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1 3d Iteatoal Cofeece o Multmeda Techology ICMT 2013) Image ecypto va poecto-pusut based bld souce sepaato Luo Shguag1,Luo Chag2,Ca Zhaoqua3 Abstact:A ovel mage cyptosystem by usg poecto pusut based bld souce sepaato s poposed ths wok, whee the platexts eed to be ethe depedet o sub-depedet. I the poposed cyptosystem, fo ecypto, the platexts ae mxed lealy wth each othe fst, ad the mxed olealy wth the cphes. As fo decypto, a poecto pusut based bld souce sepaato method s employed. The pocesses of both ecypto ad decypto ae fast, thus t s sutable fo lage scale of mages. I addto, the cphes ca be used epeatedly. Smulatos ae gve to llustate the avalablty ad the secuty of ou cyptosystem. Key Wods: Image ecypto, bld souce sepaato, poecto pusut I. Itoducto Wth the fast developmet of the electoc commece, a lage umbe of mage sgals ae eeded to tasmt by publc etwoks evey day. Sce cuet etwok systems ae fa fom pefect, the fomato secuty has bee attactg moe ad moe atteto. To potect the keel fomato, mage ecypto becomes a atual choce. Thee exst seveal ecypto methods, such as the tadtoal data ecypto stadad (DES) ad Rvest, Sham, ad Adlema (RSA) [1]-[3], the aalog ecypto [4], the chaotc system based method [5], etc. Recetly, a ew techology based o bld souce sepaato (BSS) has bee appled to mage cyptosystem, whee the decypto s cast to a BSS poblem whch ams to sepaate the mxtues (cphetexts) to the poduct of the mxg coeffcets ad the souces (platexts) [6][7]. The secuty of ths kd of cyptosystem eles o the dffculty of solvg ll-codtoed BSS poblem, stead of the tadtoal appaetly tactablty of the computatoal poblem. The BSS based scheme has bought a ew vewpot fo mage Ths wok was suppoted pat by the Natoal Natual Scece Foudato of Cha ude Gat ad ). 1 LuoShguag,Depatmet of Appled Mathematcs, GuagDog Uvesty of Face, Guagzhou ,Cha 2 LuoChag(luoc1@sa.com),Natoal Egeeg Reseach Cete fo E-Leag, College of Vocatoal ad Cotug Educato,CCNU,Wuha, , P.R. Cha. 3 Ca Zhaoqua,Huzhou Uvesty, Huzhou, , P.R. Cha The authos - Publshed by Atlats Pess 787

2 ecypto, howeve, egadg as the pactcal BSS methods, t suffes fom the espectve toubles, e.g., BSS based o depedet compoet aalyss, the platexts ae equed to be mutually depedet [7], ad oegatve matx factozato based method, the mxg matx should be oegatve [6]. I ths pape, a poecto-pusut (PP) based BSS method s utlzed fo mage ecypto. I the poposed cyptosystem, the platexts ae mxed olealy fo ecypto ad the fast PP algothm s voked fo decypto [8]. Compaed wth the exstg BSS based ecypto method, the poposed scheme ca acheve the decypto esults a shot tme. Thus, t has advatages fo the ecypto of lage scale of mages. Also, due to the usage of the o-egatvty of the mages, t gets out of the platextdepedece estcto. The emade of ths pape s ogazed as follows. I Secto II, the PP based BSS method s toduced, ad the mage cyptosystem s poposed Secto III. I Secto IV, the poposed cyptosystem s tested by dffeet kds of mages. Fally, coclusos ae gve Secto V. The followg otatos ae used the whole pape: x, x Colum vecto, the th elemet of x. X,x, Matx, the th colum of X,the, th ety of X x X t Matx wth t colums II. PP based BSS 2.1 BSS Model BSS ams to sepaate the souce sgals fom the mxtues, whee the mxg matx s ukow. Typcal BSS model s as followg [8] [9]: X AS (1) whee X deotes the obseved mxtues, A deotes the mxg matx, ad S deotes the souce matx.bss algothms ca be able to ecove the souces S fom the mxtues X, wthout kowg the mxg matx. Ths s vey helpful fo sgal decypto, ad thee ae lots of pactcal algothms fo solvg BSS poblem. Hee, fo pocessg the mage sgals whose values ae oegatve, we toduce the followg fast ad effcet poecto pusut (PP) algothm. 2.2 PP Algothm The PP algothm s maly developed [8], ad t s used fo the pocess of oegatve sgals. Based o the aalyss [8], ths algothm s much faste tha tadtoal methods, wth hghe pecso, ad ts ma steps ae as follows fo a gve X : 788

3 u u,, u, 1 2 u Step 1: Calculate T whee x s the costat(typcally, le 6 ). Step 2: Suppose 0 eplaced by q M : by solvg the followg poblem: u x 0 (2) s. t. 1, th ety of X ad s a small postve u, ad let U be the detty matx wth the q th ow T u ad compute the dagoal matx D by : T T D dag 1 u X (3) whee deotes the compoetwse dvso. Ad Map X to X ~ by ~ X UXD (4) Step 3: Set v 0, ad adomly geeate a full-ak squae matx W. Update v by v : v w (5) whee f max w ~ 1 T X 0,select by the followg ule, 0, ad max w X max w 1 0 max 1 0 max X v X v X 1 1 The, the updatg pocess (5) stops f Wx ~ ~ Wx ~ fo all, k v, X â 1 s estmated by Othewse, select by 0, ad aˆ 1 x, ag max v X (6) k, ad (7) m w X m w X m v X mv X (8) 789

4 The, the updatg pocess of (5) stops f Wx ~ ~ Wx ~ fo all, k v, X â1 s estmated by I (6) ad (8), aˆ 1 x, ag m v X T ~ t w xt max w X, t max 1 1 f w1 X t w x m w X, t f max w X t k, ad (9) 1 1 Step 4: Estmate the othe colums of A the followg way: fo 1,2,, 1; update  by Aˆ aˆ,, ˆ 1 a update  by A T T I A A A A H update W by ˆ 1 ˆ ˆ ˆ ˆ ˆ W1:,1: Aˆ W1:, 1: Aˆ estmate a 1 by (7) [o (9)] usg the meshod Step 3; ed fo Aˆ aˆ,, ˆ, ad estmate the souce matx by S ˆ Aˆ 1 X. Step 5: Let 1 a III. Poposed Image Cyptosystem 3.1 Pepocessg ad Ecypto Fst of all, the ogal mage sgal s dvded to N fames by usg the segmet spltte [7], ad each fame s put to P segmets wth the same legtht. The, each segmet s omalzed to be [0, 1], ad the coespodg wavefom fomato s stoed a defte fomat. Fally, the paametes N, P, T ad ths fomato ae seted to the head data of the ecypted sgal a pe-defte fomat fo tasmsso. Afte pepocessg, the sgals (called platexts) s, s, 1 2, s ae ecypted though the followg steps: Step 1: geeate mxg matx A adomly wth dstbuto [-1, 1], ad costuct the lea mxtues: X AS T T T T, whee S s, s,, s ] ; [ 1 2 Step 2: obta the cphe sgal matx U usg the key geeato wth secet seed, ad costuct the followg olea mxtues 790

5 Y exp( X U) log( U 1) (10) whee s a paamete used fo fully maskg the platexts. The platexts ae ecypted fame by fame usg the model (10), whee the cphe U ca be used epeatedly. 3.3 Decypto ad Recostucto Afte ecevg the ecypted fames (.e., cphetexts Y ) fom publc etwok, oe ca obta the followg mxtues, combg wth the egeeated cphes ad the tasmtted paamete: X log( Y log( U 1)) U (11) Note that X s calculated aalytcally. Thus, t s a copy of the souces S mxed by the matx A. The, we ca voke the PP based method show Secto II to decypt the platexts fom Y. Howeve, ust lke othe BSS based decypto methods, the output s the matx composed of seveal segmets wth ambgutes of pemutato ad scale. To solve the pemutato poblem,a smple method based o the umbe of zeo-cossgs (zc) s used [7]. Howeve, the dex zc s ofte ustable. Hee, we utlze the spasty degee dex to sot the souces ad the ecovees [10][11]. 3.4 Requemets of the Cphes ad the Mxg Matx The cphes ca be geeated adomly by compute. Ulke the ICA o the sub-bad ICA based method, thee s o specal equemet fo the cphes the poposed mage cyptosystem. Usually, the cphe matx has the same sze wth the platext matx, ad the values ae oegatve fo bette maskg the latte. As fo the mxg matx, t eeds to be ethe oegatve o spase. The oly equemet s that t should be full ak, ad t s qute easy to satsfy ths codto by omal compute softwae. IV. Smulatos I ths secto, two smulatos ae gve to vefy the pefomace of the poposed cyptosystem, ad the esults ae compaed wth othe BSS based ecypto method, whee the compaed algothms ae ICA used [7], WPSDICA [12] ad TF [13]. Eachmethod s mplemeted usg MATLAB R2009a stalled a pesoal compute wth Itel(R) Celeo(R) 2.4 GHz CPU,2 GB memoy ad Mcosoft Wdows 7 opeatoal system.the elapsed CPU tme s used to measue the computgspeed. The souce sepaato pefomace s measued bythe mea of the sum squae eo (M-SSE) dex defed as [14] 2 e ˆ 1 S, S m s sˆ (12) 1 791

6 whee s s the th ow of the souce matx S, ŝ s the th ow of the estmated souce,, 1 matx Ŝ, T,, ad 1 π 1,2,,, s the set of all pemutatos of 1,2,,. Hee, the L2-oms of s ad ŝ, ae omalzed to be 1.The optmzato (12) ams to fd the best match betwee the ogal souces ad the estmated souces, whch ca be solved by the algothm [15]. 4.1 Smulato 1 I ths smulato, fou pats of the wdely used Lea face mage (see Fg. 1(a)) ae used as the souces (o platexts) to test the poposed mage cyptosystem, whch the paametes ae set as N 1, P 4, T 128. The model (10) s used fo ecypto, whee the key sgal matx U s geeated adomly by Matlab softwae, ad 2. Fg. 1(b) ad (c) show the cphes ad the ecypted sgals, espectvely. Table I gves the M-SSE ad the computato tme ( t ) dces of the compaed methods. Oe ca see that ou method has the hghest pecso ad the least tme cost. The coespodg decypted mages ae gve Fg. 1(d)-(g), espectvely. Fom the vsual compaso, ou method s supeo to othe methods. Table I Idces of M-SSE ad t (s) of the compaed methods fo face mages PP ICA WPSDICA TF M-SSE t

7 Fg. 1 Souces, cphes, cphetexts, ad the decyptos usg dffeet methods fo face mages; (a) Souces; (b) Cphes; (c) Cphetexts; (d) Decyptos usg PP; (e) Decyptos usg ICA; (f) Decyptos usg WPSDICA; (g) Decyptos usg TF. 4.2 Smulato 2 I ths smulato, a achtectual desg dawg s used to test the poposed mage cyptosystem. It s splt to fou segmets o souces. Smla to smulato 1, the key sgal matx U s geeated adomly, ad the volved paametes ae N 1, P 4, T 128, 2. Table II gves the M-SSE ad the tme t dces of the compaed methods. Ad the souces, cphes, ecyptos ad decyptos ae show Fg. 2(a)-(g), espectvely. Compaed wth Fg. 2(a) ad Fg. 2(d), oe ca see that ou method decypts the souces pefectly whch s cosstet to the esults Table II. 793

8 Table II Idces of M-SSE ad t (s) of the compaed methods fo dawg mages PP ICA WPSDICA TF M-SSE t Fg. 2 Souces, cphes, cphetexts, ad the decyptos usg dffeet methods fo dawg mages; (a) Souces; (b) Cphes; (c) Cphetexts; (d) Decyptos usg PP; (e) Decyptos usg ICA; (f) Decyptos usg WPSDICA; (g) Decyptos usg TF. V. Coclusos I ths pape, a ew mage cyptosystem s poposed, whee a complex olea system s used fo ecypto ad a PP based BSS method s used fo decypto. The stuctue of the cyptosystem s toduced detal, cludg the ecypto ad the decypto pocesses. 794

9 Fally, smulatos of face mages ad achtectualdesgpape pctues ae gve to vefy the avalablty ad the advatages of the poposed cyptosystem. Refeeces [1] MeezesA, OoschotP, ad Vastoe S(1996) Hadbook of AppledCyptogaphy. Boca Rato, FL: CRC [2] Deg DE(1982) Cyptogaghy ad Data Secuty. Readg, MA:Addso-Wesley [3] ChakavathyKK ad SvasMB(2003)Speech ecodg ad ecypto VLSI, Poc. Desg Automato Cof. ASP-DAC, pp [4] Ma FL,Cheg J, ad Wag YM(1996) Wavelet tasfom-based aalogspeech scamblg scheme, Electo. Lett., vol. 32, o. 8, pp [5] L K., SoYC, ad L ZG(2003) Chaotc cyptosystem wth hgh sestvtyto paamete msmatch,ieee Tas. Ccuts Syst. I, Fudam.Theoy Appl., vol. 50, o. 4, pp , Ap. [6] Xe S, Yag Z, ad Fu Y(2008)Noegatve matx factozato appled to olea speech ad mage cyptosystems,ieee Tasacto o Ccuts ad Systems I, vol. 55, o. 8, pp [7] L QH, Y FL, Me TM, ad Lag HL(2006) A bld soucesepaato-based method fo speech ecypto,ieee Tas. CcutsSyst. I, Reg. Papes, vol. 53, o. 6, pp [8] Yag Z, Xag Y, RogY, XeS(2013) Poecto-pusut-based method fo bld sepaato of oegatve souces, IEEE Tasactos o Neual Netwoks ad Leag Systems, vol. 24, o. 1, pp [9]YagZ, Zhou G, XeS, et al(2011)bld spectal umxg based o spase oegatve matx factozato, IEEE Tasactos o Image Pocessg, vol. 20, o. 4, pp [10] HoyePO(2004) No-egatve matx factozato wth spaseess costats,j. Mach. Lea. Res., vol. 5, o. 1, pp [11] YagZ, XagY, XeS, ad DgS(2012) Noegatve bld souce sepaato by spase compoet aalyss based o detemat measue,ieee Tasactos o Neual Netwoks ad Leag Systems, vol. 23, o. 10, pp [12] KopvaIad Seš cd(2008) Wavelet packets appoach to bld sepaatoof statstcally depedet souces,neuocomputg, vol. 71, os. 7 9,pp [13] ReuVG, KohSN, ad SooIY(2009) A algothm fo mxg matxestmato stataeous bld souce sepaato,sgal Pocess.,vol. 89, o. 3, pp [14] ChaTH, MaWK, ChCY, ad WagY(2008) A covex aalyssfamewok fo bld sepaato of oegatve souces, IEEE Tas.Sgal Pocessg, vol. 56, o. 10, pp [15] Tchavsk ýp ad Koldovsk ýz(2004) Optmal pag of sgal compoetssepaated by bld techques,ieee Sgal Pocessg Lettes, vol. 11,o. 2, pp