1. Four-scanning attack on hierarchical digital watermarking method for image tamper detection and recovery Source: Pattern Recognition, Vol. 41, Issue 2, Feb. 2008, pp. 654-661 Authors: Chin-Chen Chang,Yi-Hsuan Fan, and Wei-Liang Tai Reporter: 陳德祐 Date: 2008/10/31

2. 2 Outline Introduction A Hierarchical Digital Watermarking Method for Image Tamper Detection and Recovery  Phen-Lan Lin, Chung-Kai Hsieh, and Po-Whei Huang, Pattern Recognition, Vol. 38, Issue 11, 2005 The Proposed attacks  The four-scanning attack  The blind attack Experimental Results Conclusions Comments

3. 3 Introduction Received ImageDelivered Image

4. 4 Preparation~ block mapping Non-overlapping blocks of 4 × 4 pixels A block-mapping sequence A → B → C → D →· · ·→A X' = [f (X) = (k × X) mod N] + 1 X ', X : the block number ( ∈ [0,N −1]) k : a secret key (a prime and ∈ [0,N − 1]) N : the total number of blocks in the image ( ∈ Z − {0}) The original block The look up table X '=13 × X mod 64 +1

5. Watermark Embedding (1/2) 13911 241012 571315 681416 13911 241012 571315 681416 avg_B=(I 1 +I 2 + … +I 16 )/16 avg_B s =(I 1 +I 2 +I 3 +I 4 )/4 Block B Block A avg_A s =(I 1 +I 2 +I 3 +I 4 )/4 a1a1 a2a2 a3a3 a4a4 a5a5 a6a6 a7a7 a8a8 r v, p of B (Set 2 LSBs of each pixel to zero) Watermark: v, p, r Block mapping A → B (secret key k ) num : the total # of 1’s in the six MSBs of avg_Bs

6. 6 Watermark Embedding (2/2) 69788297 3546210102 51337344 17383145126 1042299207 395561132 4266323 227198145164 011010 000101 001001 001101 Block A Block B avg_A s =(68+76+32+44)/4=55=(00110111) 2 avg_B s =(104+20+36+52)/4=53=(00110101) 2 avg_B=(104+20+96+204+ … +164)/16=97 r = 001101 v=0, p=1 104 22 39 55 00 10 11 01 104 22 39 53 Block mapping A → B (secret key k) num : the total # of 1’s in the six MSBs of avg_Bs

7. 7 Hierarchical Tamper Detection (1/3) 1042099207 395361132 4266323 227198145164 avg_B ’ s =(104+20+36+52)/4=53 (=00110101) avg_B ’ =(104+20+96+204+ … +164)/16=97 011010 000101 001001 001101 00 00 11 01 Level 1 : 104 20 39 53 v=0, p=0 v’=0, p’=0 Sub-Block is invalid, if p’ is not equal to p Sub-Block is invalid, if v’ is not equal to v

8. 8 Hierarchical Tamper Detection (2/3) 1042099207 395361132 4266323 227198145164 Level 3 : a valid block is further marked erroneous if there are five or more erroneous blocks in its 3 × 3 block-neighborhood ErrorB 1042099207 395361132 4266323 227198145164 Level 2 : a block is marked erroneous if any subblock within it is marked erroneous

9. 9 Hierarchical Tamper Detection (3/3) Level 4 : only required against the VQ counterfeiting attack 1042099207 395461132 4266323 227198145164 01101000 00010100 00100111 00110110 r = 001110(00) = 56 = avg_B1’ s Block C 69788297 3546210102 51337344 17383145126 Block B ’ avg_B ’ s =(68+76+32+44)/4=55 avg_B ’ s  avg_B1’ s 55=00110111  00110100=52 Block mapping B’ →C (secret key k)

10. 10 Tampered Image Recovery 69788297 3546210102 51337344 17383145126 1042099207 395461132 4266323 227198145164 01101000 00010100 00100111 00110110 Valid Block B 56 8297 56 210102 51337344 17383145126 r = 001110(00) = 56 Tamped Block ARecovered Block A Block mapping A → B

11. 11 Four-scanning attack The security of Lin et al.’s method is based on the block-mapping sequence  X' = [f (X) = ( k × X) mod N] + 1  k is a secret key  Unknown k, it is difficult to find the block- mapping sequence A → B → C → D →· · ·→A But…

12. 12 Generate a searched dictionary (r 1,1,r 1,2,r 1,3,r 1,4 ) (r 2,1,r 2,2,r 2,3,r 2,4 ) (r N,1,r N,2,r N,3,r N,4 ) Block 1 Block 2 Block N … … For each block, perform the searching Block i(r i,1,r i,2,r i,3,r i,4 ) (r 1,1,r 1,2,r 1,3,r 1,4 ) (r 2,1,r 2,2,r 2,3,r 2,4 ) (r N,1,r N,2,r N,3,r N,4 ) … B k dubious blocks

13. 13 Blind attack (r,v,p) is encrypted before embedding s.t. none of the 8 bits alone in a block indicate v or p or r rather than bit-by-bit direct meaning  Four-scanning attack cannot gain its purpose The watermark (v, p, r) is constant as long as avg_Bs (the average intensity for each sub-block) does not change.

14. 13911 241012 571315 681416 13911 241012 571315 681416 avg_B=(I 1 +I 2 + … +I 16 )/16 avg_B s =(I 1 +I 2 +I 3 +I 4 )/4 Block B Block A avg_A s =(I 1 +I 2 +I 3 +I 4 )/4 a1a1 a2a2 a3a3 a4a4 a5a5 a6a6 a7a7 a8a8 r v, p of B (Set 2 LSBs of each pixel to zero) Watermark: v, p, r Block mapping A → B (secret key k ) num : the total # of 1’s in the six MSBs of avg_Bs

15. 69788297 3546210102 51337344 17383145126 1042299207 395561132 4266323 227198145164 011010 000101 001001 001101 Block A Block B avg_A s =(68+76+32+44)/4=55=(00110111) 2 avg_B s =(104+20+36+52)/4=53=(00110101) 2 avg_B=(104+20+96+204+ … +164)/16=97 r = 001101 v=0, p=1 104 22 39 55 00 10 11 01 104 22 39 53 Block mapping A → B (secret key k) Keep unchanged Keep avg_Bs unchanged 011111 000000 000001 010101 00 10 11 01 124 0 7 85

16. 16 The watermarked imageThe original image

17. 17 the tampered F-16the detected tampered regions using level-2 inspection on (a) the tampered F-16 using the proposed attack the detected tampered regions using level-3 inspection on (c) the detected tampered regions using level-4 inspection on (c).

18. 18 the detected tampered regions using level-4 inspection on (a) the tampered F-16 using the proposed blind attack the detected tampered regions Using level-3 inspection on (a)

19. 19 Conclusions The four-scanning attack  tracing out the mapping correlation of blocks  create elegant and imperceptible tampered images, The blind attack  tamper any sub-block with constant average intensity in a watermarked image even though the mapping sequence is unknown.  the tampered images are noticeable

20. 20 Comments A Majority-voting Based Watermarking Scheme for Color Image Tamper Detection and Recovery  Ming-Shi Wang and Wei-Che Chen, Computer Standards & Interfaces, 29 (2007), pp.561- 570 Increase the searching complexity to resist The four-scanning attack Check bits to resist the blind attack