Double-lock for mage encrypton wth vrtual optcal wavelength Xang Peng Natonal Laboratory of Precson Measurement Technology and Instrumentaton, Tanjn Unversty, 30007 Tanjn, Chna Lngfeng Yu, and Llong Ca Department of Mechancal Engneerng, Hong Kong Unversty of Scence and Technology, Clear Water Bay, Kowloon, Hong Kong Abstract: A new method based on the concept of vrtual optcs for both encrypton and decrypton s proposed. The technque shows the possblty to encode/decode any dgtal nformaton. A vrtual wavelength and a pseudo-random coverng mask (PRCM) are used to desgn double locks and double keys for mage encrypton. Numercal experments are presented to test the senstvty of the vrtual wavelength. The possble dmensons of keys are roughly estmated and show a hgh securty level. 00 Optcal Socety of Amerca OCIS codes: (070.4560) Optcal data processng; (00.3050) Informaton processng; (090.760) Computer holography; (999.9999) Vrtual optcs References and Lnks. Ph. Refreger and B. Javd, "Optcal mage encrypton based on nput plane and Fourer plane random encodng," Opt. Lett. 0, 767-769 (995).. N. Yoshkawa, M. Itoh, and T. Yataga, "Bnary computer-generated holograms for securty applcatons from a synthetc double-exposure method by electron-beam lthography," Opt. Lett. 3, 483-485 (998). 3. J. F. Heanue, M. C. Bashaw, and L. Hesselnk, "Encrypted holographc data storage based on orthogonalphase-code multplexng," Appl. Opt. 34, 60-605 (995). 4. B. Javd and T. Nomura, "Securng nformaton by use of dgtal holography," Opt. Lett. 5, 8-30 (000). 5. B. Javd and E. Tajahuerce, "Three-dmensonal object recognton by use of dgtal holography," Opt. Lett. 5, 8-30 (000). 6. S. La and M. A. Nefeld, "Dgtal wavefront reconstructon and ts applcaton to mage encrypton", Opt. Comm. 78, 83-89 (000). 7. O. Matoba and B. Javd, "Encrypted optcal storage wth wavelength-key and random phase codes", Appl. Opt. 38, 6785-90 (999). 8. E. Tajahuerce, O. Matoba, S.C. Verrall, and B. Javd, "Optoelectronc nformaton encrypton wth phaseshftng nterferometry", Appl. Opt. 39, 33-30 (000). 9. O. Matoba and B. Javd, Encrypted Optcal Memory Usng Mult-Dmensonal Keys, Opt. Lett. 4, 76-765 (999). 0. L. Yu and L. Ca, "Iteratve algorthm wth a constrant condton for numercal reconstructon of a threedmensonal object from ts hologram," J. Opt. Soc. Am. A, 8, 033-045 (00). Informaton hdng s a fast growng research subject that has drawn ncreasng attenton from both academc and ndustral crcles as t covers a great number of applcaton areas n the feld of nformaton technology to prevent huge economc losses. Recently, a number of optcal methods have been proposed for the purpose of nformaton hdng [-9], snce the data/mage encrypton wth optcal nformaton processng has many nherent advantages such as the capablty of parallel processng, the ncrease n securty level, etc. Those optcal encrypton methods reported ether employng an all-optcs or a hybrd system (dgtal holography) to mplement the mage encrypton and decrypton. Another common feature among those optcal methods s that they utled a phase random mask as a means of encrypton. Especally, hybrd systems utle dgtal holography to reconstruct and decrypt hdden nformaton, but they all optcally record the hologram of the object wth CCD camera. #39544 - $5.00 US Receved December 7, 00; Revsed December 8, 00 (C) 00 OSA 4 January 00 / Vol. 0, No. / OPTICS EXPRESS 4
In ths paper, unlke the prevously reported optcal encrypton methods, we present a new method that s based on a concept of vrtual optcs or dgtal optcs, whch means that we mplement the encrypton and decrypton process totally wth a dgtal method. Actually the proposed dgtal optcs method comes from optcal nformaton processng technology such as optcal holography or other relevant optcal methods. It s mportant that we delberately utle dgtal recordng and encryptng technque by takng advantage of dgtal optcs or vrtual optcs, because, frst, ths process wll brng a hgher degree of freedom nto nformaton hdng, leadng to a dramatc ncrease n the securty level. For example, wavelength may be fxed and the spatal postons of the sgnal plane and the random masks should be postoned wthn a physcal scope as n the optcal encrypton methods[-9], whle by usng dgtal optcs method, one s able to vrtually select a wavelength for encodng dgtal hologram nstead of usng a specfc physcal lght source lke a laser wth a certan wavelength. Also, one s able to freely select spatal poston of the sgnal plane, pseudorandom coverng masks, etc, from a much larger and more flexble scope. Thus a dramatc ncrease of the nperceptblty and securty level wll be ntroduced. Secondly, dgtal recordng and encryptng technque totally get rd of the physcal lmtatons mposed by optcal or electronc hardware, such as the complexty of optcal hardware, lack of flexblty, and the lack of compact and low-cost optoelectroncs systems. Whle n the dgtal optcs method the whole process of optcal recordng and reconstructng can be dgtally smulated wth a computer. Fnally, dgtal methods can be expanded to encrypt/decrypt dfferent knds of nformaton, such as audo sgnals, vdeo sgnals, dgtal mages, maps, and other physcal sgnals, whle optcal methods are lmted to optcal mages. To llustrate our dea, n ths paper, we utle vrtual wavelength, n addton to a pseudo-random coverng mask (PRCM), as a means of desgnng double locks and double keys for mage encrypton. The wavelength can be selected from huge numercal range nstead of one comng from physcally exsted lght source. The pseudo-random coverng mask (PRCM) s also numercally generated to convert host mage sheet. Thus double locks are created and an authored thrd party needs the correspondng double keys to decrypt the hdden mage. x ξ PRCM plane Hologram plane Image plane (x,y, ) (x o,y o, o ) 0 y λ λ (x c,y c, c ) η Z PRCM Z o Z Fg. Dgtal holographc recordng and encryptng by vrtual wavelength and a pseudorandom coverng mask (PRCM) #39544 - $5.00 US Receved December 7, 00; Revsed December 8, 00 (C) 00 OSA 4 January 00 / Vol. 0, No. / OPTICS EXPRESS 4
The vrtual geometrc confguraton for dgtal encodng and decodng s shown n Fg.. All geometrc parameters are vrtually desgned for recordng a dgtal hologram. Under the crcumstance of vrtual plane reference wave, we can derve out a smple relaton between mage pont and object pont as: λ = + () λo c where ( x, y, ) s a spatal poston of reconstructed mage pont (here a real mage s consdered) n three-dmensonal space, ( xo, yo, o) s a spatal poston of object pont source, ( xc, yc, c) s a pont source of reconstructng wave. The object (.e. mage cover sheet) s a lnear superposton of pont sources. The wavelength, λ, s a vrtual one that we can secretly select to dgtally encode hologram, and λ s that of beng used for reconstructon. A PRCM numercally generated s placed at PRCM, a dstance from the PRCM plane to the dgtal hologram plane n whch the orgn of Cartesan coordnate system of dgtal hologram s defned as shown n Fg.. Suppose that the cascade of host mage sheet and random mask s llumnated wth a vrtually coherent wave. Thus, the output sgnal adjacent PRCM output plane becomes a randomly scattered lght feld and the orgnal mage has been converted by the PRCM n ths way. Now we assume, for smplcty, that a vrtual plane reconstructon wave s employed to decode dgtal hologram wthout losng generalty. Thus, the Eq. can be rewrtten as: λ = o () λ When λ = λ,thenwehave = o. However, the parameter λ can be secretly selected durng the process of encryptng and encodng dgtal hologram, so t s an unknown for unauthored thrd partes. If unauthored partes attempt to decrypt host mage wthout the knowledge of encodng process, t wll be extremely dffcult to determne the decodng wavelength λ to decode be hologram because vrtual wavelength can be a value selected from huge numercal range nstead of one comng from physcally exsted lght sources. For nstance, at least, any value n the whole vsble spectrum range can be chosen as a vrtually recordng wavelength. Ths also mples that a slght msmatch between recordng and reconstructng wavelength wll change the poston of reconstructed mage a lot, leadng to ts dsappearance n space. In other words, vrtual wavelength can be utled to desgn another lock, n addton to PRCM, n the process of mage encrypton. In ths paper, dscrete Fresnel transformaton s used to smulate the transformaton of both the PRCM plane and the mage plane to the holographc plane. A dgtally generated plane reference wave, as we have assumed, s employed to nterfere wth dgtal wavefront (generated from the PRCM and the mage plane) at ξ-o-η plane to form an off-axs dgtal hologram. Decodng dgtal hologram s numercally performed wth a spectrum manpulaton algorthm [0] n spatal frequency doman. Thus we can obtan the complex wavefront at any poston along the drecton as shown n Fg.. The reconstructed complex dstrbuton at spatal poston = o s gven as the encrypted data, and denoted by C =.Bythesame procedure, we can also record another dgtal hologram of the PRCM to prepare a keymould for key fabrcaton. All the above process use a secretly and arbtrarly selected vrtual wavelength ( λ = 0. 63µ m ). As n the smulatons of ths paper, the geometrc parameters used are: o =. m, PRCM =. m. The se of hologram s set to be 6 mm by 6 mm wth 56 56 pxels. Fg. - show the orgnal host mage, and the converted mage wth the PRCM. Dgtal hologram of both the object and the PRCM s recorded by usng the arbtrarly selected wavelength ( λ = 0. 63µ m ), the holograms are shown n Fg. 3 -. #39544 - $5.00 US Receved December 7, 00; Revsed December 8, 00 (C) 00 OSA 4 January 00 / Vol. 0, No. / OPTICS EXPRESS 43
enlarged object: (c) Fg. Image encrypton wth PRCM and secretly selected vrtual wavelength: Orgnal mage sheet to be hded, Enlarged object n the orgnal mage, (c) Converted mage Fg.3 The hologram of the object (both the mage and the PRCM). The hologram of the PRCM. (c) (d) Fg.4 Decrypton wthout correct key for PRCM Decrypton wth correct key for PRCM and correct wavelength (c) Wth correct PRCM but wavelength drftng s 0.0000nm. (d) Wth correct PRCM but wavelength drftng s 0.0000nm. #39544 - $5.00 US Receved December 7, 00; Revsed December 8, 00 (C) 00 OSA 4 January 00 / Vol. 0, No. / OPTICS EXPRESS 44
The reconstructed nformaton at =. m s gven as Fg. 4, where the correct wavelength of 0.63µ m s used but wthout a correct key for PRCM. Whle n the process of decrypton, authored partes use the wavelength λ = λ as n encrypton, and wth the gven nformaton of the dgtal hologram of PRCM, they can calculate ts correspondng complex wavefront C ( PRCM ) = at the poston of = o, where the real mage of the mage plane locates. Then the encrypted data C ( DATA) = can be decoded as: ( DATA) = C C( PRCM ) (3) C = = = λ But wth dfferent decodng wavelength, say, λ, the reconstructed poston of PRCM wll shft along drecton, as predcted n Eq., thus the complex wavefront C ( PRCM ) wll loss ts meanng for decrypton. The decrypton results wth a correct key for PRCM, but wth dfferent decodng wavelengths are shown n Fg.4 -(d), from whch we can see that the msmatch senstvty of vrtual wavelength s around an amount computed at two out of ten tmes fve nanometers. That s, f recordng or reconstructng wavelength s drfted from recordng wavelength by 0.0000nm, then host mage wll dsappear n space even f one employs a correct key for decryptng PRCM. These results demonstrate the possblty of generatng double locks wth both a vrtual wavelength and an assocated PRCM n order to encrypt mage wth a hgher securty level. Equvalently, the proposed technque also suggests a concept and methodology for the desgn of double keys for decryptng the hdden host mage. Now let s roughly estmate the securty level of the method. It s obvous that a large dmenson of key comes from the PRCM. For example, f the PRCM s set to be 8-bt real valued random nose wth 0 0 pxels. Thus the total number of possble masks could be 8 0 ( ) 0, whch s a huge number. The vrtual wavelength wll also ntroduce a huge key dmenson because t can be selected from a huge numercal range nstead of one comng from physcally exsted lght source. For example, f both the recordng and the reconstructng wavelength are randomly selected from a scope between 500nm and 500nm, and snce ther senstvtes are around 0.0000nm, thus the possble dmenson resulted from the wavelength 6 could be 0. So the total key dmenson s a huge number and t s really dffcult for any dgtal methods to successfully attack the encrypted nformaton. And comparng the possblty to use real optcal system to attack the dgtally encoded nformaton, t s even more dffcult than dgtal methods, because even f all the optcal parameters and the physcal parameters are known, the tolerance of 0.0000nm may be too small to reale or the vrtual wavelength may not ext n real world. In concluson, we have proposed a new mage encrypton method based on the concept of vrtual optcs for both encrypton and decrypton. The technque shows the possblty to encode/decode any dgtal nformaton. Vrtual wavelength and a pseudo-random coverng mask (PRCM) are used to desgn double locks and double keys for mage encrypton. The senstvty of the vrtual recordng or reconstructng wavelength are tested wth the numercal experments, whch prove our dea. The dmenson of the keys are roughly estmated and shows a hgh securty level. We would lke to thank fnancal support to ths work by the Research Grants Councl of the Hong Kong (Project No. HKUST675/00E and HKUST605/0E). #39544 - $5.00 US Receved December 7, 00; Revsed December 8, 00 (C) 00 OSA 4 January 00 / Vol. 0, No. / OPTICS EXPRESS 45