The Digital Fingerprinting Method for Static Images Based on Weighted Hamming Metric and on Weighted Container Model

Transcription

1 Journal of Computer and Communcatons, 04,, -6 Publshed Onlne July 04 n ScRes. The Dgtal Fngerprntng Method for Statc Images Based on Weghted Hammng Metrc and on Weghted Contaner Model Sergey Bezzateev, Natala Voloshna Informaton Securty Technologes Department, Sant-Petersburg State Unversty of Aerospace Instrumentaton, Sant-Petersburg, Russa Emal: bsv@aanet.ru, natal@vu.spb.ru Receved May 04 Abstract The algorthm of fngerprnt constructng for stll mages based on weghted mage structure model s proposed. The error correctng codes that are perfect n weghted Hammng metrc are used as a base for fngerprnt constructng. Keywords Fngerprntng, Error Correctng Codes, Perfect Codes n Weghted Hammng Metrc, Weghted Contaner Model, Dgtal Rghts Management. Introducton The author rghts protecton s one of the most mportant problems for the multmeda data dstrbuton. Two knds of methods are used to solve ths problem such as dgtal watermarkng (DWM and dgtal fngerprntng (DFP [] []. In the DWM methods the addtonal nformaton about author (watermark s embedded nto ntal data (for example mage to protect t. Ths nformaton should be resstant aganst wde class of attack (flterng, compresson, etc. on the watermarked mage as long as the level of vsual qualty s hgher than predefned level. The second type of protecton means that the addtonal nformaton (fngerprnt should be formed based on the ntal nformaton (mage based on ts specfc salent features. For example n [3] the edges and corners obtaned from an mage were used as salent features. The fngerprnt s used then to fnd copes of orgnal mage ncludng llegal ones. Fngerprntng method should provde stable fngerprnt formng process for dfferent knd of mage processng (flterng, compresson, etc.. Man dfferences between these copy rght protecton methods are: Some part of the ntal obect s changed whle watermark embeddng process (for example LSB method. Fngerprntng does not mply any changes of ntal nformaton. Dgtal watermark s constructed by the user (author. It can be represented n dfferent forms (ID nformaton, pcture, text, etc. to prove author rghts. Dgtal fngerprnt does not contan any author nformaton. It forms based on ntal nformaton. How to cte ths paper: Bezzateev, S. and Voloshna, N. (04 The Dgtal Fngerprntng Method for Statc Images Based on Weghted Hammng Metrc and on Weghted Contaner Model. Journal of Computer and Communcatons,, -6.

2 S. Bezzateev, N. Voloshna The combnaton of these two types of author rghts protecton methods s proposed n ths paper. The dea s to add small dstortons to the ntal mage to get stable fngerprnt. In ths paper the term salent feature refers to a specal vector b n weghted Hammng metrc obtaned from the mage and to nearest (L, G code perfect n the weghted Hammng metrc [4]. The nearest means a code that have codeword a on the mnmal dstance n weghted Hammng metrc from the vector b.. Proposed Method Descrpton The author rghts protecton systems are developed n a way they gve stable nformaton about the person that has author rghts on t. Ths nformaton should be stable for wde class of dstortons that could happen. At the same tme author rghts protecton method should not change the ntal nformaton more than t defned for exact markng obect. For example t should keep vsual qualty of the mage. Fngerprntng methods do not change ntal obects. They only use salent features of these obects to construct fngerprnt. The problem s that not always such features could be found or they could be not resstant to attacks. At the same tme t s not necessary to avod any dstortons of ntal nformaton (for example for dgtal mages. In ths case t s possble to use watermarkng approach that changes some part of ntal nformaton to embed addtonal author nformaton. But t s not always possble to embed watermark wth acceptable dstorton level due to nconsstency of watermark and protected obect structure. The method of dgtal fngerprnt constructon based on the property of codeword presence n mage (F5 concept [5] s proposed. If the codeword can t be found then codeword should be added by the watermarkng approach. For example for the stll mages the essence of the method can be explaned as followng. The ntal mage or ts part s transformed nto bt stream. Ths bt stream s dvded nto blocks a wth length n. These blocks a are looked at as a code words of code G wth error vector e. If a s a codeword of G then e = 0 and syndrome s = 0. It means that ths block has requred for fngerprntng property. If s 0 then ths block does not have requred property. It s necessary to decode ths codeword.e. to correct ts errors to get ths property. As a result the dstortons wll be added to the ntal nformaton. The problem of gettng s = 0 for any block of bt stream could be solved by perfect codes usage [4]. It s possble to use several codes wth equal parameters that are defned for weghted Hammng metrc. For ths approach the code sequence G that s formed as a result of the blocks a decodng and for whch the blocks are the closest to ther code words can be looked at as a fngerprnt. The structure of the blocks a should be weghted because the error corrected codes that are concerted wth the weghted Hammng metrc are used to construct fngerprnt. These weghted blocks could be looked at as a weghted contaner that s formed for weghted watermarkng [6] [7]. It s necessary to dved ntal mage nto several zones to construct weghted blocks a. The dvson s performed based on the nfluence of the errors that happened durng the decodng process on the resultng dstortons (vsual qualty of resultng mage. Blocks a are formed as a combnaton of the parts of these dfferent sgnfcance zones. The basc scheme of the proposed fngerprntng method s shown n the Fgure. 3. Error Correctng Codes Consstent wth Weghted Hammng Metrc Error correctng codes n weghted Hammng metrc are defned as followng [4]: l Length n of a code word s n, n,, nl, n= n. = l l n n nl = have the weght ω. Let us consder these weghts as growng sequence.e. ω < ω < ω < < ωl. The weght of the code word a n weghted Hammng metrc s defned as followng: Any poston of the code word a ( a a a a a a a wt ( a = ω. It s obvous that Hammng dstance between two vectors n weghted Hammng metrc can be defned as l l l l a a a a a a a a b= b b b b b b b : a 0 = ( n n n and ( n n n l l

3 S. Bezzateev, N. Voloshna Fgure. The basc scheme of the fngerprntng method for three zone contaner.. For bnary codes n weghted Hammng metrc t s possble to wrte the Hammng dstance for code wth parameters the same way as for codes n ordnary Hammng metrc where -number of a code words n the code (for bnary lnear code -number of vectors of length n a sphere of radus n weghted Hammng metrc. where. Therefore we can defne a perfect code,.e. the code wth parameters les on ths bound. For lnear bnary code we obtan the followng equaton:. Codes that are perfect n a weghted Hammng metrc can be constructed by usng well-known methods for optmal codes constructon (for example Glbert-Varshamov bound. But such constructon method has hgh calculaton complexty and doesn t gve any desgn decodng method for such codes. By usng specal classes of Goppa codes n weghted Hammng metrc t s possble to solve both these problems. Specal Class of Goppa Codes n Weghted Hammng Metrc To construct Goppa codes consstent wth a weghted Hammng metrc the constructon of generalzaton (L,G codes wth poston numerators of dfferent degrees [4] s used. Therefore we use locator set where s formal dervatve of denomnator, and 3

4 S. Bezzateev, N. Voloshna s an rreducble polynomal on F [ ] m x. Goppa polynomal for such code s rreducble polynomal G x, G x F x, deg G x = τ ω, ( ( m [ ] ( l ( G( x u ( x = = nl gcd,, :, Number of dfferent Goppa codes wth the same parameters ( nkd,, from ths class s determned by the number of dfferent rreducble polynomals wth degree τ on F [ ] m x. 4. Fngerprnt Calculaton Algorthm Based on Famly of Goppa Codes Γ(n,k,d Perfect n Weghted Hammng Metrc We descrbe here the smplest verson of the fngerprnt calculatons algorthm for statc mage that contans dfferent sgnfcance zones that s based on the famly of Goppa codes perfect n the weghted Hammng metrc. Wthout loss of generalty we consder here a statc mage that contans three zones. Thrd zone does not assume any dstortons,.e. ω 3 =. Second zone has relatve weght ω of dstortons equal to. Frst zone allows to make the maxmum number of dstortons wthout maor consequences for the qualty of the resultng mage and therefore has mnmal relatve weght ω =. For such mage let us chose a famly of Goppa codes perfect n weghted Hammng metrc Γ ( nkd,, wth a followng parameters: m m m n= n+ n = +, n =, m m n =, k= + = m m md, 5. As mentoned n the prevous secton the number of dfferent codes n ths famly s determned by the numm ber of rreducble polynomals of second degree wth coeffcents from GF ( : I GF m m =. ( m ( = that s obtaned from mage that was prelmnarly spltted nto dfferent sgnfcance zones can be represented n the weghted Hammng metrc as followng: Obvously as we consder perfect codes any vector a ( a a an a an where ( a a an a an = ( c c cn c cn ( e e en e en, ( c c cn c ( cn Γ L G wt ( e e en e e n t,, = Thus usng for vector a varous Γ ( L, G codes of the famly Γ ( nkd,, n decodng procedure we wll get error vectors wth dfferent weghts t, 0 t. Fngerprnt wll consder as a set of numbers λ, λ,, λr of a codes from the famly Γ ( nkd,, cor- respondng to the vectors obtaned from the mage splttng nto zones as follows: Vector a = ( a a an a an assgn the smallest number λ of such Γ ( L, G code for whch error vector e= ( e e en e en provdes the least weght by decodng procedure. That means ( ( λ = mn : wt e e e e e n n = mn wt e e e e e. n n l The algorthm of fngerprnt calculaton based on a famly of Γ ( L, G codes can be descrbed as: The mage s dvded nto zones of dfferent sgnfcance. In accordance wth found mage zones the blocks are formed and the approprate parameters of the codes 4

5 S. Bezzateev, N. Voloshna famly are selected. 3 Fngerprnt λ, λ,, λm s formed n followng way. Found error vectors e= ( e e en e en are corrected and correspondng blocks a = ( a a an a an of source mage are converted to code words of the Goppa codes from the famly Γ ( nkd,,. For example the frst block s transformed nto a codeword ( c c cn c cn Γ( L, G. λ λ The dstorton of the source mage wll be mnmal accordng to the pre- vously descrbed algorthm of obtanng the numbers λ. 5. The Fngerprnt Checkng and Its Resstance to Random and Delberate Dstortons In accordance wth the descrbed algorthm of fngerprnt λ, λ,, λr creaton n the processed mage P there are R blocks ( c c cn c cn Γ( Lλ Gλ,, =,, R. Each block should be the codeword of correspondng Goppa code from the famly Γ ( nkd,,. The presence of the fngerprnt λ, λ,, λr s verfed by the decodng the blocks a by the correspondng code. The fngerprnt s decded to be found f all syndromes for all blocks s = 0. The presence of mnor dstorton n the processed mage P may cause errors n these blocks. So n dstorted mage P* there are blocks ( b b bn b ( ( bn = c c cn c cn e e en e e n = ( c c cn c ( cn e e en e e n wt ( ˆ ˆ ˆ ˆ ˆ e e en e en = wt, ( c c cn c cn, ( cˆ ˆ ˆ ˆ ˆ c cn c cn Γ( L, G,,, R λ λ =. ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ, Usng fngerprnt λ, λ,, λr and corrupted mage P* t s easy to fnd an approprate error vector ( eˆ eˆ ˆ ˆ ˆ en e en and the weght wt correspondng to ths vector. Obvously that n case of small corrup- tons ( c c c c c = ( cˆ cˆ cˆ cˆ cˆ and therefore ( e e e e e = ( eˆ eˆ eˆ eˆ eˆ. n n n n R Let s defne now the penalty functon weght coeffcents f { f, f } F = wt f = wt n n n n. In the smplest case t s possble to consder that the wt of the penalty functon have the same value and are equal to. However the more flexble way where f f s possble too. By takng nto account the nature of the corruptons and ther mpact on the percepton of the resultng mage.e. ts vsual qualty we can chose dfferent values of the weght coeffcents. Decson of the defnte fngerprnt avalablty n an exstng pcture P* s made by the value of the penalty functon F and threshold values B and B that are defne the events of the false alarm and skp goal respectvely. 6. Concluson A new method of fngerprnt constructon that uses the features of the orgnal mage structure (weghted contaner assocated wth the dfferent degree of ts senstvty to the corruptons n dfferent zones of the contaner s proposed. In order to use ths property of the contaner t s proposed to use the weghted Hammng metrc unlke used n prevously known schemes usual Hammng metrc. For effectve use of ths metrc t s proposed a famly of generalzed Goppa codes perfect n weghted Hammng metrc. Thanks to the usage of such famly of codes t s possble to make the mnmum number of dstortons when fngerprnt s constructed. Addtonally the use of error-correctng codes constructon allows to correct random corruptons that can occurred durng contaner (mage storng or transmttng. Stll open queston n optmal choce of the coeffcents n the penalty 5

6 S. Bezzateev, N. Voloshna functon provdes the mnmal probablty of false alarm and skp goals when decdng on the avalablty of the fngerprnt presence n the analyzed mage. References [] Durc, Z., Johnson, N.F. and Jaoda, S. (999 Recoverng Watermarks from Images. Techncal Report ISE-TR-99-04, Center for Secure Informaton Systems, George Mason Unversty. [] Johnson, N.F., Durc, Z. and Jaoda, S. (999 A Role for Dgtal Watermarkng n Electronc Commerce. Accepted for Publcaton ACM Computng Surveys. Publcaton TBA. [3] Johnson, N.F., Durc, Z. and Jaoda, S. (999 On Fngerprntng Images for Recognton. In: Multmeda Informaton Systems, 4-. [4] Bezzateev S. and Shekhunova N. (0 Bnary Generalzed (L, G Codes That Are Perfect n a Weghted Hammng Metrc. Problems of Informaton Transmsson, 48, [5] Westfeld, A. (00 Hgh Capacty Despte Better Steganalyss (F5-A Steganographc Algorthm. In: Moskowtz, I.S., Eds., Informaton Hdng. 4th Internatonal Workshop. Lecture Notes Computer Scence, Vol. 37, Sprnger-Verlag, Berln, Hedelberg, New York. [6] Bezzateev, S., Voloshna, N. and Zhdanov, K. (0 Specal Class of Error-Correctng Codes for Steganography Systems. Proceedngs TUSUR (Novosbrsk,, -8. [7] Neeta, D. (006 Implementaton of LSB Steganography and Its Evaluaton for Varous Bts. Dgtal Informaton Management, st Internatonal Conference. 6