Enhance Embedding Capacity of Generalized Exploiting Modification Directions in Data Hiding Source: IEEE Access, Vol. 6, Dec. 2017, pp. 2169-3536 Authors: Yanxiao Liu, Chingnung Yang, Qindong Sun Speaker: Guanlong Li Date: 7/12/2018

Outline Related Works Propose Scheme Experimental Results Conclusions Exploiting Modification Direction(EMD) Generalized Exploiting Modification Direction(GEMD) Propose Scheme Experimental Results Conclusions

Related Works(1/4) - EMD g1 g2 … gn . Input: cover image 𝐼 and secret data S→(2n+1) - array Output:stego image 𝐼′ 1. Calculate 𝑓 𝐸𝑀𝐷 =𝑓𝑎(g1, g2, g3,…gn) using 𝑓𝑎 (g1, g2, g3,…gn) = 𝑖=1 𝑛 (gi ×𝑖) 𝑚𝑜𝑑 (2𝑛+1) 2. Calculate the difference d=(S− 𝑓 𝐸𝑀𝐷 ) mod (2n+1) 3. If (d = 0) then (g'1,g'2,g'3, …g′n) = (g1,g2,g3, …gn); else if (n > d), then (g′1, g'2, …, g'd, …g'n) = (g1, g2,…, gd+1,… gn); else (g′1, g'2,…, g'(2n+1)-d,… g'n) = (g1,g2,…,g(2n+1)-d -1,…gn). 4. Modify the (g1, g2, g3,… gn) in 𝐼 by (g′1, g'2, g'3,… g'n) to create 𝐼′ Extracting phase S = 𝑖=1 𝑛 (gi ×𝑖) 𝑚𝑜𝑑 (2𝑛+1)

Related Works(2/4) - EMD An example: 𝐼 = (1,2,3,4,6) , S = 7 1. Calculate 𝑓 𝐸𝑀𝐷 = 𝑓𝑎(1,2,3,4,6) using 𝑓𝑎 (1,2,3,4,6) = 𝑖=1 𝑛 (gi ×𝑖) 𝑚𝑜𝑑 (2𝑛+1) = (1*1+2*2+3*3+4*4+6*5) mod (2*5+1) = 5 2. Calculate the difference d = (7−5) mod (2n+1) = 2 3. Have ( n > d ), then (g′1, g′2, g′3, g′4, g′5) = (g1, g2+1, g3, g4, g5) = (1,3,3,4,6) 4. Modify the (g1, g2, g3, g4, g5) in 𝐼 by (g′1, g′2, g′3, g′4, g′5) to create 𝐼′ Extract secret S = 𝑖=1 𝑛 (gi ×𝑖) 𝑚𝑜𝑑 (2𝑛+1) = (1*1+3*2+3*3+4*4+6*5) mod (2*5+1) =7

Related Works(3/4) - GEMD Input: cover image 𝐼 and secret data S→(2n+1) - array Output:stego image 𝐼′ 1. Calculate 𝑓 𝐺𝐸𝑀𝐷 =𝑓𝑏(g1, g2, g3,…gn) using 𝑓𝑏 (g1, g2, g3,…gn) = 𝑖=1 𝑛 gi ×( 2 𝑖 −1) 𝑚𝑜𝑑 2 𝑛+1 2. Calculate the difference d = ( S − 𝑓 𝐺𝐸𝑀𝐷 ) mod 2 𝑛+1 3. If (d = 0) then g 𝑖 ′ = g 𝑖 ; else if(d = 2 𝑛 ) then g 𝑛 ′ = g 𝑛 +1 , g 1 ′ = g 1 +1; else if (0 < d < 2 𝑛 ), then d → ( 𝑏 𝑛 , 𝑏 𝑛−1 ,…, 𝑏 1 , 𝑏 0 )2 else d’ = 2 𝑛+1 − d , then d’ → ( 𝑏 𝑛 , 𝑏 𝑛−1 ,…, 𝑏 1 , 𝑏 0 )2 and for i = n to 1 do { If ( 𝑏 𝑖 = 0 & 𝑏 𝑖−1 = 0) or ( 𝑏 𝑖 = 1 & 𝑏 𝑖−1 = 1) then g 𝑖 ′ = g 𝑖 ; else if ( 𝑏 𝑖 = 0 & 𝑏 𝑖−1 = 1) then d : g 𝑖 ′ = g 𝑖 +1 𝑑 ′ : g 𝑖 ′ = g 𝑖 −1 ; else if ( 𝑏 𝑖 = 1 & 𝑏 𝑖−1 = 0) then d : g 𝑖 ′ = g 𝑖 −1 𝑑 ′ : g 𝑖 ′ = g 𝑖 +1 .} Extracting phase S = 𝑖=1 𝑛 gi ×( 2 𝑖 −1)

Related Works(4/4) - GEMD An example: 𝐼 = (6,9,5) , S = 13 1. Calculate 𝑓 𝐺𝐸𝑀𝐷 = 𝑓𝑎(6,9,5) using 𝑓𝑎 (6,9,5) = 𝑖=1 𝑛 gi × 2 𝑖 −1 𝑚𝑜𝑑 2 𝑛+1 = (6*1+9*3+5*7) mod (16) = 4 2. Calculate the difference d = (13−4) mod 2 𝑛+1 = 9 3. Have (0 < d < 𝟐 𝒏 ), then d′ = 2 𝑛+1 −𝑑=7 → (0111) 2 (g′1, g′2, g′3) = (g1, g2, g3-1) = (6,9,4) 4. Modify the (g1, g2, g3, g4, g5) in 𝐼 by (g′1, g′2, g′3, g′4, g′5) to create 𝐼′ Extract secret S = 𝑖=1 𝑛 gi × 2 𝑖 −1 𝑚𝑜𝑑 2 𝑛+1 = (6*1+9*3+4*7) mod (16) =13

Propose Scheme(1/4) – Enhanced GEMD Input: two cover image 𝐼 1 = (g1, g2, g3,…gn1) 、 𝐼 2 = (g1, g2, g3,…gn2) , n= 𝑛 1 + 𝑛 2 and secret data S→(2n+2) - array Output: two stego image 𝐼′ 1 、 𝐼′ 2 Convert the n+2 bits data s into decimal 𝑆 (10) Let 𝑆 (10) = 2 𝑛 1 +1 ×𝑐+𝑟 , where c and r are integers and r < 2 𝑛 1 +1 Embedding r,c into 𝐼 1 , 𝐼 2 using the embedding approach in GEMD respectively Extracting phase Extracting c and r from 𝐼′ 2 and 𝐼′ 1 respectively using the extraction approach in GEMD. Computing 𝑆 (10) = 2 𝑛 1 +1 ×𝑐+𝑟

Propose Scheme(2/4) – Enhanced GEMD An example: 𝐼 = (6,9,5) , S = (11010) 2 𝐼 into 𝐼 1 = (6,9) and 𝐼 2 = (5) , S = (11010) 2 = (26) 10 26 = 2 𝑛 1 +1 ×𝑐+𝑟 = 2 2+1 ×3+2 3. Embed 2 and 3 into 𝐼 1 and 𝐼 2 using the embedding approach in GEMD respectively 4. 𝐼′ 1 =(7,9) , 𝐼′ 2 =(7) Extract secret 𝐼 ′ 1 : 7× 2 1 −1 +9× 2 2 −1 𝑚𝑜𝑑 2 3 =2 , 𝐼′ 2 :7× 2 1 −1 𝑚𝑜𝑑 2 2 =3 𝑆 (10) = 2 𝑛 1 +1 ×𝑐+𝑟 = 2 2+1 ×3+2 = 26

Propose Scheme(3/4) – Enhanced GEMD Input: k cover image 𝐼 1 , 𝐼 2 , … , 𝐼 𝑘 , n= 𝑖=1 𝑘 𝑛 𝑖 and secret data S→(2n+k) - array Output: k stego image 𝐼′ 1 , 𝐼′ 2 , … , 𝐼′ 𝑘 Convert the n+k bits data s into decimal 𝑆 (10) Let 𝑆 (10) = 2 𝑛 1 +1 × 𝑐 1 + 𝑟 1 , 𝑐 1 = 2 𝑛 2 +1 × 𝑐 2 + 𝑟 2 , . . . 𝑐 𝑘−2 = 2 𝑛 𝑘−1 +1 × 𝑐 𝑘−1 + 𝑟 𝑘−1 , Embedding 𝑐 𝑘−1 into 𝐼 𝑘 and embedding 𝑟 1 , 𝑟 2 , … , 𝑟 𝑘−1 into 𝐼 1 , 𝐼 2 , … , 𝐼 𝑘−1 using embedding approach in GEMD. Extract secret Extracting 𝑟 1 , 𝑟 2 , … , 𝑟 𝑘−1 and 𝑐 𝑘−1 from 𝐼 1 , 𝐼 2 , … , 𝐼 𝑘 respectively using the extraction approach in GEMD. Computing 𝑐 𝑘−2 = 2 𝑛 𝑘−1 +1 × 𝑐 𝑘−1 + 𝑟 𝑘−1 , . . . 𝑐 1 = 2 𝑛 2 +1 × 𝑐 2 + 𝑟 2 , 𝑆 (10) = 2 𝑛 1 +1 × 𝑐 1 + 𝑟 1

Propose Scheme(4/4) – Enhanced GEMD An example: 𝐼 = (6,9,5,8,12,3) , S = (101100101) 2 , k = 3 𝐼 into 𝐼 1 = (6,9,5) and 𝐼 2 = (8,12) and 𝐼 3 = (3) , S = (101100101) 2 = (357) 10 , n + k = 9 357 = 2 𝑛 1 +1 ×22+5 22 = 2 𝑛 2 +1 ×2+6 3. Embed 5 , 6 and 2 into 𝐼 1 , 𝐼 2 and 𝐼 3 using the embedding approach in GEMD respectively 4. 𝐼′ 1 =(7,9,5) , 𝐼′ 2 =(7,13) , 𝐼′ 3 =(2) Extract secret 𝐼 ′ 1 : 7× 2 1 −1 +9× 2 2 −1 +5× 2 3 −1 𝑚𝑜𝑑 2 4 =5 , 𝐼′ 2 : 7× 2 1 −1 +13× 2 2 −1 7× 2 1 −1 +13× 2 2 −1 𝑚𝑜𝑑 2 3 =6 , 𝐼′ 3 :2× 2 1 −1 𝑚𝑜𝑑 2 2 =2 𝑐 1 = 2 𝑛 2 +1 × 𝑐 2 + 𝑟 2 = 2 2+1 ×2+6=22 , 𝑆 (10) = 2 𝑛 1 +1 × 𝑐 1 + 𝑟 1 = 2 3+1 ×22+5 = 357

Experimental Results(1/2) Comparison of Embedding Capacities Comparison of PSNRs Between Three Schemes

Experimental Results(2/2) Capacities and PSNRs of Generalized Enhanced GEMD

Conclusions In two group, it improve the embedding capacity of GEMD from 𝑛+1 𝑛 bpp to 𝑛+2 𝑛 bpp. In k group, it can improve embedding capacity by choosing a larger parameter k , however the PSNR will decrease when k increases.