Reversible Digital Watermarking

Transcription

1 Reversble Dgtal Watermarkng Chang-Tsun L Department of Computer Scence Unversty of Warwck Multmea Securty an Forenscs 1

2 Reversble Watermarkng Base on Dfference Expanson (DE) In some mecal, legal an mltary applcatons, slght changes to content ue to watermarkng s not acceptable. So allowng the orgnal content to be completely restore from the watermarke mea s useful. Watermarkng wth ths capablty s calle reversble or lossless watermarkng. Ths work has nspre many others: J. Tan, Reversble Data Embeng Usng a Dfference Expanson, IEEE TCSVT, 13(8), 2003 Multmea Securty an Forenscs 2

3 What s Dfference Expanson (DE) Gven two greyscales x an y & a bt b to be embee x y Average a, Dfference x y (1) 2 If x = 206, y = 201 & b = 1 x y a x y ' b ' 2 b (=5) has been expane nto '(=11) Multmea Securty an Forenscs 3

4 Multmea Securty an Forenscs 4 Embeng Data Bt n x & y x' & y': watermarke verson of x an y From we get (2) 2 ' ', 2 1 ' ' a y a x ' ' ' ' a y a x (1) y x y x a, 2

5 Extractng Data Bt an Recoverng x & y From (1) x' y' a' 203 a 2 2 (Notea' a) b ' x' y' ' / 2 & b = 1 has been correctly extracte! From (2) x a y a x = 206 an y = 201 have been recovere! Multmea Securty an Forenscs 5

6 Expanable Dfference Values Overflow (x' > 255 or y' > 255) an unerflow (x' < 0 or y' < 0) must be avoe when expanng ther fference,.e., ' 1 ' 0 x' a 255 ' 2 an 0 y a ' 2(255 a) an ' 2a 1 If ' 2 b mn then s expanable. 2(255 a),2a 1, b 0, 1 Expanable fference values allow orgnal (x, y) to be recovere wthout other arrangement. Multmea Securty an Forenscs 6

7 Changeable Dfference Values 2 LSB( ) 2 If LSB() can be replace by a ata bt b an 2 mn2(255 ),2 1, {0,1 } 2 b a a b then s changeable. A changeable (but not expanable) fference value oes NOT allow orgnal (x, y) to be recovere wthout other arrangement. An expanable nteger s also changeable. Multmea Securty an Forenscs 7

8 Embeng Algorthm 1. Form a set of m pxel pars (x, y) an calculate ther fference values usng Eq. (1) 1,, m 2. Partton nto 4 sets: EZ, EN (=EN1U EN2), CN an NC 3. Create a bnary locaton map L such that an perform lossless compresson on L 1, f EZ EN1 0, otherwse 4. Collectng LSBs of the n EN2 U CN to form C 5. Embe bt stream L C P by expanng n EZ U EN1 changng n EN2 U CN (P s the actual payloa or watermark) 6. Perform Eq. (2) ' 1 ' x ' a, y' a 2 2 L Multmea Securty an Forenscs 8

9 Step 1 - Embeng Algorthm Step1. Form a set of m pxel pars (x, y) an calculate ther fference values Each par can be horzontally neghbourng pxels vertcally neghbourng pxels forme n a pseuo ranom manner uner the control of a secret key other ways Multmea Securty an Forenscs 9

10 Step 2 - Embeng Algorthm Step2. Partton nto 4 sets: EZ, EN (=EN1U EN2), CN an NC EZ: all expanable = 0 an = -1 EZ s separate from ZN because = 0 an = -1 together wth = 1 an = -2 when s n EN2 consttute 4 specal cases whch can ncrease embeng capacty (see escrpton of Step 4). EN: all expanable not n EZ Expanson ncurs more sgnfcant storton, so epenng on the payloa, only a subset of EN s selecte for expanson. EN1: selecte for expanson; EN2: not selecte for expanson EN = EN1 U EN2 (See Tan s paper for etals) CN: all changeable not n EZ U EN NC: all non-changeable Multmea Securty an Forenscs 10

11 Step 3 - Embeng Algorthm Step3. Create a bnary locaton map L such that L 1, f EZ EN1 0, otherwse an perform lossless compresson on L The locaton map L s requre because the extracton se nees to know whch have been expane. L nees to be compresse because t wll have to be embee an compresson reuces the payloa Multmea Securty an Forenscs 11

12 Step 4 - Embeng Algorthm Step 4. Collectng LSBs of the n EN2 U CN to form C The LSB of n EN2 U CN are changeable only, so ther orgnal LSB nee to be save, otherwse they cannot be recovere. We o not want to expan those n EN2 n orer to reuce storton Specal cases: for = 1 an = -2 n EN2 U CN, ther LSBs o not have to be save because they reman unchange after embeng. Multmea Securty an Forenscs 12

13 Step 5 - Embeng Algorthm Step 5. Embe bt stream L C P by expanng n EZ U EN U CN (P s the actual payloa or watermark) Let B f elsef EZ EN1 L C : 2 P { b1, b1, b1,...} b EN 2 CN : 2 2 b (Expanable) (Changeabl e) Multmea Securty an Forenscs 13

14 Multmea Securty an Forenscs 14 Step 6 - Embeng Algorthm Step 6. Perform Eq. (2) to get the watermarke mage 2 ' ', 2 1 ' ' a y a x

15 Extracton & Recoverng Algorthm 1. Form a set of m pxel pars (x', y') an calculate ther fference values usng Eq. (1) 2. Partton ' nto 2 sets: CH (CHangeable) an NC (Non-Changeable) 3. Collectng LSBs of the ' n CH to form 4. Decompress locaton map L ' ' 1,, m L C P 5. Restore orgnal fference values (to be explane later) 6. Authentcate content by comparng the extracte P aganst ts orgnal verson B b1, b2, b3, Recover (x, y ) base on usng Eq. (3) 1 x a, y a 2 2 Note a remans unchange after embeng, so a x' (3) y' 2 Multmea Securty an Forenscs 15

16 Step 5 - Extracton Algorthm Step 5. Restore orgnal fference values Let B L C P f ' f CH L else f ' ' 1 ( th bt of locaton map L) else 1 or ' 2 ' ( ' / 2 b b1, b2, b3,... / 2 2 s expane) Multmea Securty an Forenscs 16

17 Conclusons Each fference value can be allowe to carry more than one bt. If k( k Z ) s the largest nteger that satsfes k k 2 b mn 2(255 a),2a 1 b{0,1,2,...,2 1} then the hng capacty of s k. k = 1 s the specal case that we have scusse To mnmse embeng storton wth small magntue s preferre (see Tan s paper for etals) ( x ( y wth greater hng capacty s preferre when full capacty s not neee Mult-layer embeng s possble Embee mage can be embee agan The overall hng capacty of each layer ecrease as the number of expanable fference values s nversely proportonal to the number of layers. x') h y') Multmea Securty an Forenscs 17 2

18 Steganography an Steganalyss Chang-Tsun L Department of Computer Scence Unversty of Warwck Multmea Securty an Forenscs 18

19 Steganography Steganography: s the act of covert communcatons wth the am of preventng the thr party from knowng that secret communcaton s takng place s about hng secret message n the cover mea such that the stego mea remans nnocuous Man requrement: Unetectablty of secret communcatons Multmea Securty an Forenscs 19

20 Steganography & Watermarkng Both are forms of ata hng Dfferent purposes: Watermarkng: protectng the cover/host mea or authentcatng the cover/host mea. It s all about the cover/host mea. Steganography: It s all about the hen message, not the cover/host mea. The user can use any sutable cover mea from a large space of cover mea. Dfferent goals: Watermarkng: Make the act of ata hng known Steganography: Conceal the act of ata hng Dfferent payloas (szes of secret messages): Watermarkng: small Steganography: large Multmea Securty an Forenscs 20

21 Steganographc Moel Secret Message Secret Message Host Mea Embeer Stego Mea Comm. Channel Extracter Secret Key Secret Key Multmea Securty an Forenscs 21

22 Where to He Sequental: e.g. sequentally replacng the LSBs of each mage pxel wth message bts startng from the upper left corner Easy to mplement, But also easy to etect. E.g., analysng statstcal propertes of pxels n the same orer an lookng for suen changes of statstcal propertes can etect covert comm f not all pxels are carryng secret ata. Ranom: select elements of the cover mea accorng to a secret key. E.g., use pseuo-ranom number generator (PRNG) an a secret key to generate a ranom walk through the cover mea. Greater securty Multmea Securty an Forenscs 22

23 Where to He Aaptve: Select elements of the cover mea base on the content of the cover mea Why: Statstcal etectablty of ata hng s lkely to be content base. E.g. ata hen n nosy mages or hghly texture areas of an mage s more unetectable than the same ata hen n smooth areas. He more n texture areas an less n smooth areas Multmea Securty an Forenscs 23

24 Statstcs/Moel Preservng Steganography Moulatng the cover mea so that statstcal propertes, such as hstogram, or moels of the cover mea, are preserve n the stego mea. Example: LSB Embeng replacng the LSBs of pxels wth message bts Let the orgnal pxel value be (72) 10 = ( ) 2 If Message bt = 0 ==> stego pxle = ( ) 2 = (72) 10 If Message bt = 1 ==> stego pxle = ( ) 2 = (73) 10 Multmea Securty an Forenscs 24

25 Detectablty of Statstcs /Moel Preservng Steganography Tougher for the embeer: The embeer carres the buren of ensurng the preservaton of as many statstcs as possble. Easer for the aversary / steganalyst: The steganalyst s etecton of one sngle statstcs unpreserve by the embeer wll jeoparse the covert communcaton. Multmea Securty an Forenscs 25

26 Problem wth LSB Embeng E.g.The orgnal pxel value be (72) 10 = ( ) 2 If Message bt = 0 ==> stego pxle = ( ) 2 = (72) 10 If Message bt = 1 ==> stego pxle = ( ) 2 = (73) 10 For any orgnal pxel wth gray level 2g, g = 0,, 127, the probablty that the stego pxel s gray level remans the same (2g) an becomes (2g + 1) are both equal to 0.5. Ths create an unusual hstogram lke the secon plot. cover mage stego mage Multmea Securty an Forenscs 26

27 Maskng Embeng as Natural Processng Many types of evce-epenent nose reman n mages: e.g. Photo Response Non-Unformty ue to sensor mperfecton Dark current prouce when the sensor s not expose to lght Colour emosackng errors ue to colour nterpolaton Maskng embeng storton as evce nose to make t ffcult to tell whether the slghtly ncrease nose level of the stego mage s ue to ata hng or to the evce Multmea Securty an Forenscs 27

28 Steganalyss Steganalyss s about Detectng the presence of a secret message gven a stego mea Recoverng message attrbutes such as message length or content (.e., forensc staeganalyss) Multmea Securty an Forenscs 28

29 Categores of Steganalyss Categores of steganalytcal methos Targete steganalyss: focusng on specfc steganagraphc algorthms Bln steganalyss: Amng at all types of steganagraphc algorthms Both categores can be seen as classfcaton problem so pattern recognton an machne learnng technques are applcable n steganalyss Multmea Securty an Forenscs 29

30 Steganalyss as Classfcaton Problem It s a two-class classfcaton problem - cover mea or stego mea (.e., absence or presence of secret message) The mensonalty of the space of all mea s too hgh features that characterse mea are use nstea Fourer Transform of the ntensty of hstogram of an mage s a goo example, each component representng a feature. The bounary between the clusters of cover an stego mea can be learnt through a tranng phase. The feasblty of the bounary - etermnes false postve & false negatve rates - epens on the scrmnatng power of the feature set. Multmea Securty an Forenscs 30

31 Targete Steganalyss The steganalyst knows the steganographc algorthm or assumes that t s use The knowlege about the steganographc algorthm can be turne nto useful features. E.g., f LSB embeng s use, then we know LSB embeng as nose to stego mages It ncreases fference between neghbourng pxels Large sum of absolute fference between neghbourng pxels suggests true postve, whle small sum ncates low postve Is sum of absolute fference a goo feature? Probably not! the ntra-class varaton may be greater than the nter-class varaton ue to the versty of the cover mea. feature selecton s a major research area. Multmea Securty an Forenscs 31

32 Bln Steganalyss No pror knowlege about the steganographc algorthm s avalable cannot create stego mea for tranng purpose. Two optons Generate stego mea wth a we varety of known steganographc algorthms One-class learnng: the classfer learns knowlege about cover mea n the feature space an labels a pece of mea as» Cover mea f the feature set of the mea n queston s close to the centro of the cluster of cover mea,» Stego mea f not close enough Multmea Securty an Forenscs 32

33 Conclusons The choce of the cover mea plays a key factor n etermnng the securty of steganographc algorthm It s more ffcult to etect hen message n nosy or hghly texture mages than n mages wth large smooth areas. Ths s because the ntra-class varaton of the clusters of cover an stego mages of the former type are greater. It s more ffcult to etect messages of the same length hen n smaller mages than n larger mages because features compute from a smaller sample space are more nosy. Colour mages are poorer cover mea for ata hng than greyscale mages because colour mages prove more ata for statstcal analyss. Multmea Securty an Forenscs 33