| Abstract: | 秘密金鑰分享技術是近代密碼學中，一個非常熱門的研究主題。秘密金鑰分享技術的基本概念，將金鑰拆成許多份子金鑰並分配給許多人來保存，如此可以防止秘密金鑰被單一使用者所遺失，因而產生洩密情況。當一些條件成立時，就有辦法將金鑰解回來。
依循此概念，Shamir首先提出(t,n)門檻方法，來做秘密金鑰的分享。以(t,n)門檻方法為基礎之秘密金鑰的分享技術，將秘密金鑰分成n個子金鑰，並將此n個子金鑰分配給n個合法使用者保管。當任意t個合法使用者交出自己的子金鑰，才有辦法將金鑰解回來。隨後Thien和Lin兩位學者，利用Shamir所提出的(t,n)門檻方法，來做秘密影像的分享。然而， Thien和Lin兩位學者之秘密影像分享技術，所產生的shadow影像是毫無意義的影像。由於毫無意義的影像，會吸引非法使用者的目光，張教授等人將Thien和Lin之方法所產生的shadow影像，藏入偽裝影像中，並將向量編碼(Vector Quantization)的概念運用到影像隱藏技術，藉以解決Thien和Lin之方法的缺點。
然而，張教授等人之秘密影像分享技術，必須參考到原始偽裝影像區塊之索引值。而要使(t, n)門檻方法正常運作，必須讓不同偽裝影像相同位置的區塊，擁有不同的索引值。一旦在不同偽裝影像相同位置的區塊具有相同索引值時，其中一個區塊就必須做區塊的取代，以改變區塊的索引值。然而，區塊的取代會導致偽裝影像品質的快速下降。另外將shadow影像的直接藏入原始偽裝影像，也會對原始偽裝影像造成傷害。
為了避免區塊的取代， 在本計畫中捨棄原來向量編碼法(Vector Quantization)的概念，研究改以雜湊函式(hash function)來達到相同的目的。因為使用當雜湊函式，當使用相同的影像來當偽裝影像，可以預期的對偽裝影像的品質不會產生太大傷害。另外為了不要將shadow影像的直接藏入偽裝影像，導致對偽裝影像品質造成傷害，本計畫中研究以動態程式規劃的方式，來搜尋最佳的“一對一取代表＂，利用“一對一取代表＂轉換shadow影像，使轉換後的資料近似於偽裝影像中欲取代的位元，因而降低對偽裝影像品質的傷害。此最佳的“一對一取代表＂可視為解出shadow影像之金鑰。只有握有金鑰的人，才有辦法從轉換過的資料中，反轉回原來的shadow影像。任意t張以上的shadow影像合作，才有辦法將秘密影像恢復回來。
可預期的，本計畫所研究出的秘密影像分享技術，不但使得已藏資料之偽裝影像具有高品質，同時對藏入偽裝影像的shadow影像，提供更安全的保護。此技術之研發成果，將在秘密影像分享技術領域中，提供偉大的貢獻。
Secret key sharing technique is a popular research topic in the modern cryptography. The basic concept of secret key sharing technique is to divide a secret key into several shares and assign them to certain legal persons. Therefore, a compromised share will not lead to the reveal of the secret information. Only if certain conditions are held, the secret key can be recovered to decrypt the secret.
Obeying this concept, Shamir proposed (t, n) threshold scheme to do secret key sharing. In a (t, n) threshold scheme, a secret key is divided into n shares. These shares then are assigned to n legal persons. Later, any t out of n legal persons can cooperate to derive the secret key by collecting their shares. After that, Thien and Lin applied the (t, n) threshold mechanism to do secret image sharing. In Thien and Lin’s method, meaningless shadow images will be produced. This may catch illegal persons’ eyes. Chang et al. hence improved Thien and Lin’s method by embedding shadow images into cover images to form meaningful stego-images. Moreover, Chang et al.’s improved version applied the concept of Vector Quantization to overcome the drawbacks of Thien and Lins’ method.
Precisely, Chang et al.’s method used the indices of cover image to do secret image sharing. In order to apply (t, n) threshold concept, any two blocks at the same position of cover images must have different indices. If any two blocks refer to the same index, one of them must change its index by the block replacement procedure. However, the procedure often seriously degrades the quality of cover images. Besides, embedding shadow images into cover images may distore the cover images.
In order to avoid the effect of block replacement, in this project, we use hash function to achieve the same goal instead of Vector Quantization. Therefore, stego-images still possess good quality while all cover images are the same. Besides, we adopt the dynamic programming strategy to find an optimal one-to-one substitution table for each cover image and its corresponding shadow image. After transforming the shadow image according to its optimal one-to-one substitution table, the transformed data will be similar to the bits used to embed data in the cover image. Note that, the optimal one-to-one substitution table can be viewed as a key. Only the person having the key can convert the transformed data to a shadow image. Once collecting any t out of n shadow images, the secret image can be revealed.
Expectably, this secret image sharing technique not only has good quality of stego-images but also improves the security of embedding data. The result of this project will effectively contribute to the area of secret image sharing. |
