Đề tài Một thuật toán giấu tin trên ảnh có bảng màu

1 A New Data Hiding Algorithm in Palette Images Đỗ Vă T Vă Abstract - This paper proposes a new algorithm to embed data in palette image. In each image block of original image, this algorithm can hide a bit by modifying at most one pixel of block. New color of modified pixel resembles the color of its some neighborhood pixels, so the image after hiding very close to the original image. The experimental results showed that, the invisible of proposed algorithm is better than algorithms Fridrich and Ez Stego. Keywords: data hiding, steganography, security watermarking, Palette images Tóm tắt - Trong bài báo này đề xuất t thuật toán giấu tin trên ảnh có bảng àu. Với ỗi h i c ảnh g c, thuật toán có th giấu đ c t b t và ch thay đổi t i đ t đi ảnh c h i. Màu ới c đi ảnh b th y đổi sẽ gi ng với àu c t s đi liền ề với nó, vì vậy ảnh s u hi giấu tin rất gần với ảnh g c. t uả th c nghi cho thấy, t nh ch giấu c thuật toán đề xuất t t h n các thuật toán ri rich và t go. 1. GIỚI THIỆU . Theo [1 : Theo 2,9,10 che gi [3]-[8]. , b ẻ 3 4 7 8 7 c, Gc, Bc 2 p heo 3 4 √ i, Gi, Bi j, Gj, Bj . ( ẻ) ẻ ( ) (theo ) sau khi tin, trong [6] G. Pan, Z. Wu, Y. Pan cho 3×3, tin 8 (nominated color) 3×3 nhau tin M. Wu [11] Y. C. Tseng[12 ẻ ẻ ẻ 3 4 2. ỘT SỐ HIỆU V ĐỊNH NGHĨA - × hàng và n c t . - , (i,j) ch u n t đ n v tr Fi,j i,j u n t đ n cả v tr và giá tr . Hai Fi,j, Fu,v ẻ Fi,j# Fu,v Đị ĩa 2.1 ng v  hai ma tr n C = A  B v Ci,j = Ai,j × Bi,j =1 … = 1 … Đị ĩa 2.2 Ph U n U (A) : ∑∑ 3 Đị ĩa 2.3 O × C = MOD(F) v Ci,j = Fi,j =1 . = 1 …,n Đị ĩa 2.4 tr n ( ) l ( ) : (i,j)(u,v) Max{|u-i|, |v-j|}= 1 Đị ĩa 2.5 i ỳ (i,j) (u,v) Ki,j=Ku,v=1 (pt,qt), t=1 … 1, tt qpK , t= 1,..k (i,j)(p1,q1)(p2,q2)....(pk,qk)  (u,v) 3. THU T T N Đ U T nh õ con. 3.1 a con - 11 ẻ -Lee, Fi,j 1 1 1 Fi,j ́ ̀ ̣ . có giấu tin n G : - 1≤ SUM(MOD(G)K) ≤ SUM(K) – 1 (3.1) - SUM(GK) mod 2 = b (3.2) - (3 1) (3. ) 3.2 Nội dung thuật toán gi u tin B ớ 1: s = SUM(MOD(F)K) B ớ 2: K : 1) = = U ( ) 2) 1≤ ≤ U ( )-1 3 B ớ 3: X hai : 1) = = 2) 4 B ớ 4: X ∏ ∏ { { ̃ ̀ } ́ { ̉ ̀ } ́ { ̀ } ́ D ∏ . B ớ 5: 1) ( )  ∏ 2) ( ) sao cho: (u,v)  ( ) Fu,v # Fi,j (Th o đ nh ngh c , lu n t n t i u,v nh vậy 3) Thay Fi,j u,v = 4 N é 1: t th c t i ớc ho c ớc , (3 1) (3 ) ≠ Ø 4 N é 2: ( ) ( ). D ( ) (u,v) ( ) (i,j)  ∏ ( ) = { ( )| ( )  ∏} ( ) ( ) p,q. (i,j), ( ) ( ) ẻ Fi,j:  jiqpji FFvajiqpqp ,,, #),(),(|),(  ( )  ji, ( ) ji, p,q. ( ) : ̀ C - - ẻ ( ) (Ki,j=1), i,j ẻ SUM(FK) ẻ (3 ) ( ) (i,j). 3.3 Min ọa : 0 1 0 1 0 1 0 1 1 H 3.1 D : b1b2b3b4 = 1100 4 F 1 F 2 145 46 253 139 179 200 120 34 46 47 78 78 105 230 139 16 39 39 245 76 34 195 246 195 78 53 57 57 249 230 53 78 64 231 23 199 F 3 F 4 H 3.2 : SUM(K) = 5 i i (i = 1,2,3,4). 1 =1 1 : s = SUM(MOD(F 1 )K)= 1, do 0<s<SUM(K) sang B 3 = 1, G 1 = F 1 2=1 2 : s = SUM(MOD(F 2 )K)= 4, U ( ) 3 s mod 2 b2 4 ∏={(1 ) (2,1), (3,2), (3,3)} (1 )=0, g(2,1)=0, g(3,2)=1, g(3,3)=1, n (i,j)=(3,2); : Ω3,2={(2,2),(2,3),(3,1)} f(2,2)=1, f(2,3)=1, f(3,1)=0. C ( ) = ( ) thay F23,2 F 2 2,2, G 2 =F 2 . 3= 3 : s = SUM(MOD(F 3 )K) = 1, U ( ) 3 s mod 2 b3 4 ∏ = {(1,2), (2,1), (3,2), (3,3)} 5 (1 )= g(2,1)=1, g(3,2)=1, (3 3)= (i,j)=(2,1) Ω2,1={(1,1), (2,2), (3,1)} v (1,1)=0, f(2,2)=1, f(3,1)=1 C (u,v)=(3,1), thay F32,1 3 3,1 3 = F 3 . 4=0 v 4 : s = SUM(MOD(F 4 )K) = 3, U ( ) 3 s mod 2 b4 4 ∏ = {(1,2), (2,1), (2,3), (3,2), (3,3)} ( ) = (1 ) ( ) = (1 1). Thay F 4 1,2 F 4 1,1 G 4 = F 4 . i sau: G 1 G 2 145 46 253 139 179 200 120 34 46 47 78 78 105 230 139 16 78 39 245 76 34 195 195 195 53 53 57 57 249 230 53 78 64 231 23 199 G 3 G 4 H 3.3 3.4 T (3 1) (3 ) B ớ 1: = U ( O ( )K) B ớ 2: N u = = U ( ) = 3.5 T a × mxn , v , 4. T NH Đ NG Đ N A THU T T N Q1 ={(i,j)| Ki,j =1 i,j ẻ} (4.1) Q2 ={(u,v)| Ku,v =1 u,v } (4.2) (4 1) (4 ) Q1 ∩ Q2 = Φ |Q1| + |Q2| = SUM(K) (4.3) Bổ : Q1 Φ Q2 Φ ( ) ( ) sao cho: (i,j)  (u,v), (i,j)  Q1 (u,v)  Q2 Chứng minh bổ đề Do Q1 Φ Q2 Φ ( 0,j0)  Q1 ( 0,v0)  Q2. (i0,j0)(u0,v0) ( )= (i0,j0) (u,v) = (u0,v0) (i0,j0) ( 0,v0) ( t,qt), t = 1,…,k sao cho: tt qp K , = 1, t= 1,..k (i0,j0)(p1,q1)(p2,q2)....(pk,qk)(u0,v0) Q2, ( ) = ( 0,j0) ( ) = ( 1,q1) ãy có t nhất t phần tử  Q1), ( h,qh) Q1 = ( ) = ( k,qk) ( ) = ( 0,v0) do (ph,qh) Q1 6 (ph+1,qh+1) Q2 (i,j)=(ph,qh) ( ) = ( h+1,qh+1). ứ ú ắ a : (4 1) s = SUM(MOD(F)K) = |Q1| (4.4) 1 3 ≠ Ø. =1 = U ( )-1 1 U ( )-1. 1) N u s thì th o ớc c ∏ = {(i,j) | Ki,j = 1, Fi,j  (u,v): (u,v)( ) Fu,v # Fi,j} (4 3) (4 4) |Q1| = s = 1 |Q2| = SUM(K) - |Q1| = SUM(K) -1 Q1 Φ Q2 Φ (u,v)  Q1, (i,j) Q2 (u,v)(i,j). Q1, Q2 : Fu,v ẻ Ki,j= 1 i,j suy ra (i,j)  ∏, v ∏ Φ. 2) N u s M - 1 thì th o ớc ∏={(i,j) | Ki,j = 1, Fi,j ẻ,  (u,v): (u,v)( ) Fu,v#Fi,j} (4 3) (4 4) |Q1| = s = SUM(K) - 1 |Q2| = SUM(K) - |Q1| =1 Q1 Φ Q2 Φ (i,j)  Q1, (u,v) Q2 ( )( ) Q1, Q2 : Ki,j = 1, Fi,j ẻ Fu,v suy ra (i,j)  ∏, v ∏ Φ. 3) N u s M - thì th o ớc ∏ = {(i,j) |Ki,j = 1, (u,v): (u,v)( ) u,v # Fi,j} (4 3) (4 4) 1< |Q1| < SUM(K) - 1 |Q2| = SUM(K) - |Q1| >1 Q1 Φ Q2 Φ (i,j)  Q1, (u,v) Q2 ( )  ( ) Q1, Q2 : Ki,j = Ku,v =1, Fi,j ẻ Fu,v suy ( ) ( ) ∏, v ∏ Φ. 5. TH NGHIỆ Ez Stego - 4 1 - 8 × 256 a) 4 1 : b) a 7 c) a Fridrich d) a Ez Stego K nh Fridrich, Ez Stego , n 6. ẾT LU N × Trong [6], G. Pan, Z. Wu, Y. Pan Q 8 4 1 . T ệ a [1] Ấ n, M t s nhận xét về ph ng pháp giấu tin c Ch n – Pan – Tseng, 7 [2] Ấ , Thuật toán giấu tin ung l ng c o, 1 7 [3] J. Fridrich, Secure steganographic methods for palette images, Proceeding of 3rd int. Workshop on Information Hiding,1999. [4] J. Fridrich, J.Du Secure Steganographic Methods for Pallete Image. The 3 rd Information Hiding Workshop, Lecture Notes in Computer Science. 1768, 47-60 (2000) [5] M.Y. Wu, Y. H. Ho, Jia-Hong Lee, An iterative method of palette-based image steganography, Pattern Recognition Letters 25, 301–309, (2004) [6] Gang Pan, Zhaohui Wu, Yunhe Pan, A Data Hiding Method for Few – Color Images. IEEE Proceedings of the 2002 International conference on Acoustic, Speech, and Signal Processing, ICASSP 02, Vol. 4, 13-17 May 2002 [7] R. Machado. EZ Stego [8] S.M. Kim, Ziqiang Cheng, Kee Young Yoo, A New Steganography Scheme based on an Index-color Image, Sixth International Conference on Information Technology, (2009) 8 [9] S. Kr Ghosal, A New Pair Wise Bit Based Data Hiding Approach on 24 Bit Color Image using Steganographic Technique. IEM, (2011) [10] V. K. Sharma, V. Shrivastava, A Steganography Algorithm For Hiding Image In Image By Improved Lsb Substitution By Minimizedetection, Journal of Theoretical and Applied Information Technology (2012) [11] M. Wu, J. Lee. A novel data embedding method for two-color fascimile images. In Proceedings of international symposium on multimedia information processing. Chung-Li, Taiwan, R.O.C, 1998 [12] Yu-Chee Tseng, Hsiang-Kuang Pan. Secure and Invisible Data Hiding in 2-Color Images. INFOCOM 2001. Twentieth Annual Joint Conference of the IEEE Computer and Communications Societies. Proceedings IEEE, 887 - 896 vol.2