Introduction Pixel Value Difference Pixel Value DifferencePVD Data

Introduction Pixel Value Difference

Pixel Value Difference(PVD) Data Embedding Wu and Tsai’s (2003) Scheme Original Image d=| 60 -77 | xi xi+1 60 77 d 17 wm= um - lm +1 wm= 23 - 8 +1=16 t=log 2(wm) t=log 2(16)=4 bits Secret Message(M) = 11011100… Select 4 bits from M: 1101 v=13 d’=lb+v m=d’-d d’=8+13=21 m=21 -17=4

Pixel Value Difference(PVD) Wu and Tsai’s (2003) Scheme Original Image d=| 60 -77 | xi xi+1 60 77 d 17 wm= um - lm +1 wm= 23 - 8 +1=16 t=log 2(wm) t=log 2(16)=4 bits Secret Message(M) = 11011100… Select 4 bits from M: 1101 v=13 d’=lb+v m=d’-d d’=8+13=21 m=21 -17=4 If xi ≥ xi+1 and d’ > d then xi = xi + ceiling (m/2) and xi+1 = xi+1 - floor(m/2)

Pixel Value Difference(PVD) Wu and Tsai’s (2003) Scheme Original Image d=| 60 -77 | xi xi+1 60 77 d 17 wm= um - lm +1 wm= 23 - 8 +1=16 t=log 2(wm) t=log 2(16)=4 bits Secret Message(M) = 11011100… Select 4 bits from M: 1101 v=13 d’=lb+v m=d’-d d’=8+13=21 m=21 -17=4 If xi ≥ xi+1 and d’ ≥ d then xi = xi - ceiling (m/2) and xi+1 = xi+1 + floor(m/2)

Pixel Value Difference(PVD) Wu and Tsai’s (2003) Scheme Original Image d=| 60 -77 | xi xi+1 60 77 d 17 wm= um - lm +1 wm= 23 - 8 +1=16 t=log 2(wm) t=log 2(16)=4 bits Secret Message(M) = 11011100… Select 4 bits from M: 1101 v=13 d’=lb+v m=d’-d d’=8+13=21 m=21 -17=4 If xi < xi+1 and d’ ≤ d then xi = xi + ceiling (m/2) and xi+1 = xi+1 - floor(m/2)

Pixel Value Difference(PVD) Wu and Tsai’s (2003) Scheme Original Image d=| 60 -77 | xi xi+1 60 77 Secret Message(M) = 11011100… Select 4 bits from M: 1101 v=13 d’=lb+v d 17 wm= um - lm +1 wm= 23 - 8 +1=16 t=log 2(wm) t=log 2(16)=4 bits xi’ xi+1’ 58 79 Stego Image m=d’-d d’=8+13=21 m=21 -17=4 If xi < xi+1 and d’ > d then xi = xi - floor(m/2) and xi+1 = xi+1 + ceiling(m/2)

Pixel Value Difference(PVD) Data Extraction Wu and Tsai’s (2003) Scheme Stego Image d’=| 58 -79 | xi’ xi+1’ 58 79 d’ 21 wm= um - lm +1 wm= 23 - 8 +1=16 t=log 2(wm) t=log 2(16)=4 bits v=d’- lb v=21 -8=13 Convert v into 4 bits binary form i. e. : 1101

Comparison PVD based Scheme

Difference Expansion (DE) Data Embedding Tian’s (2003) Scheme Original Image d=| 120 -127 | xi xi+1 120 127 d 7 Average v = floor ((120+127)/2)= 123 Secret Message(M) = 11011… d’ = d x 2 + w w is 1 bit data. d’ = 7 x 2 + 1 = 15 If xi ≥ xi+1 then xi ’ = v+ ceiling (d’/2) xi+1 ’ = v- floor (d’/2)

Difference Expansion (DE) Tian’s (2003) Scheme Original Image d=| 120 -127 | xi xi+1 120 127 Secret Message(M) = 11011… d’ = d x 2 + w w is 1 bit data. d’ = 7 x 2 + 1 = 15 If xi < xi+1 then xi ’ = v - floor (d’/2) xi+1 ’ = v + ceiling (d’/2) d 7 Average v = floor ((120+127)/2)= 123 xi’ xi+1’ 116 131 Stego Image 120 < 127 then xi ’ = 123 - floor (15/2) xi+1 ’ = 123 + ceiling (15/2)

Difference Expansion (DE) Tian’s (2003) Scheme stego Image xi ’ xi+1 ’ 116 131 d’=| 116 -131 |d’ 15 Average v’ = floor ((116+131)/2)= 123 Extract 1 bit from LSB of d’ i. e. 1 d = d’/2 d = 15/2=7 If xi ’ ≥ xi+1 ’ then xi = v+ ceiling (d/2) xi+1= v- floor (d/2) Data Extraction

Difference Expansion (DE) Tian’s (2003) Scheme stego Image xi ’ xi+1 ’ 116 131 Extract 1 bit from LSB of d’ i. e. 1 d = d’/2 If xi ’ < xi+1 ’ then xi = v - floor (d/2) xi+1= v + ceiling (d/2) d’=| 116 -131 |d’ 15 Average v’ = floor ((116+131)/2)= 123 xi xi+1 120 127 d = 15/2=7 Original Image 116 < 131 then xi = 123 - floor (7/2) xi+1= 123 + ceiling (7/2)

Exploiting Modification Direction (EMD) Data Embedding Zhang and Wang’s Method (2006) Divided Cover image into several blocks of n pixels(x 1, x 2, . . . , xn), where n>=2. Let n=2 Cover image C (H x W) Select pixel pair 113 120

Exploiting Modification Direction (EMD) Zhang and Wang’s Method (2006) Secret Message(M) 1100100111110010…. . Cover image C (H x W) Divide M into K bits 1100100111110010…. . . Select pixel pair 113 120 k = floor(log 2(2 n + 1)) = floor(log 2(2*2 + 1)) = floor(log 2(5)) = 2

Embedding Procedure Zhang and Wang’s Method(2006) Zhang and Wang’s Method (2006) So, divide M into 2 bits 1000100111110010…. . . Cover image C (H x W) Select 2 bits from M and convert into (2 n+1) ary notational system form d Select pixel pair 113 120 So, (10)2 is converted i. e. d = (2)5

Embedding Procedure Zhang and Wang’s Method(2006) Zhang and Wang’s Method (2006) d = (2)5 Cover image C (H x W) f(x 1, x 2, . . , xn) = (x 1 * 1 + x 2 * 2 +. . Xn *n) mod(2 n + 1) So, f (113, 120) = (113× 1+120× 2) mod 5 = 3 Select pixel pair 113 120 f () If d = f , then x’ 1= x 1 and x’ 2 = x 2 else calculate S as S = (d - f) mod (2 n+1) If S < n pixel value of xs is increased by 1 else pixel value of x 2 n+1−s is decreased by Here, 2 ≠ 3, calculate S as S = (2 − 3) mod 5 = 4. Here, 4 ≥ 2, so the pixel value of x(2*2+1)− 4 = x 1 i. e. 113 is decrease by 1. x’ 1= x 1 – 1 = 113 – 1 = 112 x’ 2 = x 2 = 120

Extraction Procedure Zhang and Wang’s Method(2006) Zhang and Wang’s Method (2006) Data Extraction Since, n=2 , divided Stegoimage into several blocks of 2 pixels. Stego image S (H x W) f(x 1, x 2, . . , xn) = (x 1 * 1 + x 2 * 2 +. . Xn *n) mod(2 n + 1) Select pixel pair So, f (112, 120) = (112× 1+120× 2) mod 5 = 2 112 120 f () So, d = (2)5 Then convert d value into 2 bits binary form i. e. 10.

Comparison EMD based Scheme