1. (r, n)-Threshold Image Secret Sharing Methods with Small Shadow Images Xiaofeng Wang, Zhen Li, Xiaoni Zhang, Shangping Wang Xi'an University of Technology, Xi'an, Shaanxi, 710048, P.R.China

2. 2 Outline Introduction Proposed Scheme  Multi-Secret Sharing Mode  Priority Sharing Mode Experimental Results Conclusions

3. 3 Introduction(1/1) the characters of the proposed methods ：  the sizes of generated shadow images are smaller;  provided a lossless secret image recovery approach with smaller shadow images

4. 4 Multi-Secret Sharing Mode( 1/3) Original image I Dividing I into four non- overlapping sub-image: I 1, I 2, I 3, I 4 Dividing each sub-image into 8×8 non-overlapping blocks Generating difference matrix of each 8×8 block Huffman coding Generating row vectors: D 1, D 2, D 3, D 4 Pre-processing

5. 5 Multi-Secret Sharing Mode( 2/3) Generating sharing share Generating sub-shadow images s i (1), s i (2),s i (3), s i (4), s i (5), s i (6) Combing the 24 sub-shadow images, generating four shadow images Embedding these four shadow images to carrier images as watermark Shadow generation

6. 6 Multi-Secret Sharing Mode( 3/3) Taking a pixel from each of the shadow images Using r pixels and Lagrange’s interpolation to generate the coefficients of the Lagrange polynomial Converting the coefficients into binary numbers, and then, Huffman decoding is used to obtain the pixels of difference image Inverse difference transformation Recovered secret image Recovery

7. 7 Priority Sharing Mode(1/9) Pre-processing Original image I Dividing the secret image I into n bit-level images combing them to generate four combined bit-level images Dividing into 2×2 image blocks, every minimum of blocks constructed matrix

8. 8 Priority Sharing Mode(2/9) Defining matrix that would be used in recovery phase, the elements of are as follows: j, k=1,2,…,N/2 i=1,2,3,4 Pre-processing

9. 9 Priority Sharing Mode(3/9) Dividing into 8×8 image blocks and computing the difference matrix (i=1, 2, 3, 4) Combining to generate matrix u=1,..., N/16×N/16, Pre-processing

10. 10 Priority Sharing Mode(4/9) Re-arranging elements of by row to generate a row vector, and compressing it by Huffman coding, then converting the output into 0~255 decimal numbers, noted as Pre-processing(4/4)

11. 11 Priority Sharing Mode(5/9) Shadow generation Taking every four pixels from as a sharing share, denoted as, then construct Lagrange polynomial for each sharing share Generate six sub-shadow images, Combining the 24 sub-shadow images, then generate four shadow images

12. 12 Priority Sharing Mode(6/9) The algorithm of generating shadow images

13. 13 Priority Sharing Mode(7/9) Secret image reconstruction algorithm Taking a pixel from each of the shadow images Using r pixels and Lagrange’s interpolation to generate the coefficients of the Lagrange polynomial Converting the coefficients into binary numbers, and then, Huffman decoding is used to obtain the difference bit-level images Using inverse difference transformation to obtain the bit-level images

14. 14 Priority Sharing Mode(8/9)

15. 15 Priority Sharing Mode(9/9) Accumulating and the corresponding matrix to obtain, and obtain the recovered secret image

16. 16 Experimental Results(1/4) Fig. 1. Four shadow images generated by using the multi-secret sharing mode (a) (b) (c) (d)

17. 17 Experimental Results(2/4) (e) (f) (g) (h) (i) (j) (k) Fig. 2. Reconstructed images by using different numbers of shadow images in multi-secret sharing mode, where (a)-(f) are recovered images by using two shadow images, (g)-(j) are recovered images by using three shadow images, and (k) is recovered image by using four shadow images.

18. 18 Experimental Results(3/4) Fig. 3. Shadow images generated by using the priority sharing mode. (a) (b) (c) (d)

19. 19 Experimental Results(4/4) (e) (f) (g) (h) (i) (j) (k) Fig. 4. The reconstructed images by using priority sharing mode. (a)-(f) are reconstructed images by using two shadow images, (g)-(j) are reconstructed images by using three shadow images, and (k) is reconstructed image by using four shadow images.

20. 20 Conclusions Smaller shadow images Saving storage space and transmission time