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### Transcript of ïƒ’ Introduction ïƒ— LSB algorithm ïƒ— Jsteg...

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• Introduction LSB algorithm Jsteg algorithm ^2 test Adaptive algorithms LSB Substitution Compatible Steganography(LSCS) Adaptive DCT-based Mod-4 method(ADM) Novel LSB based steganography algorithm Conclusion 2
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• 1.Introduction 3
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• Embedding process can be done in either: 1.Spatial Domain 2.Transform Domain(DCT) LSB Jsteg 4
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• Each pixel of color image represented by 24 bits. LSB of each pixel replaced with the bits of hidden message. Example: 24 bit Image: (11100011 11000011 11110101) (10101010 00110101 10000110) (11100011 11111111 00111110) Bits of hidden message:110000001 (11100011 11000011 11110100) (10101010 00110100 10000110) (11100010 11111110 00111111) 5
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• Derek Upham Its embedding algorithm sequentially replaces the least significant bit of DCT coefficients with the messages data. JPEG Use the least significant bits as redundant bits. Embedding messages bits sequentially. 1.compute 8*8 block DCT transform. 2.Quantize DCT coefficients with 6
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• Important rule in Jsteg embedding algorithm: Many of the coefficients are zero. Changing these coefficients makes noticeable distortion in Image. So we dont change 0,1,-1 coefficients. 7
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• Westfeld & Pfitzmann(1999) They observed that for a given Image,the embedding process change the histogram of color or DCT coefficients. n i =number of pixels with DCT coefficients equal to i before embedding. n i *=number of pixels with DCT coefficients equal to i after embedding. |n 2i -n 2i+1 |>|n 2i *-n 2i+1 *| 10
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• 11 Weak point: Pair of values Histogram of pixel values before and after RS and Chi-square attacks developed based on this weak point xixi mimi yiyi xixi mimi yiyi 111404 302515 415100 404313 111100 100011 213111 415415 404302 100313 504000 111213 011404 313302 202000
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• 15 Introduced in 2001 Define Divide picture and compute For a cover: For a LSB-replaced stego:
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• Provos(2001) Outguess improves selection of redundant bits by using a pseudo-random generator to select DCT coefficients at random. Outguess is robust against 2 test but 2 test can be modified to detect steganography. 16
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• Adaptive algorithms are classified with the target they choose. Targets are chosen respect to the robustness against steganalysis attacks. Different targets can be chose such as histogram preserving,minimum LSB error and 18
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• 19 LSB-matching introduced in 2001 If cover bit does not match with message bit, added or subtracted by one randomly. Else unchanged. cover data: 76 (01001100) b + message bit: 1 = stego data: 75 (01001011) b or 77 (01001101) b
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• 20 No pair of values anymore, difficult to detect Best-known detector based on COM of histogram Introduced in 2003, improved in 2005 Not a perfect detector. Type I and type II errors appear. Newer LSB methods, more difficult to detect or still undetectable! LSB matching revisited and Novel LSB
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• Define four sequences: h:histogram of the cover Image. t:the number of pixel modification for every gray level. L:number of pixels modified from k to k-1. R:number of pixels modified from k to k+1. t[k]=L[k]+R[k] Target of this algorithm is histogram preserving so this algorithm is robust against all the attacks which are based on change of histogram of the image such as 2 test. Hung-Min Sun(2007) Spatial Domain algorithm 21
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• L[0]=R[255]=0 R[k]=t[k]-L[k] If t[k]-R[k-1]>0 L[k+1]=min(t[k]-R[k-1],t[k+1]) LSB algorithm LSCS algorithm So algorithm is robust against 2 test. 22
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• First scenario 0 0 3 3 1 1 5467 Pixel values 0344 t array t[k]=L[k]+R[k] 3 23
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• Second scenario 0 0 3 2 0 0 5467 Pixel values 0322 t array t[k]=L[k]+R[k] 2 24
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• Merit functions: LenaMSEDivergence LSCS2168.60.001781 LSB5219.40.003426 LSB matching4170.60.002650 BaboonMSEDivergence LSCS6409.20.003543 LSB7256.00.003785 LSB matching6861.80.003613 25
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• 27 Main idea: Fewer changes for same capacity Picture divided to consecutive pixel pairs One pixel carries one bit of information A function of two bits carries the other The function should have these properties: has both properties
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• 28 if m i = LSB (x i ) if m i+1 f (x i, x i+1 ) y i+1 = x i+1 +- 1 else y i+1 = x i+1 end else if m i+1 = f (x i -1,x i+1 ) y i = x i 1 else y i = x i + 1 end y i+1 = x i+1 end xixi x i+1 mimi m i+1 yiyi y i+1 110021 110101 111010 or 2 111111 120002 120122 121012 121111 or 3 210021 210120 or 2 211031 211111 220021 or 3 220122 221012 221132
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• 29 Average changes per pixel: Assuming random message 0.375 is expected. 0.5 is expected for conventional LSB method Better quality with same capacity
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• 31 Introduced 2003, expanded 2005 Main idea: increasing the capacity Adaptive embedding: more data hidden in edges Edge: 2 consecutive pixels with high difference Picture divided to consecutive pixel pairs Six ranges for possible differences R i [l i, u i ] of width w i R 1 [0 7] R 2 [8 15] R 3 [16 31] R 4 [32 63] R 5 [64 127] R 6 [128 255]
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• 33 P i =100, p i+1 =162, R 4 =[32 63], t=(00000) b, d i =32, m=30, p i
• 34 Idea: PVD for high ranges, LSB for low ranges If R=R 3, R 4, R 5, R 6, Embed data using PVD If R=R 1 or R 2, Replace three LSBs of each pixel with three data bits New difference should not exceed R 2 : p i =30, p i+1 =15, data=(111000) b, p i =31, p i+1 =8, d i =23>15, p i =23, p i+1 =16 Extraction is straightforward
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• 35 Great capacity gain comparing PVD-only, without loosing much quality PSNR quality criteria: PVD-onlyPVD and LSB Cover image (512*512) capacity (bytes) PSNR (dB) Capacity (bytes) PSNR (dB) Lena5121938.949575536.16 Baboon5714633.43 8973132.63 Peppers5090737.079628135.34 Jet5122437.429632035.01 Tank5049941.999608937.38 Airplane4973940.139779036.6 Truck5006542.729667837.55 Elaine5107441.189502337.11 Couple5160438.819529436.13 Boat5263534.899459633.62
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• 36 OriginalPVD-onlyPVD&LSB Cover & Stego messagemessage
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• Block diagram 37
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• Xiaojun Qi et al(2005) Target of this algorithm is preserving of histogram of DCT coefficients so this algorithm is robust against all the attacks which are based on change of histogram of DCT coefficients of the image such as 2 test. Transform Domain algorithm 38
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• Valid GQC definition GQC is defined to be a group of 2*2 non-overlapping spatially adjacent quantized DCT coefficients. If valid GQC(vGQC) Number of vGQCs depends on the texture of the image. Noisy image will have more vGQCs while a relatively smooth image will yield a lower number of vGQCs. 39
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• vGQC are used as the secret message carriers. vGQCs are extracted from the image and stored in a buffer according to the order determined by a PRNG. The maximum capacity of the cover image is computed to be twice the number of vGQCs. 41
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• Mod-4 embedding algorithm If Q is a vGQC we define following parameters: Obviously the range of is {00,01,10,11} 42
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• Mod-4 embedding algorithm Embedding process: 1.If ||>MC the embedding process halts. Otherwise random bits of length MC-|| are padded to the secret message. Let be the encrypted message coded in some binary representation. 2.To embed the i th pair of binary message bits xy i the coefficient of Q i are modified so that: 43
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• Embedding rules Coefficient with magnitude of less than 2 is ignored. Magnitude of a coefficient is always increased, i.e, addition to positive and subtraction from negative coefficient. Coefficient with larger magnitudes are modified first. The shortest route scheme is used to ensure the minimum number of modifications per DCT coefficients. 44
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• Shortest route scheme If xy=00 (,4)plusminusroute 000No change 131-1 or +3 222+2 or -2 313-3 or +1 45
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• Example (,4)plusminusroute 000No change 131-1 or +3 222+2 or -2 313-3 or +1 32 1 If xy=00 53 1 46
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• Example (,4)plusminusroute 000No change 131-1 or +3 222+2 or -2 313-3 or +1 If xy=00 -3-2 5 -3-2 6 47
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• Hong-Juan Zhang et al(2007) Spatial Domain algorithm Target of this algorithm is robustness against statistical attacks especially 2 test and RS analysis. This method provides high capacity for embedding