1. New Visual Secret Sharing Schemes With Non-Expansible Shadow Size Using Non-binary Sub Pixel Ching-Nung Yang Yun-Hsiang Liang Wan-Hsiang Chou National Computer Symposium on Information security

2. Outline 介紹 NEVSS (Non-Expansible VSS) 介紹 Visual Cryptography 上的 Contrast 和 Security 結論

3. NEVSS vs. Conventional VSS 不同點 : 1. Addition “ ADD ” vs. Boolean “ OR ” 2. Non-Binary{W,G,B} vs. Binary{W,B} 3. Non-Expansible vs. Expansible

4. Non-Expansible Method Original Image Shadow Image I -- A (2,2) NEVSS Scheme Example: Shadow Image II

5. Non-Expansible Method Pixel Value: --0: white --1: gray --2: approximate black --C 0 is used to represent “ white ”. --C 1 is used to represent “ black ”. 可知 : Shadow image: {white,gray} target image: {white,gray,black} -- A (2,2) NEVSS Scheme Example:

6. NEVSS--Contrast Definition -- a (2,2) NEVSS Scheme Example: When stacking two shadows. The dominant color is “ 0 ” (white), because “ 0 ” is the biggest contrast among the colors “ 0 ”, ” 1 ”, ” 2 ” in λandγ. P λ and P γ are the probabilities of the dominant color in the set λandγrespectively. Now, P λ =1/2, P γ =0, the difference P λ - P γ =1/2, the holds the first and the second condition.

7. NEVSS--Security Definition We randomly chooses one column matrix in C 0 and C 1. So for each shadow every pixel will be “ 0 ” (white) or “ 1 ” (gray) half and half, and one cannot see any thing from the shadow.

8. NEVSS The major difference between two schemes is that our scheme uses non-binary operation and the conventional scheme uses Boolean operation.

9. 他的結論 In this paper, we have presented new (2,2),(2,n), and (k,k) NEVSS schemes. However, the general method for constructing (k,n) NEVSS schemes may need the further studies. 在 2001 年, 提出動態式的 NEVSS

10. 曾 經 滄 海 難 為 水

11. 我的結論 此篇論文 : Contrast and Security 不能兼顧 M. Naor and A. Shamir : 可同時兼顧 Contrast and Security 我認為我的論文也可同時兼顧 Contrast and Security

12. 我的論文 Contrast : 已歸納在各個 scheme 中可擁 有的最大 contrast, 也就是論文中的 T 值 Security : 由於 Shadow Image( 小學生 ) 和 Recovered Image( 高中生 ) 是處在 2 個 不同的 Grayleve 上, 所以分享者最多只能 知道 Recovered Image ’ s graylevel ( 國中 生, 高中生, 大學生 …… ) 必大於 Shadow Image.