1. Secret image sharing with steganography and authentication
Chang-Chou Lin, Wen Hsiang Tsai
The Journal of Systems and Software
Volume 73 , Issue 3 (November-December 2004)
Reporter: 周美君

2. Outline
Introduction
Proposed scheme
Experimental Results
Conclusions

3. Secret sharing Shamir's secret sharing (1979)
A secret integer value s for the (k, n)- threshold.
F(x) = s + m1 × x + m2 × x mk-1 × xk-1
Choose freely: m1,…, mk-1 and x1…xk .(distinct)
The ith secret sharing participant get the secret shares: (xi, F(xi))
Compute the secret value s as F(0).

4. An example of Shamir's secret sharing
Ex: (2,3) threshold system (The secret key s =4)
F(x) = 4 + 2x
3 shares: (1,6), (5,14), (8,20) x y
F(x)
(1,6)
(5,14)
(8,20)
F(0)=4

5. Secret image sharing
secret image
recovery image ……
shares

6. Proposed scheme Using (2, 3)-threshold Watermark signal p=1
Parity Check
Secret image
Camouflage images 27 31 28 61 60 59 58
200
198
197 60
F(xi) = 60 + m1 × xi

7. 27 25 30 26 27 31 28 61 62 61 60 59 58
200
198
197
200
203
194
193
(∵ p=1, ∴parity check b=0) 27 27 25 30 26 01
110
010

8. 27 25 30 26 61 62 27 61
Check the Parity Check (p=1) is correct or not.
F(27) = s + m × 27 = = 114
F(61) = s + m × 27 = = 182 }
F(0) = s = 60 60

9. Experimental results Gray images Cover Image Stego Image 39.21 39.16
Secret image
Experimental results
Gray images
Cover Image
Stego Image
39.21
39.16
39.16

10. Experimental results Color images Cover Image Stego Image 39.07 39.08
Secret image
Experimental results
Color images
Cover Image
Stego Image
39.07
39.08
39.08

11. Authentication-Tamper detection
Experimental results
Authentication-Tamper detection
(a) (b) (c)
The stego-image in which fragile watermark signals are embedded.
The image with modifications added to (a).
The result of authentication.

12. Conclusions Three levels of security
Secret sharing
Camouflage images
Authentication
The quality of recovery image is nearly lossless.