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Secret Image Sharing with Steganography and Authentication

Secret Image Sharing with Steganography and Authentication. Authors: Chang-Chou Lin, Wen-Hsiang Tsai Source: The Journal of System and Software, Volume: 73, Issue: 3, Nov.-Dec., 2004, PP. 405-414 Speaker: Nan-I Wu ( 吳男益 ) Date: 2004/12/017. Introduction.

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Secret Image Sharing with Steganography and Authentication

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  1. Secret Image Sharing with Steganography and Authentication Authors: Chang-Chou Lin, Wen-Hsiang Tsai Source: The Journal of System and Software, Volume: 73, Issue: 3, Nov.-Dec., 2004, PP. 405-414 Speaker: Nan-I Wu (吳男益) Date: 2004/12/017

  2. Introduction • The proposed method based on a (k, n)-threshold scheme with the additional capabilities of steganography and authentication. • Steganography is different from visual cryptography schemes. • The fragile image watermarking is adopted for image authentication during the secret sharing process. • The proposed scheme as a whole offers a high secure and effective mechanism for secret image sharing that is not found in existing secret image sharing methods.

  3. Shamir method for secret sharing(1979) • (k, n)-threshold secret sharing scheme 將密秘訊息y分成n份次訊息，只要集合k份次訊息，即可恢復原始密秘訊息y。 F(x) = y + m1 * x + m2 * x2 + … + mk-1 * xk-1mod P Secret data P是大質數 且滿足P ≥ y 任意數且只要介於 [1, P]即可 • 任選不為0的n個不同值，分別為X1,X2,X3,…,Xn • 即n份次訊息的識別碼 • 求得每組識別碼的F(Xi)值，並將(Xi,F(Xi))分送給n份人保管

  4. 假設要把密秘訊息7，分給5個人而且只要3個人，即可得7假設要把密秘訊息7，分給5個人而且只要3個人，即可得7 • 任選一個2次多項式如 F(x) = 4x2+8x+7 mod 17 • 選定5個人的編號如 1、2、3、4、5。 • 將編號值依序帶入2次多項式則得 F(1)=2, F(2)=5, F(3)=16, F(4)=1, F(5)=11 • 將(1, 2), (2, 5), (3, 16), (4, 1), (5, 11)等五組值，分別送給五個人保管。 選取任意三組且使用Lagrange多項式方法 ，即可得原多項式即可得y值。

  5. (2, 3)- threshold secret sharing scheme F(x) = y + m1 * x + m2 * x2 + … + mk-1 * xk-1mod P Size: m x m Size: 2m x 2m Size: 2m x 2m Size: 2m x 2m

  6. (2, 3)- threshold secret sharing scheme F(x) = y + m1 * x + m2 * x2 + … + mk-1 * xk-1mod P • 所有pixels value最大為250，故P大質數選為251 • m1,m2,…,mk-1可隨機產生。 • 若識別號有相同時，做 +1， -1 • 計算F(X1), F(X2), F(X3)的值。且將 F(X1), F(X2) • F(X3)分別藏在各自的Wi, Vi, Ui Pixel value 198

  7. (2, 3)- threshold secret sharing scheme F(x) = y + m1 * x + m2 * x2 + … + mk-1 * xk-1mod P Ex: y = 198且設 F(x)=198+3x mod 251 則 F(X1) = (198+3*163) mod 251 = 185 F(X2) = (198+3*153) mod 251 = 155 F(X3)= (198+3*143) mod 251 = 125 F(X1) =185(10)=10111001(2) F1F2F3F4F5F6F7F8

  8. (2, 3)- threshold secret sharing scheme F(x) = y + m1 * x + m2 * x2 + … + mk-1 * xk-1mod P F(X1) =185(10)=10 111 001(2) F1F2F3F4F5F6F7F8 and 設 b1 = 0

  9. Recovery Algorithm (163, 185), (153, 155), (143, 125) Ex1: (163, 185), (153, 155) 設 F(x)=ax+y mod 251 F(163) = (a*163+y) mod 251 =185 F(153) = (a*153+y) mod 251 =155 解聯立 得 a=3, y=198 Ex2: (163, 185), (143, 125) F(163) = (a*163+y) mod 251 =185 F(143) = (a*143+y) mod 251 =125 解聯立 得 a=3, y=198

  10. Experimental Results(The PSNR of stego-image about 39.2dB)

  11. Conclusions • The proposed scheme has three levels of security protection. (1) the (k, n)-threshold function is adopted. (2) data hiding technique is employed. (3) has the capability of authentication.

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