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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

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Introduction• The proposed method based on a (k, n)-threshold sch

eme 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.

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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

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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。

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(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

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

X1: 識別碼 W1

V1 U1

X2: 識別碼 W2

V2 U2

X3: 識別碼 W3

V3 U3

Pixel value198

• 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

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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

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

X1: 163 W1:162

V1:163 U1:166

X2: 153 W2:152

V2:153 U2:156

X3: 143 W3:142

V3:143 U3:146

F(X1) =185(10)=10111001(2)

F1F2F3F4F5F6F7F8

X1: 163 W

W1W2W3W4W5B1F1F2

V

V1V2V3V4V5F3F4F5

U

U1U2U3U4U5F6F7F8

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

X1: 163

W1:16210100010

W1’10100010162

V1:16310100011

V1’10100111167

U1:166 10100110

U1’s10100001161

F(X1) =185(10)=10 111 001(2)

F1F2F3F4F5F6F7F8 and 設 b1 = 0

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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

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

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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.