W H (0) UACI C (, j) C (, j) 00%, W H 55 =, j () W and H are the wdth and heght of C or C. Tests have been performed on the proposed algorthm, about one-pxel change nfluence on a 56 gray-scale mage of sze We obtaned PCR=99.44% and UACI=3.63%. The results show that a swftly change n the orgnal mage wll result n a sgnfcant change n the cphered mage, so the algorthm proposed has a good ablty to ant dfferental attac. The results s llustrated n table 3, shows that a swftly change n the orgnal mage wll result n a sgnfcant change n the cphered mage, so the algorthm proposed has a good ablty to ant dfferental attac wth compared to mage encrypton based on 3D chaotc map [6]. Table 3: Comparson of dfferental attac analyss. Experments Gesl et al. scheme [6] Proposed scheme PCR 98.53% 99.44% UACI 3.47% 3.63% 6.4 Encrypton Effect Measurement The pea sgnal to nose rato (PSR) n decbels (db) s defned as: MAX PSR = 0 log () 0 RMSE MAX s the mage depth, n ths study 8 pxels depth mage are used whch s gray scale level, so MAX = 8 = 55, and RMSE s the root mean square error and defned as: RMSE = M f ( x, y ) f ( x, y ) (3) M x y where, and M are the wdth and heght of the mages n pxels. f s the orgnal mage and f s the cpher-mage. As llustrated n Table 4, the PSR values accordng to DWT selected sub-band of the proposed scheme compared to the values n Seo et al. scheme [4]. Table 4: The encrypton effect n terms of PSR (n db) Selected DWT sub-band Seo et al scheme [4] Proposed scheme LL LL4-HH

7 IJCSS Internatonal Journal of Computer Scence and etwor Securty, VOL.0 o., ovember Selected DWT sub-band Seo et al scheme [4] Proposed scheme Level Level 4-HH It s showed that the best mage qualty s obtaned when the all Level 4 sub-bands and HH3 sub-band from level 3 are utlzed for combned encrypton and turbo codng, whch gve us the ablty to reduce the computaton tme to mplement the encrypton and therefore preserve wreless energy. 6.5 Encrypton speed analyss Chuanmu algorthm Proposed algorthm 56X56 5X5 04X04 048X048 Fgure 0: Encrypton speed comparson Apart from the securty consderatons, some other ssues for mage encrypton algorthm are mportant aspect, ncludes the runnng speed, partcularly for real tme mage encrypton n wreless-related applcatons. Some expermental tests are gven to demonstrate the effcency of our scheme compared wth other algorthm wth respect to the fastness ssue for Lena mage wth dfferent szes. The tme analyss has been done on a destop computer has the followng specfcaton: Pentum-dual-core processor wth 04 MB RAM runnng wth Mcrosoft wndows 7 as operatng system. Table 5 shows the test results of encpherng speeds of the proposed encrypton algorthm compared wth Chuanmu et al Algorthm [0] for Lena mage wth dfferent szes. 6.5 Bt Error Rate Performance Addtve Whte Gaussan ose (AWG) channel and Bnary Phase Shft Keyng (BPSK) modulaton are consdered. The bt error rate performance of overall system s nvestgated over moble communcaton channels for varous Sgnals to ose Ratos. The bt error rate (BER) s computed after decodng, as a functon of sgnal to nose rato Eb/o where Eb s the energy receved per nformaton bt and o s the nose power spectral densty. The reconstructed mage for channel wth Eb/o=8 db wthout and wth combnaton of turbo codng and D chaotc encrypton are shown n Fgures (a) and (b), respectvely. Table 5: Performance of encrypton speed analyss Image sze Chuanmu et al. [0] Proposed scheme 56X X X Fgure (a) Reconstructed mage wthout turbo codng, PSR=8.86 Fgure (b) Reconstructed mage wth turbo codng, PSR= X We can see from Fgure 0 the proposed algorthm reduce the computaton tme of encrypton process to the half wth compared to Chuanmu et al. Algorthm [8] and ths serve the requrement of wreless channel. From Fgure (a), t s observed that t s not possble to reconstruct the mage clearly wthout the combnaton of turbo codng. But wth combned encrypton and turbo channel codng ( teraton decodng), the mage s reconstructed wthout dstorton and no addtonal retransmsson therefore ncreases the throughput of the system that s defned as the useful transmsson rate n bts/second accountng for the loss due to channel errors. The Eb/o vs. bt error rate (BER) wth and wthout turbo channel codng (wth sngle teraton decodng) s shown n Fgure,

8 86 IJCSS Internatonal Journal of Computer Scence and etwor Securty, VOL.0 o., ovember 00 whch obvously clears that the proposed scheme s effectve for secure mage communcaton over wreless nosy channel. Fgure : Bt Error Rate (BER) Performance over AWG Channel 7. Conclusons In ths paper, combnaton of mage encrypton and error correcton code has been proposed. Image encrypton based on D chaotc maps and error control codng based on turbo channel codng. Smulaton results show that the proposed scheme s effectve and secure. The proposed scheme has larger ey space. It can resst dfferental attac, plantext attac, chosentext nown attacs and varous brute-force attacs. The proposed scheme s suggested for secure mage communcaton over wreless channels. From the results, t s concluded that the scheme s very effectve for secure mage communcaton over wreless nosy channels. Further wors purpose an optmzaton scheme for the securty ssues and error correcton code for wreless mage transmsson. References [] C. anjunda, M. Haleem and R. Chandramoul, Robust Encrypton for Eecure Image Transmsson over Wreless Channels, IEEE ICC Conference, pp.87 9, Korea, May 005 [] C. Mathur, K. arayan and K. Subbalashm, On the Desgn of Error-Correctng Cphers, EURASIP Journal on Wreless Communcatons and etworng, Vol.006, pp.-, ovember 006. [3] M.Wllams, F. J. and. A. Sloane: The Theory of Error Correctng Codes. I and II. Amsterdam: orth-holland Publshng Co., Vol. 6, 977. [4] W. Stallngs, Cryptography and etwor Securty: Prncples and Practce, Prentce-Hall, USA, nd edton, 999. [5] Stnson, D., Cryptography: Theory and Practce, Second Edton. CRC/C&H., 00. [6] J. Fowler and B. Popescu, An Overvew on Wavelets n Source Codng, Communcatons, and etwors, EURASIP Journal on Image and Vdeo Processng, Vol. 007, pp. -7, Aprl 007. [7] Deergha Rao, A Robust and Secure Scheme for Image Communcaton over Wreless Channels, IEEE CAS on ETW Conference, pp.88-9, 005. [8] A. Padmaja and M. Shameem, Secure Image Transmsson over Wreless Channels, IEEE ICCIMA Conference, Svaas, Taml adu, pp.44-48, January 007. [9] D. Glgoros, S. Knapsog, and S. Andova, Cryptcodng - Encrypton and Error Correcton Codng n a Sngle Step, Internatonal Conference on Securty and Management, pp.-7, June 006. [0] H. Cam, V. Ozduran and O. Ucan, A Combned Encrypton and Error Correcton Scheme: AES-Turbo, Journal of electrcal & electroncs engneerng, Vol., 009, pp [] M. Asm and V. Jeot, On Image Encrypton: Comparson between AES and A ovel Chaotc Encrypton Scheme, IEEE ICSC Conference, 007, pp [] H. Ahmed, H. Kalash, and O. Farag Allah., An Effcent Chaos-Based Feedbac Stream Cpher (ECBFSC) for Image Encrypton and Decrypton, IEEE Informatca, Vol.3, pp. 9, October 007. [3] G. Sheng and G.Qang, The applcaton of Chaos and DWT n Image Scramblng, Informatca Vol.3, pp , October 006. [4] Seo Y., Km D., Yoo J., Dey S. and A. Agrawal, Wavelet Doman Image Encrypton by Subband Selecton and Data Bt Selecton, World Wreless Congress (3G Wreless) Conference, pp.-6, May 003. [5] A. Pommer and A. Uhl, Selectve Encrypton of Wavelet Pacet Subband Structures for Obscured Transmsson of Vsual Data, IEEE Benerux Sgnal Processng Symposum, pp. 5-8, 00. [6] M. El-lsandaran, S. Darwsh and S. Abuguba, A Robust and Secure Scheme for Image Transmsson over Wreless Channels, IEEE ICCST Conference, Prague, Czech Republc, pp. 5 55, October 008. [7] K.Deergha and K.Sudha, Chaotc Image Encrypton and Decrypton A Comparatve Study, Proc. of Internatonal Conference on Systemcs, Cybernetcs and Informatcs, Hyderabad, pp , -5 Feb.004. [8] J. Luo and H. Sh, Research of Chaos Encrypton Algorthm Based on Logstc Mappng, IEEE Internatonal Conference on Intellgent Informaton Hdng and Multmeda, Pasadena, CA, USA pp , December 006. [9] C.Berrou and A. Glaveux,"ear Optmum Error Correctng Codng and Decodng: Turbo Codes."IEEE transactons on communcatons Vol.44, o: 0, pp.6-7, 996. [0] Chuanmu L., Lanx H., A ew Image Encrypton Scheme based on Hyperchaotc Sequences, IEEE IWASID Worshop, 007, pp [] Shannon CE., Communcaton Theory of Secrecy System, Bell Syst Tech. J 949;8: [] M. Zeghd, M. Machhout, And R. Tour, " A Modfed AES Based Algorthm for Image Encrypton", Waset, Vol., 008.

9 IJCSS Internatonal Journal of Computer Scence and etwor Securty, VOL.0 o., ovember [3] S. Behna, A. Ahshan, and A. Ahavan,"A Fast Chaotc encrypton scheme based on pecewse nonlnear chaotc Maps". Physcs Letters A 366 (007) [4] Fuyan S.,Shutang Lu, Zhongqn L, and Zongwang Lü, " A ovel Image Encrypton Algorthm based on Spatal Chaos Map," Chaos Solutons and Fractals 38 (008) [5] Ibrahm F. Elashry, S. El-Rabae, and Fath E. Abd El- Same, "Homomorphc Image Encrypton," J. Electron. Imagng Vol. 8, Jul. 4, 009. [6] Gesl J. and Vlce K., Image Encrypton Based On Strange Attractor, Internatonal Journal on Graphcs, Vson and Image Processng, Vol.9, o., pp.9-6, 009.