All-optical encrypted movie

Transcription

1 All-optcal encrypted move Faban Mosso, 1 John Fredy Barrera, 3 Myran Tebald, 1, Néstor Bolognn, 1,2 and Roberto Torroba 1 1 Centro de Investgacones Óptcas (CONICET La Plata-CIC) and UID OPTIMO, Facultad de Cencas Exactas, Unversdad Naconal de La Plata, P.O. Box 3 C.P 1897, La Plata, Argentna 2 Facultad de Cencas Exactas, Unversdad Naconal de La Plata, P.O. Box 3 C.P 1897, La Plata, Argentna 3 Grupo de Óptca y Fotónca, Insttuto de Físca, Unversdad de Antoqua, A.A 1226 Medellín, Colomba myranc@cop.unlp.edu.ar Abstract: We ntroduce for the frst tme the concept of an all-optcal encrypted move. Ths move jonts several encrypted frames correspondng to a tme evolvng stuaton employng the same encodng mask. Thanks to a multplexng operaton we compact the encrypted move nformaton nto a sngle package. But the decrypton of ths sngle package mples the exstence of cross-talk f we do not adequately pre-process the encoded nformaton before multplexng. In ths regard, we ntroduce a gratng modulaton to each encoded mage, and then we proceed to multplexng. After approprate flterng and synchronzng procedures appled to the multplexng, we are able to decrypt and to reproduce the move. Ths move s only properly decoded when n possesson of the rght decodng key. The concept development s carred-out n vrtual optcal systems, both for the encryptng and the flterng-decryptng stages. Expermental results are shown to confrm our approach Optcal Socety of Amerca OCIS codes: ( ) Optcal securty and encrypton; ( ) Data processng by optcal means; ( ) Optcal processng; ( ) Speckle. References and lnks 1. G. Stu and J. Zhang, Multple-mage encrypton by wavelength multplexng, Opt. Lett. 30(11), (2005). 2. J. F. Barrera, R. Henao, M. Tebald, R. Torroba, and N. Bolognn, Multplexng encrypton-decrypton va lateral shftng of a random phase mask, Opt. Commun. 259(2), (2006). 3. J. F. Barrera, R. Henao, M. Tebald, R. Torroba, and N. Bolognn, Multplexng encrypted data by usng polarzed lght, Opt. Commun. 260(1), (2006). 4. J. F. Barrera, R. Henao, M. Tebald, R. Torroba, and N. Bolognn, Multple mage encrypton usng an aperture modulated optcal system, Opt. Commun. 261(1), (2006). 5. J. F. Barrera, R. Henao, M. Tebald, R. Torroba, and N. Bolognn, Code retreval va undercover multplexng, Optk (Jena) 119, (2008). 6. P. Refreger and B. Javd, Optcal mage encrypton based on nput plane and Fourer plane random encodng, Opt. Lett. 20(7), (1995). 7. J. Ojeda-Castañeda and E. E. Scre, Theta-modulaton decoder based on the Lau effect, Opt. Commun. 59(2), (1986). 8. J. W. Goodman, Introducton to Fourer Optcs (Roberts & Company Publshers, 2004), pp Introducton Snce optcal technques appear as practcal tools n securng and valdatng nformaton, researchers adopted sgnfcant efforts to nvestgate these technques under the nsght of cryptoanalyss. Researchers cast doubts on the effcency n the sense f the technques were able to endure attacks from cryptoanalyss. There are some common crtera for evaluatng the effectveness of these methods n practce: the key functons should be dffcult to fnd by chance, the mages delvered openly should be ntensty patterns for use n Internet communcaton, and decrypton should be relatvely easy for recevers wth the keys. One # $15.00 USD Receved 3 Jan 2011; revsed 3 Mar 2011; accepted 5 Mar 2011; publshed 11 Mar 2011 (C) 2011 OSA 14 March 2011 / Vol. 19, No. 6 / OPTICS EXPRESS 5706

2 mportant feature that renforces optcal encrypton s the multplexng concept. Ths procedure brngs the chance for storng multple messages n a sngle recordng medum. In ths regard, multplexng proposals have a practcal applcaton n optcal encrypton, ncreasng the total number of possble combnatons yet mprovng the robustness of the encryptng system. In multplexng arrangements, the encrypton of an nput mage s assocated to a determned status of the encryptng parameters. There exst a bunvocal relaton between each nput mage and ts encrypted verson. The multplexng basc prncple conssts on encryptng several mages nto a sngle package n order to not only to brng the change for multple users, but also to ncrease data securty. Several multplexng encrypton methods were proposed, for nstance, wavelength multplexng [1], multplexng by randomphase mask shftng [2], modfyng the polarzaton state [3], or usng multple apertures that change between exposures [4,5]. In case of usng a sngle encodng mask, the problem for the end user wll be the cross talk among the overlappng of decoded mages. To avod ths cross-talk, a classcal soluton nvolves settng the encryptng optcal parameters n a way to defne separately the encoded mages or to modfy the encryptng machne. So far, multplexng methods were performed such that the encrypted mages are completely uncorrelated. In ths case, the man ssue s the superposton of the decrypted nformaton over the non-decrypted data, ths last actng as nose. These protocols refer to the dea of multple users sharng common multplexed peces of nformaton and n possesson of an authorzed decodng key to get a sngle pece. Each pece of nformaton represents a statc mage. We can extend the dea to a sngle user wth the capablty of decodng a whole sequence of ndvdually encrypted but assocated events. The new concept thus nvolves the dea of encodng a dynamc stuaton. Besdes, to retreve the complete dynamc nput nformaton, t s necessary not only to properly decrypt the mages but also to compose them. As we ntend to use a sngle encryptng mask, we have to solve the crosstalk problem arsng from the spatal superposton of the multplexed mages. We suggest the use of an nner spatal modulaton of the speckles contaned n each encrypted mage before multplexng. Thanks to ths modulaton, we are able to ntroduce a later flterng procedure to overcome the cross-talk ssue. If all nput data correspond to a sequence of mages representng successve frames of a movng scene, then we are encryptng and multplexng a move. It only remans to synchronze the recoverng procedure to adequately dsplay the decoded move. In ths contrbuton, we propose and mplement the frst reported technque to obtan an all-optcal encrypted move carred out wth only vrtual optcal systems. The frames that compose the move are encrypted and frnge modulated separately before multplexng. The encrypton of each frame s performed usng the same codng key and wthout changng the encryptng vrtual optcal system. Before sendng the multplexng results, we perform ts phase conjugaton. Durng recoverng, each phase conjugated encrypted frame s obtaned from the multplexng by means of a flterng process. Fnally, usng the rght codng key durng decrypton, each frame s recovered. Ths process along wth the synchronzaton n the flterng steps results n the adequate reconstructon of the move. 2. Descrpton of the method We select as encryptng protocol the classcal 4f double random phase encodng archtecture [6]. The goal of our proposal s to encrypt decrypt a synchronzed sequence of frames that compose a dynamc scene consttutng a move. Referrng to Fg. 1, n the frst step we show n each row a sngle frame encryptng procedure usng the same encodng mask R and wthout modfcatons of the encryptng vrtual optcal system for every frame. But a multplexng at ths step by consderng a sngle encodng mask leads, after decodng, to severe mage degradaton due to cross-talk. Ths degradaton s caused by the smultaneous # $15.00 USD Receved 3 Jan 2011; revsed 3 Mar 2011; accepted 5 Mar 2011; publshed 11 Mar 2011 (C) 2011 OSA 14 March 2011 / Vol. 19, No. 6 / OPTICS EXPRESS 5707

3 spatal overlappng of the decoded frames. Therefore we have to desgn strateges to overcome ths ssue. We now recall the well known theta modulaton method appled to speckle patterns wth gratngs to prmarly store dfferent mages nto a sngle record [7]. Ths approach leads us to recover each frame wthout the nfluence of the remanng ones. We wll use ths approach to ntroduce an external tool that allows one to spatally separate the dfferent frames F. For ths reason n step 2 of Fg. 1, we ntroduce a physcal gratng G n contact wth each encrypted frame E, and we rotate the gratng for the dfferent frames. In ths way, we assgn dfferent spatal labels for each frame. Once ths procedure s accomplshed we proceed to multplex all frames. The multplexng operaton results from the addton of the modulated encrypted nformaton obtaned by the gratng attachng procedure above descrbed for each encrypted nput frame. In general, ths procedure wll be extended to not only the gratng rotaton but also to a smultaneous ptch varaton n a way to expand the possbltes to ncrease the number of labeled frames. Step 1 Step 2 R F 1 R E 1 G 1 Modulated speckle pattern R F R E G R F n R E n G n Multplexng Fg. 1. Step 1: encrypton process (R: random phase mask, F : -th frame; R : key mask, E : -th encrypted frame, : Fourer transform); step 2: theta speckle modulaton and multplexng (G : -th ampltude gratng). All shown speckle patterns correspond to enlarged verson of the actual patterns. Fgure 2 shows an enlarged regon of an encrypted frame modulated by the gratng. We can see the dfferent speckles covered wth horzontal lnes correspondng to that gratng orentaton. We recall that the ext pupl of the encodng 4f archtecture controls the average speckle sze. It s mportant to note that the gratng does not affect ths speckle sze dstrbuton. Fg. 2. Enlarged verson of an encrypted gratng modulated frame. # $15.00 USD Receved 3 Jan 2011; revsed 3 Mar 2011; accepted 5 Mar 2011; publshed 11 Mar 2011 (C) 2011 OSA 14 March 2011 / Vol. 19, No. 6 / OPTICS EXPRESS 5708

4 We now send to the user the complex conjugate of the multplexng together wth a copy of the orgnal encodng key. The recoverng procedure performed by the user conssts on flterng and decryptng steps. Although we show for clarty these steps n two separate fgures, they are performed nto a sngle decodng unt whch conssts n a vrtual optcal system. We now analyze n Fg. 3 the flterng process. A Fourer transform () of the nput reveals the exstence of pared spots belongng to each labeled frames located a dfferent spatal postons. We have to remember that these postons depend on the ptch and orentaton of the labelng gratng. To speed up data collecton to arrange the move, we prefer to dsplay the labeled par nformaton n concentrc crcles expandng ther radus as we ncrease the number of stored frames. The expermental concepton prevous to the flterng process, bearng n mnd the fnal synchronzaton procedure, lead us to choose the ntal step by usng a gratng wth ther lnes vertcally orented. Then we start to sequentally change the nput frame as we start a 180 degree rotaton of the gratng. Therefore, we acheve the nner most labeled crcle to be observed at the flterng plane. In order to defne the next outer crcle, we reduce the gratng ptch and proceed n the same way as before. As a consequence the frst gratng defnes the largest ptch nvolved. For reconstructon, the order establshed above before multplexng, should be mantaned to retreve the moton n ts natural sequence. We flter out all but a gven spot, n order to obtan, after a new, a sngle encrypted frame. In ths way, we solate each encrypted frame from the nformaton of the remanng encrypted frames. Consequently, we are avodng the exstence of possble cross talkng durng the next decodng step. We keep only one spot as the dsplay of the pared spots wll ntroduce a pollutng gratng structure on the fltered mage. The mnmum ptch selecton should be as to detect at least two frnges n each speckle. In ths pont, we want to hghlght that the fnal number of frames to be processed s lmted by several aspects: a) the mnmum resolved speckle modulaton spacng; b) as the parameters of the encryptng optcal procedure defne the area of each spot assocated to each frame at the flterng plane we have a lmted number of spots provded that overlappng s avoded, c) the number of spots that fall on the avalable area wthn the flterng plane. The detaled dscusson of the nfluence ths lmtaton mposes on the number of frames as well as on cross-talk reducton wll be addressed n a future contrbuton. Accordngly n Fg. 4 we proceed wth the classcal decodng of each sngle frame for the 4f decryptng archtecture. Fnally, the entre procedure leads to clearly vsualze each sngle frame wthout the nfluence of the others. Phase conjugated multplexng Fourer plane Flterng process E 1 E E n Fg. 3. Flterng process. Ths method represents a soluton to the problem of a sngle user wth a sngle decodng mask tryng to vsualze a set of encrypted mages. Wthout the external gratng labelng to each encrypted frame and ther subsequent flterng process, the vsualzaton of each separate # $15.00 USD Receved 3 Jan 2011; revsed 3 Mar 2011; accepted 5 Mar 2011; publshed 11 Mar 2011 (C) 2011 OSA 14 March 2011 / Vol. 19, No. 6 / OPTICS EXPRESS 5709

5 NMSE frame wll be hndered. Addtonally, we are reconstructng each decoded frame wth the same vsual qualty. The qualty was checked by comparng each nput frame wth ther correspondng decoded outputs by the well known normalzed mean root square error (NMSE) metrc, gvng the almost flat response depcted n Fg. 5. In fact, ths curve ndcates a unform qualty along the process for the complete move. Ths technque leads to the dea that each frame could be assocated to a tme evolvng phenomenon. If we dsplay these consecutve frames n a tme sequental order, we can reconstruct a move of ths phenomenon. Then, we are developng the frst dea of an all-optcal encrypted-decrypted move. The user n possesson of not only the rght decodng mask but also the rght tme sequence could see the move. E 1 R F 1 E R F E n R F n Fg. 4. Decrypton process (E : -th complex conjugated encrypton frame). 1,0 0,8 0,6 0,4 0,2 3. Expermental results 0, Frame Fg. 5. Normalzed NMSE for all frames n the move. In our experment we take 22 frames of an orgnal move and submtted to the procedure above descrbed. After decrypton we synchronze the dsplay to 10 frames per second to get a 2.2 seconds move, shown n Fg. 6(a) (Meda 1). We clearly see the flud movement of the move subject. If we ntend to reproduce the move wthout placng the rght decodng key R we get the bolng speckled move of Fg. 6(b) (Meda 2). We want to emphasze that the speckle s ever present n the entre process as we are performng operatons wth vrtual optcal systems. The object sze s 5.7 x 5.7 mm 2. The lenses nvolved n the s n the dfferent steps of the vrtual optcal system have dentcal focal length of 100 mm. The # $15.00 USD Receved 3 Jan 2011; revsed 3 Mar 2011; accepted 5 Mar 2011; publshed 11 Mar 2011 (C) 2011 OSA 14 March 2011 / Vol. 19, No. 6 / OPTICS EXPRESS 5710

6 wavelength s nm. The area of the flterng plane s 45 x 45 mm 2. The spot dameter and the separaton between adjacent spots at the flterng plane are both 6.5 mm. 4. Conclusons Fg. 6. (a) Full decrypted optcal move (Meda 1) and (b) full non-decrypted optcal move (Meda 2). In the present contrbuton we developed the concept of an encrypted-decrypted move to dsplay a tme evolvng phenomenon. As descrbed n the paper, we perform a labelng of each encrypted frame to avod the cross talk that arses when recoverng the nformaton after multplexng. The labelng allows an approprate selecton of non overlapped frames and together to the logcal synchronzaton; we are able to fnally dsplay the move. We want to stress that the applcaton s ntended for a sngle user n a frendly envronment, as the user requres a sngle synchronzng-decryptng unt that performs the fnal dsplayng task. The expermental results llustrate the feasblty of the proposal. As we only ntend to ntroduce the concept, we defer the logcal optmzaton of the whole procedure to future contrbutons. Appendx Let us mathematcally descrbe the encrypton-decrypton set-up (see Fg. 1, Fg. 3, and Fg. 4). The whole procedure can be expressed as follows. The ampltude A for each nput frame s gven by: A F R where F s the correspondng -th frame ampltude and R s the nput random phase mask. By multplyng ts Fourer transform by the key code mask R results n: F R R. Note that R and R are used for every frame. Then, each encrypted frame for the 4 f encryptng archtecture s: E F R R (1) where represents the convoluton operaton. By consderng the second step of the encrypton procedure (see Fg. 1), the encrypted output E s multpled by a snusodal gratng G whose expresson follows the tradtonal defnton n optcs (see Ref [8]. page 80). Ths gratng has a ptch d whch fulflls d S t (where St s the transversal average speckle sze) and St s nversely proportonal to the output pupl sze of the system. The multplexng procedure mpled to encrypt n frames. We have to stress that the whole stored encrypted nformaton M s expressed as: n M E G 1 (2) # $15.00 USD Receved 3 Jan 2011; revsed 3 Mar 2011; accepted 5 Mar 2011; publshed 11 Mar 2011 (C) 2011 OSA 14 March 2011 / Vol. 19, No. 6 / OPTICS EXPRESS 5711

7 Ths procedure can be expermentally accomplshed by storng each ndvdual term of the above equaton nto a photorefractve crystal, or alternatvely by addng nto a sngle frame each captured term of Eq. (2). As usual, n order to recover the orgnal nformaton a phase conjugate operaton must be carred out. At ths pont we have to perform ths phase conjugaton operaton, whch can be realzed for nstance by llumnatng the photorefractve crystal wth a phase conjugated reference beam or by dgtally changng the sgn of the phase n the stored multplexed pattern. Then, after ths phase conjugaton operaton and another Fourer transform (see Fg. 3) t results M n E G n E G 1 1 As t s well known, the Fourer transform of the snusodal gratng gves rse to three terms one centered n the optcal axs and the other two symmetrcally located around the centered term. The locaton of these spots depends on the gratng orentaton and ptch and the sze depends on the parameters of the optcal system (see Ref [8]. page 81). We have to recall that we are storng n frames; therefore we are obtanng several dffracted spots as can be seen n the second mage from the rght n Fg. 3. The flterng procedure s performed on the plane where these spots are dsplayed, by adequately postonng a crcle of untary transmttance scaled to the sze of the dffracted order whle assgnng zero transmttance to the rest. By adequately selectng the flter poston, we retan from the -th term of Eq. (3) only one dffracted spot assocated to E from the correspondng two symmetrcally spots located around the center. In Fg. 3 ths procedure s dsplayed n the two last columns for three cases. Then, an nverse Fourer transform operaton allows obtanng each conjugated encrypted frame E. As descrbed n Fg. 4, the decodng process requres of another 4f scheme. At ths step, the conventonal decryptng procedure allows recoverng the frame F by the operaton and fnally another Fourer transform gves E R F R R R E R F R Ths operaton must be sequentally carred out n tmes n order to decrypt all move frames. It s nterestng to remark that we dsplay the move n ntensty form, therefore ths ntensty operaton removes the phase mask nformaton R. Acknowledgments Ths research was performed under grants COLCIENCIAS, CODI -Unversdad de Antoqua (Colomba), TWAS-UNESCO Assocateshp Scheme at Centres of Excellence n the South, CONICET No. 0863, ANCyT PICT 1167 and Facultad de Ingenería, Unversdad Naconal de La Plata No. 11/I125 (Argentna), blateral project CO/08/16 between MINCyT (Argentna) and COLCIENCIAS (Colomba). (3) (4) (5) # $15.00 USD Receved 3 Jan 2011; revsed 3 Mar 2011; accepted 5 Mar 2011; publshed 11 Mar 2011 (C) 2011 OSA 14 March 2011 / Vol. 19, No. 6 / OPTICS EXPRESS 5712