Robust Image Encryption Based on Balanced Cellular Automaton and Pixel Separation

Transcription

1 548 D. TRALIC, S. GRGIC, ROBUST IMAGE ENCRYPTION BASED ON BALANCED CA AND PIXEL SEPARATION Robust Image Encrypton Based on Balanced Cellular Automaton and Pxel Separaton Djana TRALIC, Sonja GRGIC Dept. of Wreless Communcatons, Faculty of Electrcal Engneerng and Computng, Unversty of Zagreb, Unska 3, HR000 Zagreb, Croata Manuscrpt receved March 0, 206 Abstract. The purpose of mage encrypton s to protect content from unauthorzed access. Image encrypton s usually done by pxel scramblng and confuson, so process s possble to reverse only by knowng secret nformaton. In ths paper we ntroduce a new method for dgtal mage encrypton, based on a 2D cellular automaton and pxel separaton. Novelty n the proposed method les n the applcaton of the balanced 2D cellular automata wth extended Moore neghborhood separately on each level of pseudorandom key-mage. Ths process extends key space several tmes when compared to the prevous methods. Furthermore, pxel separaton s ntroduced to defne operaton for each pxel of the source mage. Thanks to pxel separaton, decrypton process s more dffcult to conduct wthout knowng secret nformaton. Moreover, encrypton s robust aganst dfferent statstcal attacks and analyss, does not affect mage qualty and can cope wth loss of encrypted mage content. Keywords Image securty, encrypton, decrypton, cellular automaton, statstcal tests. Introducton Nowadays mages are wdely used n varous applcatons, such as communcaton, multmeda systems, medcal magng, telemedcne, montorng, and mltary communcaton, so ther securty s becomng ncreasngly mportant. Generally, encrypton s used to effectvely protect mages transmtted through publc channels, because t makes mages unrecognzable, unless decrypted by a secret key. There are several conventonal encrypton methods, but these algorthms have lmtaton n encryptng mages such as low effcency, bulky data, and hgh correlaton among pxels []. Image encrypton algorthm s consdered relable f: the scheme s secure aganst dfferent statstcal and plantext attacks; there s no vsual degradaton of decrypted mage; corrupton of encrypted mage part does not propagate on the whole decrypted mage; key space s large enough to make t mpossble to guess correct secret nformaton; encrypted mages show random propertes. Good canddates for mage encrypton are cellular automata (CA), thanks to ther propertes lke parallelsm, homogenety and unpredctablty [2 4]. Cellular automata are dstrbuted systems wth a large number of rules that can smulate complcated and pseudorandom behavors [5]. In recent years, CA has been used for mage cryptography n followng areas: watermarkng [6], [7], secret mage sharng [8 ], and mage encrypton [2 8]. The frst mage encrypton system based on cellular automata was desgned wth one-dmensonal elementary CA [6]. Ths approach uses only two neghbors to defne CA rules so ts key space s qute small. Later, 2D cellular automata are ntroduced for mage encrypton. Most of approaches use Von Neumann neghborhood [2], [3], [9], [20], or ncomplete Moore neghborhood [4], whch also nfluences the capacty of key space. Later, mage encrypton method based on Moore and extended Moore neghborhoods s ntroduced [2], but t reduces possble key space volume due to Moore neghborhood sze. Chaos theory s appled n [22], however t s qute complex to be used for mage encrypton and t results n a very small key space volume. In ths paper we ntroduce a new method for dgtal mage encrypton, based on a 2D cellular automaton and pxel separaton. Frst, sender and recever exchange secret nformaton: seed and separaton values. Then 2D cellular automaton wth extended Moore neghborhood s used to generate pseudorandom key-mage based on selected seed. Encrypton s then performed by combnng source mage wth key-mage. In ths process pxel separaton s appled to defne operaton for each pxel based on secret separaton values. Operaton for each pxel s selected among ten possble operatons makng t more dffcult to decrypt the encrypted mage wthout secret nformaton. The rest of the paper s organzed as follows. In Sec. 2 the proposed method s presented. Secton 3 brngs smulaton results, and Secton 4 contans comparson to state of the art methods. Concluson s gven n Sec. 5. DOI: 0.364/re SIGNALS

2 RADIOENGINEERING, VOL. 25, NO. 3, SEPTEMBER Proposed Method The proposed method s based on the dea of combnng a source mage (the mage that should be encrypted) wth a key-mage. Pseudorandom key-mage s generated usng balanced cellular automaton rules, whch are appled on bnary levels. Also, rules are formed on extended Moore neghborhood whch extends key space. In encrypton process, pxel separaton s ntroduced to make decrypton more robust and complcated for unauthorzed party. 2. Cellular Automata Cellular automaton (CA) [24] s a dscrete system that contans a regular grd of cells, each n one fnte state. A CA can be presented by a quadruple [24]: where: C, S, N, f () C s a d-dmensonal cellular space that conssts of c cells,.e. 2-dmensonal bnary mage that conssts of M N values, S s a s-value state space,.e. s = 2 for bnary mages (0 or ), N s an n-cell CA neghborhood,.e. an arbtrarly selected group of n pxels N(p o ) spatally close to the observed pxel p o, Extended Moore neghborhood ncludes 24 pxels around the central pxel. f : S n S s a cell-state transton functon defned as a set of rules that represents the connecton of the selected neghborhood N(p o ) and the value of the observed pxel p o. Therefore, the value of pxel p o n the next tme step depends only on values of pxels n the selected neghborhood N(p o ). By consderng extended Moore neghborhood (n = 25) and bnary mages (s = 2), there are total of s n = 2 25 = possble combnatons of values n neghborhood. Also, there are possble rules. For example, rule 0 means that all combnatons of neghborng elements result n the value of the observed pxel p o equal to 0 (2). Note that a new state of the observed pxel p o for all combnatons of neghborhood presents CA rule s value n the bnary form. o f Np ( o( t))= then po( t+)=0, f Np ( o( t))= then po( t+)=0,... f Np ( ( t))= then p( t+)=0. CA rules that contan equal number of zeros and ones, meanng that half of neghborhood combnatons result n zero and other half n one, are called balanced rules. It can be proved that the mage generated by the balanced CA rules has hgher entropy than the mage generated by the unbalanced CA rules [5]. o (2) 2.2 Encrypton Encrypton of mage s done n three steps. Frst, secret nformaton s generated: seed S s chosen as a random number n the range [0, 2 32 ], and separaton values S v are generated as an arbtrary sequence of numbers from 0 to 9 (correspondng to the number of used operatons). Secret nformaton {S, S v } s transmtted usng secured channel. Then pseudorandom key-mage s created usng cellular automata and secret seed S (see Sec. 2.2.). Fnally, encrypton s done by combnng the key-mage wth the source mage usng pxel separaton algorthm and separaton values S v (see Sec ) Pseudorandom Key-Image Generaton The pseudorandom key-mage s generated by applyng CA rules on pseudorandom bnary levels and combnng t n a new mage. Generaton of the pseudorandom key-mage s done usng the followng steps: Generaton of pseudorandom numbers: Seed S s used to generate pseudorandom numbers K, = {, 2,, 8}, n range [0, ]. Each pseudorandom number K s dedcated to one bnary level of a resultng key-mage (ndex marks dedcated bnary level). Generaton of bnary levels: Each number K s frst used to generate M N pseudo random bnary matrx B (M N correspond to the sze of the source mage). Selecton of CA rules: Number K s used to choose CA rule R for bnary level. CA rule R s chosen as the balanced rule nearest to the number K, and defned as: R 2 K b Kb, nn( K ) 2 Kb balanced rule (3) where nn represents the nearest neghbors functon. In chosen CA confguraton wth 25 neghbors, there are balanced rules. Applcaton of CA rules: CA rule R s appled on M N bnary matrx B to get a new M N bnary matrx B c. For each element n matrx B, extended Moore neghborhood of 25 elements (24 neghbors around the central element) s consdered to defne a new value n matrx B c accordng to selected CA rule R. f ( B( Np ( o)) de2b( Rl ( ))) (4) then B ( p ) R( l) c o where de2b represents decmal to bnary functon. Key-mage formng: bnary mages B c, = {, 2,, 8} are formed nto a pseudorandom key-mage K by usng matrx B c as the -th bnary level of keymage K.

3 550 D. TRALIC, S. GRGIC, ROBUST IMAGE ENCRYPTION BASED ON BALANCED CA AND PIXEL SEPARATION Pxel Separaton After generaton of pseudorandom key-mage K, encrypton of mage s done usng pxel separaton: Separaton values S v are used to make a new order of operatons for combnng source mage and keymage. Ths s done by changng ndex of each operaton accordng to secret separaton values S v. O xor( I( x, y), K( x, y)), Sv(0) O xor( I( x, y), K( x, y)), Sv() O xor(shft( I( x, y),2), K( x, y)), Sv(2) OSv(3) xor(shft( I( x, y),2), K( x, y)), O xor(shft( I( x, y),4), K( x, y)), Sv(4) OSv(5) xor(shft( I( x, y),4), K( x, y)), O xor(shft( I( x, y),6), K( x, y)), Sv(6) OSv(7) xor(shft( I( x, y),6), K( x, y)), O xor( I ( x, y), K( x, y)), Sv(8) O xor( I ( x, y), K( x, y)). Sv(9) Note that last 2 operatons nvolve changng of the most sgnfcant bt of pxel I(x, y). We ntroduce 0 dfferent operatons because smaller sets do not ntroduce enough confuson n pxel values. Pseudorandom key-mage K s used to determne operaton type ndex (T) for each pxel n the source mage usng the last dgt at each locaton. (5) T mod(k,0). (6) In ths step, pxels are separated n ten dfferent groups accordng to operaton type, and we call ths process pxel separaton. Each pxel n source mage I(x, y) s then encrypted by applyng operaton O T(x, y) on mage I(x, y) and keymage K(x, y). The result of encrypton s encrypted mage E. Advantage of ths process les n the fact that encrypted mage s more dffcult to decrypt, because decrypton requres correct guessng of the used operaton for each pxel n the source mage. 2.3 Decrypton Decrypton of an encrypted mage s done usng the followng steps: Recever receves secret nformaton (seed S and separaton values S v ) through a protected channel. Recever uses seed S to generate pseudorandom keymage. Recever uses separaton values S v to make a new order of operatons for combnng encrypted mage E and key-mage K, as descrbed n Sec Note that the same operaton set s appled n decrypton process, but encrypted mage E s used nstead of source mage I n (5). The result of decrypton s the decrypted mage, whch s dentcal to the source mage. 3. Smulaton Results and Analyss Dfferent analyss and smulatons are conducted to demonstrate performance of the proposed method. To demonstrate encrypton property, results are presented for the followng fve mages: Lena.jpg, Cameraman.png, Baboon.jpg, Crcle.bmp and plan mage of sze Algorthm s developed n Matlab 203b, and run on computer wth Intel Core 7 processor under Wndows 0 operaton system. Smulaton s appled for a random seed and separaton values (as hghlghted for each presented example). 3. Key Space Analyss Secret nformaton used for encrypton of a source mage s noted as a key. The frst part of the key s seed S, selected randomly n range [0, 2 32 ]. Note that upper lmt s set accordng to Matlab lmt for pseudo number generator nput. Therefore, probablty to select the rght seed s equal to: p. 2 0 s (7) 32 Havng n mnd that we use 25 CA neghbors, there are 2 25 = possble bnary combnatons of bnary values 0 and, and possble rules. Probablty to select the rght CA rule for one bnary level s: pr. (8) The second part of the key contans separaton values. There are 0! = possble combnatons to use. Possblty of usng the rght combnaton s: psv. (9) 0! The volume of the proposed secret key s very large due to the fact that dfferent CA rule s selected for each bnary level of the key, and can be defned as: V 0! (0) Key Senstvty Test To test key senstvty, a mage (Lena.jpg) s encrypted by usng the seed S = Then, the

4 RADIOENGINEERING, VOL. 25, NO. 3, SEPTEMBER least sgnfcant bt of the seed s changed, so that the orgnal seed becomes S 2 = , and used to encrypt the same mage. Fnally, the two encrypted mages, encrypted by the two slghtly dfferent seeds, are compared. Results are presented n Fg.. The dfference between two mages encrypted wth seeds that dffer n only bt s qute large. Ths llustrates that the proposed method generates uncorrelated key-mages that cannot be predcted. We also calculated the number of pxels change rate (NPCR) between encrypted mages E and E 2 as: D,j ( ),j NPCR( E,E2) 00, NM () E(,j) E2(,j) D,j ( ) 0 otherwse where N and M s the wdth and heght of E and E 2. For two ndependent random mages, the expected value of NPCR s: E(NPCR) = ( 2 ) 00, where L s the number of bts used to represent one pxel of the mage [2]. For 8-bt per pxel gray-scale random mages, E(NPCR) = ( 2 8 ) 00 = %. Value of NPCR n our example s equal to 99.38%, whch proves that the method generates unpredctable key-mages. To measure the average ntensty of the dfferences between the two encrypted mages, the unfed average changng ntensty (UACI) s defned as: E(, j) E2 (, j) UACI ( E, E2 ) 00 (2) NM, j 255 a) Test mage Lena b) Encrypted usng seed S = c) Encrypted usng seed d) Dfference between b) and c) S 2 = Fg.. Examples of encrypton of Lena usng two very smlar seeds. where N and M s the wdth and heght of E and E 2. For two 8-bt per pxel random gray-scale mages, the expected value of UACI s E(UACI) = %. Table presents NPCR and UACI values for all tested mages wth dfferent par of seeds (S, S 2 ). Values of NPCR and UACI ndcate that encrypted mages have good randomness. Image Seed NPCR(E, E 2 ) UACI(E, E 2 ) Lena S = 25, S 2 = % % Cameraman S = 3458, S 2 = % % Baboon S = 54887, S 2 = % % Crcle S = 54, S 2 = % % Plan S = , S 2 = % % Tab.. Pxel change rate and average ntensty of the dfferences between two encrypted mages. 3.3 Image Hstogram To demonstrate robustness of the proposed method, we calculated hstogram and probablty densty functon (pdf) of two orgnal and encrypted mages. In general, more unformed hstogram results n less statstcal attacks. Fgure 2 shows pdfs of Lena and Cameraman and ther encrypted versons. Encrypted mages have almost unform pdfs regardless of the orgnal mages, so statstcal attacks are very dffcult to conduct. Correlaton between pxels s also a good ndcator of securty. The smaller correlaton means the better encrypton effect. To demonstrate encrypton effect, we calculated the correlaton coeffcent as: N ( I, E) D( x) N N N ( I I )( E 2 ( x x) D( I ) D( E) E), (3) where I represents the source mage, E the encrypted verson of the source mage, and N s the total number of pxels. The value of the correlaton coeffcent can vary between and. If s near, mages are correlated and f s near 0, there s a trval correlaton between mages. Correlaton coeffcent for Lena and ts encrypted verson (S = ), shown n Fg..b), s equal to , leadng to concluson that two mages are not correlated. Furthermore, correlaton coeffcent of Lena and ts encrypted verson (Fg..c) wth dfferent seed (S = ) s To better demonstrate correlaton between mages, we calculated correlaton of pxels n vertcal, horzontal and dagonal drectons by randomly selectng 2500 pars of adjacent pxels both from source mage and encrypted mage, and calculate the correlaton coeffcents. Results

5 552 D. TRALIC, S. GRGIC, ROBUST IMAGE ENCRYPTION BASED ON BALANCED CA AND PIXEL SEPARATION a) Baboon encrypted, H = b) Baboon decrypted, H = c) Cameraman encrypted, H = d) Cameraman decrypted, H = a) Lena and Lena encrypted Fg. 3. Entropy of encrypted (S = ) and decrypted mages. b) Cameraman and Cameraman encrypted Image Lena Cameraman Baboon Crcle Plan Fg. 2. Probablty densty functons. Image Lena Lena encrypted S = Cameraman Cameraman encrypted S = Baboon Baboon encrypted S = Crcle Crcle encrypted S = 62 Plan Plan encrypted S = Horzontal Vertcal Dagonal Source Entropy Encrypted Entropy Tab. 3. Comparson of entropy of source and encrypted mages. For mages wth random pxels whch are encoded by 8 bt, entropy should be equal to 8. However, entropy s usually smaller than 8, but a value closer to eght means that the possblty of predctablty s less and the securty level s hgher. Tab. 2. Correlaton between mage pxels. for fve mages and ther encrypted verson are presented n Tab. 2. The proposed algorthm effectvely reduces the correlaton between adjacent pxels for all tested examples. Note that correlaton s especally reduced n the case of plan mage. Fgure 3 shows examples of mage entropy for two encrypted and decrypted mages. Decrypted mages are dentcal to source mages, whch means that the proposed method does not nfluence mage qualty. Also entropy of encrypted mages s very close to 8, whch ndcates ther randomness. Table 3 shows entropy of source mages and ther encrypted versons (seed S = 7529 for all examples). Encrypted mages have entropy close to 8, whch proves that the predctablty s very low. Note that entropy s close to 8 even n the case when plan mage s used as a source mage. 3.4 Informaton Entropy Entropy of message m s one of the mportant features for randomness, defned usng probablty of symbol p(m): H ( m ) p( m ) log 2 ( p( m )). (4) 3.5 Confuson Analyss Confuson refers to makng the relatonshp between the encrypted mage and the prvate nformaton as complex and uncorrelated as possble. We prevously demon-

6 RADIOENGINEERING, VOL. 25, NO. 3, SEPTEMBER strated the dfference between two encrypted mages usng seeds that dffer n only bt (Fg. ). An excellent encrypton algorthm should be senstve to small changes n seed. In other words, a slght change n the key should cause very dfferent results. Fgure 4 demonstrates results of decrypton of encrypted Crcle mage wth dfferent seeds. Furthermore, we smulated encrypton of plan mage usng seed S = Then, encrypted mage s decrypted usng seed that dffers n only one bt (S = ). Results are shown n Fg. 5, where t s possble to notce that the proposed method does not generate relatonshp between plan mage and encrypted plan mage. Also, snce there s only bt dfference between the two seeds, the results show the hgh key senstvty of the proposed CA encrypton scheme. a) Loss of pxels Fg. 7. Survval propertes of the proposed method n the case of loss of the encrypted content. a) Gaussan nose (zero mean and σ2 = 0.0) a) Crcle decrypted usng correct seed S = b) Crcle decrypted usng seed S = Fg. 4. Decrypton of crcle usng seeds that dffer n bt. b) Decrypton of a) b) Salt and paper nose (d = 0.0) Fg. 8. Survval propertes of the proposed method n the case of corrupton of the encrypted mage. Moreover, we tested decrypton n the case when correct seed S s used, but ncorrect separaton values Sv are appled. Results are presented n Fg. 6, showng that small dfference n separaton values order leads to nablty to decrypt mage even f correct seed S s used. Analyss also showed that equal percentage of operaton type s appled to mage pxels and that operatons are dstrbuted randomly on mage. 3.6 Survval Propertes a) Encrypted usng S = a) Decrypted usng S = Fg. 5. Decrypton of plan mage usng seeds that dffer n bt. The proposed method s also robust to loss or corrupton of encrypted mage parts n a way that only the correspondng fracton s affected and the error does not propagate to other parts of the decrypted mage. Good survval propertes assure that a large area of the mage survves so the method s relable n transmssons wth hgh error rate. Fgure 7 demonstrates that loss of mage s part dd not affect other parts of the decrypted mage. Fgure 8 shows the nfluence of nose on the decrypted mage n the case when Gaussan nose and salt and pepper nose s appled on the encrypted mage. Agan, corrupton of some pxels dd not corrupt the whole mage. a) Decrypted usng separaton values Sv = b) Decrypted usng separaton values Sv = Fg. 6. Decrypton of Baboon usng dfferent separaton values. 3.7 Tme of Calculaton Tme of calculaton s an mportant factor for applcaton of any method n the real tme systems. Table 4

7 554 D. TRALIC, S. GRGIC, ROBUST IMAGE ENCRYPTION BASED ON BALANCED CA AND PIXEL SEPARATION Method Encrypton Decrypton Lena 22 ± 0.2 ms 22 ± 0.52 ms Cameraman 2 ± 0.35 ms 2 ± 0.24 ms Baboon 22 ± 0.47 ms 22 ± 0.38 ms Crcle 2 ± 0.6 ms 2 ± 0.9 ms Plan 22 ± 0.03 ms 2 ± 0.83 ms Tab. 4. Tme of calculaton for encrypton and decrypton. contans a calculaton tme of the proposed encrypton and decrypton method for 5 test mages. Note that all mages have the same sze and testng s done n the same condtons. Seed used for testng was set to S = and separaton values were set to S v = Values n Tab. 4 are determned as average values between 00 encrypton/decrypton attempts for each mage. It s possble to see that calculaton tme s qute low and t does not depend on mage content. 4. Comparson to Other Methods The volume of the securty key s much larger than the volume of the key ntroduced n [4], whch s equal to 256. It s also much larger than , 0 294, and whch are the lower bounds of the volume of the securty keys ntroduced n [2], [9], and [20], respectvely. Moreover, t s several tmes larger than the securty key ntroduced n [2], whch s defned as H!e , where H s the heght of the mage. Key space s also much larger than chaos based key space proposed n [22], whch s equal to Table 5 contans comparson of key space. By comparng the entropy wth other methods, t s possble to notce that the proposed method assures hgher entropy than [9], where entropy s and for Lena mage and two dfferent key-mages. The value of entropy for Lena mage s also hgher than as accomplshed wth the method proposed n [2]. Table 6 contans comparson of mage entropy values for Lena mage. Method Key space Von Neumann [2] Incomplete Moore [4] 256 Von Neumann [9] Von Neumann [20] Extended Moore [2] H!e Chaos theory [22] The proposed Tab. 5. Comparson of key space for dfferent methods. Method Entropy Von Neumann [9] Von Neumann [20] Extended Moore [2] Chaos theory [22] The proposed Tab. 6. Comparson of mage entropy for dfferent methods. Method NPCR UACI Von Neumann [20] % 3.82 % Extended Moore [2] % % Chaos theory [22] % % The proposed % % Tab. 7. Comparson of NPCR and UACI for dfferent methods. Values of NPCR and UACI are gven n Tab. 7. The proposed method accomplshed a bt lower value of NPCR, but t s stll above the lmt defned by (2). The value of UACI for the proposed method s hgher than for other methods. 5. Concluson Robust and relable mage encrypton s a key for effectve protecton n transmsson through publc channels. The man dea s to make mages unrecognzable and assure that decrypton s possble only usng a secret key. The proposed method combnes cellular automata and pxel separaton to provde robust mage encrypton. It reles on secret nformaton n the form of seed and separaton values. Encrypton of source mage s accomplshed usng pseudorandom key-mage, created by 2D cellular automaton. Cellular automata are good canddates for generaton of pseudorandom numbers thanks to ther propertes lke parallelsm, homogenety and unpredctablty. Dfferent CA rule s chosen for each bnary level of pseudorandom key-mage based on selected seed. Selecton s lmted to balanced rules, whch results n hgher entropy of keymage. CA rules are appled on extended Moore neghborhood, whch results n larger key space. Fnally, encrypton s performed by combnng source mage and key-mage. Pxel separaton s appled to select rght operaton for each pxel based on secret separaton values. Ten operatons are defned to make decrypton of an mage wthout secret nformaton more dffcult. Key space analyss shows that the proposed method has very large key space, whch s mportant to avod guessng of secret nformaton. Key-mages generated by the proposed method have good randomness property as demonstrated through senstvty test. Randomness s proven also by calculatng the entropy of encrypted mages, whch was very close to 8. Furthermore, mage hstograms are used to show almost unform pdfs of encrypted mages makng statstcal attacks very dffcult to conduct. By calculatng correlaton coeffcent, t s demonstrated that the algorthm effectvely reduces the correlaton between adjacent pxels. Survval propertes n the case of data loss and nose, as well as computatonal tme, are satsfactory for real tme systems. Comparson to the state of the art methods shows that the proposed method accomplshed the largest key space volume whle keepng very good randomness.

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IEEE Transactons on Systems, Man, and Cybernetcs Part B: Cybernetcs, 20, vol. 4, no. 3, p DOI: 0.09/TSMCB About the Authors... Djana TRALIĆ receved her PhD degree n Electrcal Engneerng from the Unversty of Zagreb n 205. Her research nterests nclude sgnal and mage processng, mage forenscs and broadcastng technologes. She s the author of 5 conference papers, one journal paper, one book chapter, and edtor of 3 conference proceedngs. Sonja GRGIĆ receved her PhD degree n Electrcal Engneerng from the Unversty of Zagreb n 996, where she s currently a Professor. Her research nterests nclude mage qualty evaluaton methods, televson sgnal transmsson, vdeo communcaton technologes and mage forenscs. She s the author of 5 book chapters, 20 scentfc journal papers, more than 40 papers publshed on nternatonal scentfc conferences as well as of 5 revewed studes and expert works. She was the edtor of 8 nternatonal conference proceedngs.