An Efficient Chaos-Based Feedback Stream cipher (ECBFSC) for Image Cryptosystems

Transcription

1 An Effcent Chaos-Based Feedback Stream cpher (ECBFSC) for Image Cryptosystems Hossam El-dn H. Ahmed, Hamdy M. Kalash, and Osama S. Farag Allah Abstract. The chaos based cryptographc algorthms have suggested some new and effcent ways to develop secure mage encrypton technques. Towards ths drecton, ths paper presents an effcent chaos-based feedback stream cpher (ECBFSC) for mage cryptosystems. The proposed stream cpher s based on the use of a chaotc logstc map and an external secret key of 256-bt. The ntal condton for the chaotc logstc map s derved usng the external secret key by provdng weghtage to ts bts correspondng to ther poston n the key. Further, new features of the proposed stream cpher nclude the heavy use of data-dependent teratons, data-dependent nputs, and the ncluson of three ndependent feedback mechansms. These proposed features are verfed to provde hgh securty level. A complete specfcaton for the proposed ECBFSC s gven. Several test mages are used for nspectng the valdty of the proposed ECBFSC. The results of several expermental, key space analyss, statstcal analyss, and key senstvty tests show that the proposed ECBFSC provdes an effcent and secure way for real-tme mage encrypton and transmsson from the cryptographc vewpont. Keywords: Stream cpher, Chaos, Logstc map, and Securty analyss. Introducton Durng the last decade, the use of computer networks has grown spectacularly, and ths growth contnues unabated. Almost all networks are beng nstalled, nterconnected, and connected to the global nternet. Today more and more nformaton has been transmtted over the nternet. The nformaton s not only text, but also audo, mage, and other multmeda. Images have been wdely used n our daly lfe. However, the more extensvely we use the mages, the more mportant ther securty wll be. For example, t s mportant to protect the dagrams of army emplacements, the dagrams of bank buldng constructon, and the mportant data captured by mltary satelltes. In addton, the number of computer crmes has ncreased recently. Image securty has become an mportant topc n the current computer world. Many encrypton methods have been proposed n lterature, and the most common way to protect large multmeda fles s by usng conventonal encrypton technques. Implementatons of popular publc key encrypton methods, such as RSA or El-Gamal [] cannot provde sutable encrypton rates, whle securty of these algorthms reles on the dffculty of quckly factorzng large numbers or solvng the dscrete logarthm problem, topcs that are serously challenged by recent advances n number theory and dstrbuted computng. On the other hand, prvate key bulk encrypton algorthms, such as Trple DES or Blowfsh [2], are more sutable for transmsson of large amounts of data. However, due to the complexty of ther nternal structure, they are not partcularly fast n terms of executon speed and cannot be concsely and clearly explaned, so that to enable detecton of cryptanalytc vulnerabltes. Chaotc maps present many desred cryptographc qualtes such as smplcty of mplementaton that leads to hgh encrypton rates, and excellent securty. In ths paper we propose an effcent chaos-based feedback stream cpher (ECBFSC) for mage cryptosystems. The proposed ECBFSC works usng an teratve cpher mechansm that s based on a chaotc logstc functon. The encrypton module encrypts the mage pxel-by-pxel, takng nto consderaton, n each teraton, the values of the prevously encrypted pxels. Ths feedback property, combned wth the external secret key of 256-bt, makes our stream cpher robust aganst cryptanalytc attacks. Furthermore a smple mplementaton of ECBFSC acheves hgh encrypton rates on generalpurpose computers. The rest of ths paper s organzed as follows: Secton 2 surveys some related mage cryptosystems. We dscuss some characterstcs of an mage cryptosystem and research ssues of an mage cryptosystem n Sectons 3 and 4 respectvely. Secton 5 presents chaos and cryptography ncludng characterstcs and analyss of chaotc logstc map. Secton 6 examnes the step by step procedure of SITIS

2 encrypton/decrypton modules for the proposed ECBFSC. Secton 7 explores desgn Prncples of the ECBFSC. Test, verfcaton and effcency of the proposed ECBFSC are gven n Secton 8. Secton 9 dscusses the detaled securty analyss of the proposed ECBFSC ncludng key space analyss, statstcal analyss, and senstvty analyss wth respect to key and plantext. Performance evaluaton of the proposed ECBFSC s explored n Secton 0. Fnally, Secton concludes ths paper. 2 Related Image Cryptosystems Bourbaks and Alexopoulos [3] developed method to encrypt mages. Ths method converts a 2D mage nto a D lst, and employs a SCAN language [4] to descrbe the converted result. In ths language, there are several SCAN letters. Each SCAN letter represents one knd of scan order. Dfferent knds of combnatons of SCAN letters may generate dfferent knds of secret mages. After determnng the combnaton of SCAN letters, the scheme then generates a SCAN strng. Ths strng defnes the scan order of the orgnal mage. Next, ths method scans the orgnal mage n the determned order and, moreover, encrypts the SCAN strng by usng commercal cryptosystems. Snce the llegal users cannot obtan the correct SCAN strng, the orgnal mage s therefore secure. There s no mage compresson n ths method. Therefore, the sze of the mage s very large, and thus t s neffcent to encrypt or decrypt the mage drectly. Kuo proposed an encrypton method that referred to the mage dstorton [5]. Ths method obtans the encrypted mage by addng the phase spectra of the planmage wth those of another key mage. Snce the phase spectra of the orgnal mage are randomly changed, the cphermage s unrecognzable. Thus ths method s safe, but no mage compresson s consdered. Chang and Lou [6] proposed an encrypton method for mages. Ths method employs two technologes to acheve the compresson and encrypton purposes. They are the quadtree data structure and the SCAN language, respectvely. Ths method frst compresses the orgnal mage by usng a quadtree, and then encrypts the compressed data by SCAN. So, ths method can compress and encrypt mages concurrently. Quadtree s notably a lossless data compresson technology. Therefore, ths method s also lossless. Chn-Chen Chang, Mn-Shan Hwang, and Tung-Shou Chen [7] use one of the popular mage compresson technques, vector quantzaton to desgn an effcent cryptosystem for mages. The scheme s based on vector quantzaton (VQ), cryptography, and other number theorems. The mages are frst decomposed nto vectors and then sequentally encoded vector by vector. Frdrch [8] demonstrated the constructon of a symmetrc block encrypton technque based on two-dmensonal standard baker map. There are three basc steps n the method of Frdrch [8]: (a) choose a chaotc map and generalze t by ntroducng some parameter, (b) dscretze the chaotc map to a fnte square lattce of ponts that represent pxels, (c) extend the dscretzed map to threedmensons and further compose t wth a smple dffuson mechansm. Scharnger [9] desgned a chaotc Kolmogrov-flow-based mage encrypton technque, n whch whole mage s taken as a sngle block and whch s permuted through a key-controlled chaotc system. In addton, a shft regster pseudo random generator s also adopted to ntroduce the confuson n the data. Yen and Guo [0] proposed an encrypton method called BRIE based on chaotc logstc map. The basc prncple of BRIE s bt recrculaton of pxels, whch s controlled by a chaotc pseudo random bnary sequence. The secret key of BRIE conssts of two ntegers and an ntal condton of the logstc map. Yen and Guo [] also proposed an encrypton method called CKBA (Chaotc Key Based Algorthm) n whch a bnary sequence as a key s generated usng a chaotc system. The mage pxels are rearranged accordng to the generated bnary sequence and then XORed and XNORed wth the selected key. L et al. [2] have proposed a vdeo encrypton technque based on multple dgtal chaotc systems whch s known as CVES (Chaotc Vdeo Encrypton Scheme). In ths scheme, 2n chaotc maps are used to generate pseudo random sgnals to mask the vdeo and to perform pseudo random permutaton of the masked vdeo. Chen et al. [3] have proposed a symmetrc mage encrypton n whch a two-dmensonal chaotc map s generalzed to three-dmenson for desgnng a real tme secure mage encrypton scheme. Ths approach employs the three-dmensonal cat map to shuffle the postons of the mage pxels and uses another chaotc map to confuse the relatonshp between the encrypted and ts orgnal mage. - -

3 3 Characterstcs of an Image Cryptosystem A good nformaton securty system s able to not only protect confdental messages n the text form, but also n mage form. In general, there are three basc characterstcs n the nformaton securty feld: prvacy, ntegrty, and avalablty [4].. Prvacy: an unauthorzed user cannot dsclose a message. 2. Integrty: an unauthorzed user cannot modfy or corrupt a message. 3. Avalablty: messages are made avalable to authorzed users fathfully. A perfect mage cryptosystem s not only flexble n the securty mechansm, but also has hgh overall performance. Thus, besdes the above characterstcs, the mage securty also requres the followng characterstcs:. The encrypton system should be computatonally secure. It must requre an extremely long computaton tme to break, for example. Unauthorzed users should not be able to read prvleged mages. 2. Encrypton and decrypton should be fast enough not to degrade system performance. The algorthms for encrypton and decrypton must be smple enough to be done by users wth a personal computer. 3. The securty mechansm should be as wdespread as possble. It must be wdely acceptable to desgn a cryptosystem lke a commercal product. 4. The securty mechansm should be flexble. 5. There should not be a large expanson of the encrypted mage data. 4 Research Issues of an Image Cryptosystem Accordng to the analyses stated n Secton 2, there are forth research ssues on mage cryptosystems as follows: The frst ssue s to encrypt the mage data usng the same method as for text data. Images are usually represented as 2D arrays. They should be converted nto D arrays before encpherng. Varous encrypton technques can be used and appled on the D lsts such as n [3-5]. Snce the mage s large, t s neffcent to encrypt or decrypt the pcture drectly. Applyng compresson technques to mages and then encryptng the compressed mages s also a way to use standard text encrypton algorthms. The second ssue s to use the specal features of mages. The man feature of an mage s that t allows a bt of dstorton. Therefore, pcture data can be compressed before transmttng, and be lossy decompressed wth a small dstorton after recevng the mage compresson. There are many lossy compresson technques for mages. Ths ssue s to encrypt the compressed mage usng the same method as for the text data. Snce the sze of the compressed mage s usually larger than that of text data, t s also nvald to reduce the sze of the pcture by mage compresson before encpherng. Chang and Lou's mage cryptosystem [6] s n ths form. The thrd ssue depends on the use of vector quantzaton (VQ), cryptography, number theorems and compresson. The auxlary data s encrypted only by some encrypton algorthms such as n [7]. Snce the sze of the auxlary data s usually less than that of the compressed mage, the tme complexty for encpherng auxlary data s less than that of the above two ssues. The forth ssue depends on chaotc maps that are consdered as an effcent canddate for desgn of chaos based encrypton technques such as n [8-3]. The proposed ECBFSC belongs to ths ssue. 5 Chaos and Cryptography The close relatonshp between chaos and cryptography makes chaos based cryptographc algorthms as a natural canddate for secure communcaton and cryptography Chaos based encrypton technques are consdered good for practcal use as these technques provde a good combnaton of speed, hgh securty, complexty, reasonable computatonal overheads and computatonal power etc

4 5. characterstcs of the chaotc maps The characterstcs of the chaotc maps have attracted the attenton of cryptographers snce t has many fundamental propertes such as ergodcty, senstvty to ntal condton and system parameter, and mxng property, etc [5-6]. Most propertes are related to some requrements such as mxng and dffuson n the sense of cryptography. Therefore, chaotc cryptosystems have more useful and practcal applcatons. 5.2 The logstc map and ts analyss One of the smplest chaos functons that have been studed recently for cryptography applcatons s the logstc map. The logstc map functon s expressed as: X n+ = rx n ( X n ) () Where X takes values n the nterval [0,]. It s one of the smplest models that present chaotc n behavor [7]. The parameter r can be dvded nto three segments, whch can be examned by experments on followng condtons: X 0 = When r [0,3] as shown n Fg. (a), the calculaton results come to the same value after several teratons wthout any chaotc behavor. When r [3,3.57], the phase space concludes several ponts only, as showed n Fg. (b), the system appears perodcty. When r [3.57,4], t becomes a chaotc system wth perodcty dsappeared as shown n Fg. (c). So we can draw the followng conclusons: () For r [0,3.57], the ponts concentrate on several values and could not be used for mage cryptosystem. (2) For r [3.57,4], the logstc map exhbts chaotc behavor, and hence the property of senstve dependence [8]. So t can be used for mage cryptosystem. 6 The Proposed ECBFSC In ths secton, we dscuss the step by step procedure of the proposed ECBFSC for encrypton as well as decrypton process. The proposed ECBFSC conssts of two man modules, the encrypton and decrypton module. 6. The encrypton module An overvew of ECBFSC encrypton module s depcted n Fg. 2. the proposed ECBFSC s a smple block cpher wth block sze of 8-bt and 256-bt secret key. The key s used to generate a pad that s then merged wth the planmage a byte at a tme.. For the encrypton/decrypton, we dvde planmage/cphermage nto blocks of 8-bts. Plantext and cphertext of blocks can be represented as P = P P P P... (2) P C C = C C C C... (3) The proposed mage encrypton process utlzes an external secret key of 256-bt long. Further, the secret key s dvded nto blocks of 8-bt each, referred as sesson keys. K = K K 2 K 3K 4...K 64 (n hexadecmal) (4) Here, K 's are the alphanumerc characters (0 9 and A F) and each group of two alphanumerc characters represents a sesson key. Alternatvely, the secret key can be represented n ASCII mode as K = K K 2 K 3K 4...K 32 (n ASCII) (5) Here, each K represents one 8-bt block of the secret key.e. sesson key

5 3. The ntal condton ( X 0 ) for the chaotc map and the ntal code C 0 are generated from the sesson keys as: 32 (6) R = ( M[ ]) = K X = R R (7) 0 32 (8) C 0 = ( K ) mod 256 = here K,, and M are, respectvely, the nteger equvalent of the th sesson key, the floor functon, and mappng from the sesson, key space, all ntegers between 0 and 255, nto the doman of the logstc map, all real numbers n the nterval [0,]. 4. Read a byte from the mage fle (that represent a block of 8-bts) and load t as planmage pxel P. 5. Encrypton of each planmage pxel P to produce ts correspondng cphermage pxel be expressed mathematcally as: # C 2 ( ) = P + M rx X mod 256 (9) = Where X represents the current nput for logstc map and computed as: = M [ X + C K ] # s the number of teraton of logstc map for ts current nput # = + + C X + (0) X and calculated as: K () And M2 maps the doman of the logstc map, [0,], back nto the nterval [0,255]. 6. Repeat steps 4-5 untl the entre mage fle s exhausted. C can 6.2 The decrypton module Decrypton s very smple; the same pad s generated but ths tme un-merged wth the cphertext to retreve the plantext. The dagram of ECBFSC decrypton module s gven n Fg. 3. The decrypton module receves an encrypted mage (cphermage) and the 256-bt secret key and returns the orgnal mage (planmage). In partcular, the decrypton module works n the same way as the encrypton module but now the output of the logstc map s subtracted from the correspondng cphermage pxel C provdng the planmage pxel P. The output of the decrypton module s the orgnal mage (planmage). Decrypton of each cphermage pxel C to produce ts correspondng planmage pxel expressed mathematcally as: # P 2 ( ) = C M rx X mod 256 (2) = P can be 7 Desgn Prncples of the Proposed ECBFSC The basc concept s that the encrypton of each part of the planmage depends not only on the key, but also on the prevous cphermage. The use of feedback mechansm has two desrable benefts. The frst beneft s that there can be no smple perodcty n the encrypted mage (cphermage) because the encrypton of each planmage pxel depends not only on the encrypton key, but also on the prevous cphermage pxel. The second beneft s that any changes n the planmage are cascaded forward throughout the cphermage, whch - 4 -

6 means that two almost dentcal planmages wll encrypt to completely dfferent cphermages. Ths senstvty to the planmage s also a plus to the securty of the proposed ECBFSC. The proposed ECBFSC makes heavy use of data-dependent essentals. Ths appears for the current nput of logstc map, whch s data-dependent snce t s computed as a functon of the current sesson key K, prevous computed cpher pxel C and prevous logstc output. Also, the number of teratons # for the chaotc logstc map s data-dependent snce t s computed as a functon of current sesson key K + and prevous computed cpher pxel C. As we encrypt each new block, the counter used to keep track of the current sesson key, s ncremented. The output of the logstc map s then merged wth the planmage to gve the cphermage. 8 Test, Verfcaton and Effcency of ECBFSC Results of some experments are gven to prove ts effcency of applcaton to dgtal mages. We use the gray-scale mages--lena and Effel Tower, each of sze 256 x 256, gray-scale (0-255) as the orgnal mages (planmages) and the secret key (n ASCII) s used for encrypton whose sze s 256-bt. The encrypted mages are depcted n Fgs. 4(b)- 5(b). As shown, the encrypted mages (cphermages) regons are totally nvsble. The decrypton method takes as nput the encrypted mage (cphermage), together wth the same secret key (n ASCII). The decrypted mages are shown n Fgs. 4(c)-5(c). The vsual nspecton of Fgs. (4-5) shows the possblty of applyng the proposed ECBFSC successfully n both encrypton and decrypton. Also, t reveals ts effectveness n hdng the nformaton contaned n them. 9 Securty Analyss and Test Results A good encrypton procedure should be robust aganst all knds of cryptanalytc, statstcal and brute-force attacks. In ths secton, we dscuss the securty analyss of the proposed ECBFSC such as key space analyss, statstcal analyss, and senstvty analyss wth respect to the key and planmage to prove that the proposed ECBFSC s secure aganst the most common attacks [9-22]. 9. Key space Analyss For a secure mage cryptosystem, the key space should be large enough to make the brute force 256 attack nfeasble. The proposed ECBFSC has 2 dfferent combnatons of the secret key. An mage cpher wth such a long key space s suffcent for relable practcal use. In the proposed ECBFSC, a chaotc logstc map s employed whch s senstve on the ntal condton. The ntal condton for logstc map s calculated from the secret key. Addtonally the number of teratons supported by the logstc map module s between 0 and 767, as cpher pxels take values n the nterval [0,52] and the sesson keys take values n the nterval [0,255]. 9.2 Statstcal Analyss It s well known that many cphers have been successfully analyzed wth the help of statstcal analyss and several statstcal attacks have been devsed on them. Therefore, an deal cpher should be robust aganst any statstcal attack. To prove the robustness of the proposed ECBFSC, we have performed statstcal analyss by calculatng the hstograms and the correlatons of two adjacent pxels n the planmage/cphermage

7 9.2. Hstograms analyss To prevent the leakage of nformaton to an opponent, t s also advantageous f the cphermage 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 color ntensty level. We have calculated and analyzed the hstograms of the several encrypted mages as well as ts orgnal mages that have wdely dfferent content. One typcal example among them s shown n Fg. 6(b). The hstogram of a planmage contans large spkes. These spkes correspond to color values that appear more often n the planmage. The hstogram of the cphermage as shown n Fg. 6(d), s more unform, sgnfcantly dfferent from that of the orgnal mage, and bears no statstcal resemblance to the planmage. It 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 attack on the proposed mage encrypton procedure Correlaton coeffcent analyss 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 planmage/cphermage 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)), (3) cov( x, y) r = (4), xy D( x) D( y) Where x and y are the values of two adjacent pxels n the mage. In numercal computatons, the followng dscrete formulas were used: N (5) E( x) = D( x) = x N = N N = cov( x, y) = ( x N N = E( x)) ( x 2, E( x))( y E( y)), Fg. 7 shows the correlaton dstrbuton of two horzontally adjacent pxels n planmage/cphermage for the proposed ECBFSC. The correlaton coeffcents are and respectvely for both planmage/cphermage. Smlar results for dagonal and vertcal drectons are obtaned as shown n Table. It s clear from the Fg. 7 and Table that there s neglgble correlaton between the two adjacent pxels n the cphermage. However, the two adjacent pxels n the planmage are hghly correlated. (6) (7) 9.3 Senstvty Analyss An deal mage encrypton procedure should be senstve wth respect to both the secret key and planmage. The change of a sngle bt n ether the secret key or planmage should produce a completely dfferent encrypted mage. To prove the robustness of the proposed ECBFSC, we wll perform senstvty analyss wth respect to both key and planmage Key senstvty analyss Hgh key senstvty s requred by secure mage cryptosystems, whch means that the cphermage cannot be decrypted correctly although there s only a slght dfference between encrypton or decrypton keys. Ths guarantees the securty of the proposed ECBFSC aganst brute-force attacks to some extent

8 For testng the key senstvty of the proposed mage encrypton procedure, we have performed the followng steps: (a) An orgnal mage n Fg. 8(a) s encrypted by usng the secret key (n ASCII) and the resultant mage s referred as encrypted mage A as shown n Fg. 8(b). (b) The same orgnal mage s encrypted by makng the slght modfcaton n the secret key.e (n ASCII) (the most sgnfcant bt s changed n the secret key) and the resultant mage s referred as encrypted mage B as shown n Fg. 8(c). (c) Agan, the same orgnal mage s encrypted by makng the slght modfcaton n the secret key.e. secret key (n ASCII) (the least sgnfcant bt s changed n the secret key) and the resultant mage s referred as encrypted mage C as shown n Fg. 8(d). (d) Fnally, the three encrypted mages A, B and C are compared. In Fg. 8, we have shown the orgnal mage as well as the three encrypted mages produced n the aforesad steps. It s not easy to compare the encrypted mages by smply observng these mages. So for comparson, we have calculated the correlaton between the correspondng pxels of the three encrypted mages. For ths calculaton, we have used the same formula as gven n Eq. (4) except that n ths case x and y are the values of correspondng pxels n the two encrypted mages to be compared. In Table 2, we have gven the results of the correlaton coeffcents between the correspondng pxels of the three encrypted mages A, B and C. It s clear from the table that no correlaton exsts among three encrypted mages even though these have been produced by usng slghtly dfferent secret keys. Key senstvty analyss shows that changng one bt n encrypton key wll result n a completely dfferent cphermage by more than 99% n terms of pxel gray scale values. Moreover, n Fg. 9, we have shown the results of some attempts to decrypt an encrypted mage wth slghtly dfferent secret keys than the one used for the encrypton of the orgnal mage. Partcularly, n Fg. 9(a) and Fg. 9(b) respectvely, the orgnal mage and the encrypted mage produced usng the secret key (n ASCII) are shown whereas n Fg. 9(c) and Fg. 9(d) respectvely, the mages after the decrypton of the encrypted mage (shown n Fg. 9(b)) wth the secret keys (n ASCII) and (n ASCII). It s clear that the decrypton wth a slghtly dfferent key fals completely and hence the proposed mage encrypton procedure s hghly key senstve Planmage senstvty analyss A desrable property for the proposed ECBFSC s that t s hghly senstve to small change n the planmage (sngle bt change n planmage). To test the nfluence of one-pxel change on the planmage, encrypted by the proposed ECBFSC, two common measures may be used: Number of Pxels Change Rate (NPCR) and Unfed Average Changng Intensty (UACI). Let two cphered mages, whose correspondng planmages have only one pxel dfference, be denoted by C and C2. Label the gray-scale values of the pxels at grd (,j) n C and C2 by C(,j) and C2(,j), respectvely. Defne a bpolar array, D, wth the same sze as mages C and C2. Then, D(,j) s determned by C(,j) and C2(,j), namely, f C(,j) = C2(,j) then D(,j) = ; otherwse, D(,j) = 0. The NPCR s defned as D(, j), j NPCR = 00%, (8) W H Where W and H are the wdth and heght of C or C2. The NPCR measures the percentage of dfferent pxel numbers between planmage and cphermage. The UACI s defned as UACI C(, j) C2 (, j) = 00%, W H 255 (9) j Ths measures the average ntensty of dfferences between the two mages. One performed test s on the one-pxel change nfluence on a 256 grey-level Lena mage of sze 256 x 256. Wth respect to NPCR estmaton. NPCR s obtaned usng the proposed ECBFSC and estmated to be over 99.62% showng thereby that the encrypton scheme s very senstve wth respect to small changes n the planmage

9 Wth respect to UACI estmaton. UACI s calculated to be %80.5 ndcatng that the rate of nfluence due to one pxel change s very large. Generally, these obtaned results for NPCR and UACI show that the proposed ECBFSC s very senstve wth respect to planmage (planmages have only one pxel dfference). 0 Performance Evaluaton Apart from the securty consderaton, some other ssues on mage encrypton are also mportant. These nclude the runnng speed for real-tme mage encrypton/decrypton. The smulator for the proposed ECBFSC s mplemented usng the compler n Borland C++ Development Sute 5.0. Performance was measured on a 2.4 GHz Pentum IV wth 256 Mbytes of RAM runnng Wndows XP. In addton, to mprove the accuracy of our tmng measurements, each set of the tmng tests shown n Table 3 was executed 0 tmes, and we report the average of the tmes thereby obtaned. Table 3 summarzes the encrypton/decrypton speeds for the proposed ECBFSC on mages of dfferent szes. The results emphass that the proposed ECBFSC. Smulaton results show that the average encrypton/decrypton speed s 7.46 MB/Sec for encrypton and 6.63 MB/Sec for decrypton. The peak speed can reach up to 7.6 MB/Sec for encrypton and 6.7 MB/Sec for decrypton. Conclusons In ths paper, a new way of mage encrypton scheme have been proposed whch utlzes a chaosbased feedback cryptographc scheme usng the logstc map and an external secret key of 256-bt. The robustness of the proposed ECBFSC s further renforced by a feedback mechansm, whch leads the cpher to a cyclc behavor so that the encrypton of each plan pxel depends on the key, the value of the prevous cpher pxel and the output of the logstc map. We have carred out key space analyss, statstcal analyss, and key senstvty analyss to demonstrate the securty of the new mage encrypton procedure. Accordng to the results of our securty analyss, we conclude that the proposed ECBFSC s expected to be useful for real-tme mage encrypton and transmsson applcatons. Furthermore, we have also dscussed the characterstcs of mage cryptosystems, chaos and cryptography ncludng characterstcs and analyss of chaotc logstc map, and research ssues related to mage cryptosystems. References. W. Stallngs., "Cryptography and Network Securty: Prncples and Practce," Prentce-Hall, New Jersey, Bruce Schneer, "Appled Cryptography Protocols, algorthms, and source code n C," John Wley & Sons, Inc., New York, second edton, N. Bourbaks and C. Alexopoulos, Pcture data encrypton usng SCAN patterns. Pattern Recognton 25 6 (992), pp Alexopoulos, C., 989. SCAN, A language for 2-D sequental data accessng. Ph.D. Thess, Unversty of Patras, Greece. 5. C.J. Kuo, Novel mage encrypton technque and ts applcaton n progressve transmsson. J. Electron. Imagng 24 (993), pp Chang, H.K., Lou, J.L., 994. An mage encrypton scheme based on quadtree compresson scheme. In: Proceedngs of the Internatonal Computer Symposum, Tawan, pp Chn-Chen Chang, Mn-Shan Hwang, Tung-Shou Chen, A new encrypton algorthm for mage cryptosystems, The Journal of Systems and Software 58 (200), Frdrch Jr, Symmetrc cphers based on two dmensonal chaotc maps, Int. J. Bfurcat Chaos 8 (998) (6), pp J. Scharnger, Fast encrypton of mage data usng chaotc Kolmogrov flow, J. Electronc Eng 7 (998) (2), pp J.C. Yen, J.I. Guo, A new mage encrypton algorthm and ts VLSI archtecture, n: Proceedngs of the IEEE workshop sgnal processng systems, 999, pp J.C. Yen, J.I. Guo, A new chaotc key based desgn for mage encrypton and decrypton, Proceedngs of the IEEE Internatonal Symposum Crcuts and Systems, vol. 4, 2000, pp

10 2. S. L, X. Zheng, X. Mou, Y. Ca, Chaotc encrypton scheme for real tme dgtal vdeo, Proceedngs of the SPIE on electronc magng, San Jose, CA, USA, G. Chen, Y. Mao and C.K. Chu, A symmetrc mage encrypton based on 3D chaotc maps, Chaos Soltons Fractals 2 (2004), pp W. Dffe and M.E. Hellman, New drectons n cryptography. IEEE Trans. Inf. Theory 22 (976), pp M. S. Baptsta, "Cryptography wth chaos". Phys. Lett. A, vol.240, pp.50-54, G. Jakmosk and L. Kocarev, "Chaos and Cryptography: Block Encrypton Cphers Based on Chaotc Maps," IEEE Transactons on Crcuts and Systems-I: Fundamental Theory and Applcatons, vol. 48, no. 2, February R. Devaney, "An Introducton to Chaotc Dynamcal Systems," 2nd ed. Redwood Cty, CA: Addson- Wesley, Steven Henry Strogatz, "Nonlnear dynamcs and chaos: Wth applcatons to physcs, bologym chemstry, and engneerng," frst ed., Addson-Wesley Publshng Company, Readng, Massachusetts, Shujun L, Guanrong Chen and Xuan Zheng, "Chaos-based encrypton for dgtal mages and vdeos," chapter 4 n Multmeda Securty Handbook, February Yaobn Mao and Guanrong Chen, "Chaos-based mage encrypton," n Eduardo Bayro-Corrochano, edtor, Handbook of Computatonal Geometry for Pattern Recognton, Computer Vson, Neural Computng and Robotcs. Sprnger-Verlag, Hedelberg, Aprl Yaobn Mao, Guanrong Chen, and Charles K. Chu, "A novel fast mage encrypton scheme based on 3D chaotc Baker maps," Int. J. Bfurcaton and Chaos n June Yaobn Mao, Guanrong Chen, and Shguo Lan, "A symmetrc mage encrypton scheme based on 3D chaotc Cat maps," Chaos, Soltons and Fractals 2, pages , a) teraton property when r = 2.8 b) teraton property when r = 3.2 c) teraton property when r = 3.8 Fg. Analyss of Logstc Map Orgnal mage K + K + M + X L # r =3.9 M2 P + C Encrypted mage Fg. 2 Dagram of Encrypton Module K + K + M + X L # r =3.9 M2 C - Encrypted mage P Orgnal mage Fg. 3 Dagram of Decrypton Module - 9 -

11 a) Orgnal mage b) Encrypted mage c) Decrypted mage Fg. 4 Applcaton of ECBFSC to Lena Planmage/Cphermage a) Orgnal mage b) Encrypted mage c) Decrypted mage Fg. 5 Applcaton of ECBFSC to Effel Tower Planmage/Cphermage a) Orgnal mage b) Hstogram of orgnal mage c) Encrypted mage d) Hstogram of encrypted mage Fg. 6 Hstograms of the planmage and the cphermage Fg. 7 Two horzontally adjacent pxels Correlaton n planmage/cphermage Orgnal mage Encrypted mage wth key " " Encrypted mage wth key " " Encrypted mage wth key " " Fg. 8 Key senstve test result wth ECBFSC

12 Orgnal mage Encrypted mage wth key " " Decrypted mage wth key " " Decrypted mage wth " " Fg. 9 Key senstve test result 2 wth ECBFSC Table. Correlaton coeffcents n planmage/cphermage Drecton of Adjacent pxels Planmage Cphermage Horzontal Vertcal Dagonal Table 2. Correlaton coeffcents between the correspondng pxels of the three dfferent encrypted mages obtaned by usng slghtly dfferent secret key of an mage shown n Fg. 8. Image Image Correlaton coeffcent Encrypted mage A Fg. 8(b) Encrypted mage B Fg. 8(c) Encrypted mage B Fg. 8(c) Encrypted mage C Fg. 8(d) Encrypted mage C Fg. 8(d) Encrypted mage A Fg. 8(b) Table 3 Encpherng/decpherng speed test results of the proposed ECBFSC Image sze (n pxels) Colors Encrypton n Sec. Decrypton n Sec. 256 x < < x < < x x x 52 2 < < x x x x x x x x x x x