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

Outline Introduction Proposed scheme Experimental Results Conclusions

Secret sharing Shamir's secret sharing (1979) A secret integer value s for the (k, n)- threshold. F(x) = s + m1 × x + m2 × x2 + ... + 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).

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

Secret image sharing secret image recovery image …… shares

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

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 0001 1111 27 25 30 26 01 0001 1011 0001 1100 110 010

27 25 30 26 61 62 27 0001 1001 61 0011 1110 0001 1110 0001 1010 0011 1110 0001 1110 Check the Parity Check (p=1) is correct or not. F(27) = s + m × 27 = 011100102 = 114 F(61) = s + m × 27 = 101101102 = 182 } F(0) = s = 60 60

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

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

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.

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