2.  Introduction  LSB algorithm  Jsteg algorithm  Χ^2 test  Adaptive algorithms  LSB Substitution Compatible Steganography(LSCS)  Adaptive DCT-based Mod-4 method(ADM)  Novel LSB based steganography algorithm  Conclusion 2

3. 1.Introduction 3

4. Embedding process can be done in either: 1.Spatial Domain 2.Transform Domain(DCT) LSB Jsteg … … 4

5. 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

6. Derek Upham Its embedding algorithm sequentially replaces the least significant bit of DCT coefficients with the message’s data. JPEG Use the least significant bits as redundant bits. Embedding message’s bits sequentially. 1.compute 8*8 block DCT transform. 2.Quantize DCT coefficients with 6

7. Important rule in Jsteg embedding algorithm:  Many of the coefficients are zero. Changing these coefficients makes noticeable distortion in Image. So we don’t change 0,1,-1 coefficients. 7

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9. 9

10. 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

11. 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. 15  Introduced in 2001  Define  Divide picture and compute  For a cover:  For a LSB-replaced stego:

16. Provos(2001) Outguess improves selection of redundant bits by using a pseudo-random generator to select DCT coefficients at random. Outguess is robust against χ2 test but χ2 test can be modified to detect steganography. 16

17. 2.Adaptive algorithms 17

18.  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

19. 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

20. 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

21. 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 χ 2 test. Hung-Min Sun(2007) Spatial Domain algorithm 21

22. 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 χ2 test. 22

23. First scenario 0 0 3 3 1 1 5467 Pixel values 0344 t array t[k]=L[k]+R[k] 3 23

24. Second scenario 0 0 3 2 0 0 5467 Pixel values 0322 t array t[k]=L[k]+R[k] 2 24

25. 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. 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

28. 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

29. 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

30. 30

31. 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]

32. 32

33. 33  P i =100, p i+1 =162, R 4 =[32 63], t=(00000) b, d’ i =32, m=30, p i <p i+1, d’ i <d i, p’ i =115, p’ i+1 =147.  Extraction: embedded data is difference of |p’ i -p’ i+1 | with low band of proper range  |p’ i -p’ i+1 |=32, R 4 =[32 63], l i =32, b=0, data=(00000) b

34. 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

35. 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

36. 36 OriginalPVD-onlyPVD&LSB Cover & Stego messagemessage

37. Block diagram 37

38. 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 χ 2 test. Transform Domain algorithm 38

39. 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 vGQC’s 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

40. 40

41.  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

42. Mod-4 embedding algorithm If Q is a vGQC we define following parameters: Obviously the range of δ is {00,01,10,11} 42

43. Mod-4 embedding algorithm Embedding process: 1.If |μ|>MC the embedding process halts. Otherwise random bits of length MC-|μ| are padded to the secret message. Let μ 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

44. 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

45. Shortest route scheme If xy=00 δ(σ,4)plusminusroute 000No change 131-1 or +3 222+2 or -2 313-3 or +1 45

46. Example δ(σ,4)plusminusroute 000No change 131-1 or +3 222+2 or -2 313-3 or +1 32 1 If xy=00 53 1 46

47. Example δ(σ,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

48. Hong-Juan Zhang et al(2007) Spatial Domain algorithm Target of this algorithm is robustness against statistical attacks especially χ 2 test and RS analysis. This method provides high capacity for embedding secret message. 48

49. Embedding process Select G= set of pixels of cover image with PRNG. n is calculated by l=length of secret message m=number of bits used per pixel for embedding The bit stream of embedded message is divided into bit segment of m bit length. E= 49

50. Embedding process Define LSB m (x) be the function to get the m bit LSB value from the x. Two rules:  If x i >255 then x i =x i -2 m  If x i <0 then x i =x i +2 m For i=1,2,…,n 50

51. Extraction process Select pixels according to the pseudo random number to construct G= For i=1,2,…,n We get E= and can construct the message 51

52. Example: GX0X0 X1X1 X2X2 X3X3 X4X4 LSB 1 (x i ) Sum mod2 eiei LSB 1 (x i ‘) flipping m=1 001 00 1 11 1 0001 1 0 01 2n 2n-12n+1 2n+22n+1 2n 52

53. LSB 1 (x i ‘) Sum mod2 eiei 1 1000 0 1 0 0 53

54. 3.Conclusion 54

55. 55 CapacityRobustnessImperceptibililtySecurity LSB_classicHighLowNormal LSB_matchingHighLowNormal LSB_revisitedHighNormalHigh PVDHighLowNormal PVD &LSBVery HighVery LowLowNormal

56. [1] Provos, Honeyman, “Hide and Seek: An introduction to steganography”, IEEE Security and Privacy Journal, 2003. [2]T Morkel,JHP Eloff and MS Olivier,”An overview of Image steganography”,ISSA 2005. [3]Westfeld and Pfitzmann,”Attacks on steganographic systems”,3 rd International workshop on information hiding.,1999. [4] Hung-Min Sun,King-Hang Wang,” A LSB substitution compatible steganography”,IEEE 10 region conference,2007. [5] Qi and Wong,” An adaptive DCT-based MOD-4 steganographic method”, IEEE Proceedings of ICIP, vol. II, September 2005, pp. 297-300. [6] Zhang and Tang,” A novel image steganography algorithm against statistical analysis”,International conference on machine learning and cybernetics. 56

57. 57 Questions?