視覺密碼學更具效率的設計方法及偽造防範

Abstract

視覺密碼學(Visual Cryptography)是一種將秘密的影像加密成數張分享片(Shares)的方法。如此一來只要疊足夠數量的分享片，便能解開那秘密影像。分享片通常以投影片做成，每位參予者(Participant)擁有一片投影片。之前大部分的研究，主要集中在增進兩種參數，像素擴展(Pixel Expansion)及對比(Contrast)。 傳統視覺密碼學定義，要求解開的秘密影像必須比背景黑。然而我們觀察這並不是必要條件，特別是應用在文字影像時，因此我們提出一個較佳的定義。根據這個新定義，我們發現許多傳統視覺密碼方法及其應用，都是可以精進的。根據我們的研究，對傳統視覺密碼學，我們做了以下的貢獻： 1. 我們利用這新定義，研究新視覺密碼學的特質及其界限(Bound)，並提出數個比傳統密碼學較佳的方法。 2. 我們展示三種欺騙的方法，而且應用它們來攻擊視覺密碼學。也提出了一種很有效率的方法，將所有視覺密碼學方法轉換成有防欺騙的功能。 3. 根據這新定義，我們提出了一個新方法來完成反轉視覺密碼方法(Visual Cryptography Scheme with Reversing)。跟之前的方法比較，我們的方法僅要求每一位使用者儲存兩張投影片。 4. 我們提出一種新的n 取2的延伸視覺密碼方法(Extended Visual Cryptography Scheme)，雖然這個方法的影像，沒有那麼漂亮，但比起之前的方法則有較佳的對比。 關鍵字：視覺密碼學， 視覺秘密分享法， 存取結構， 偽冒防制， 反轉， 最佳對比， 像素擴展。

Visual Cryptography (VC) is a method of encrypting a secret image into shares such that stacking a sufficient number of shares reveals the secret image. Shares are usually pesented in transparencies. Each participant holds a transparency. Most of the previous research work on VC focuses on improving two parameters: pixel expansion and contrast. The conventional definition requires that the revealed secret images are always darker than the backgrounds. We observed that this is not necessary, in particular, for the textual images. Therefore, we proposed an improved definition for visual cryptography based on our observation, in which the revealed images may be darker or lighter than the backgrounds. Based on the new definition, we find that many extensions of the original Visual Cryptography Schemes (VCSs) are improvable. According to our study, we improve the results of the original VCSs including the following contributions:

1. We studied properties and obtained bounds for visual cryptography schemes based on the new definition. We proposed methods to construct visual cryptography schemes based on the new definition. 2. We presented three cheating methods and applied them on attacking existent VC or Extended VC (EVC) schemes. We improved one cheat-preventing scheme. We proposed a generic method that converts a VCS to another VCS that has the property of cheating prevention. 3. Based on the new definition, we propose a new ideal VCS with reversing which is compatible and requires fewer stacking and reversing operations, compared to all previous schemes. Each participant is required to store only two transparencies. 4. We propose a (2,$n$)-EVCS scheme based on the new definition. Although the image of this construction is not "smooth", it has better contrast than previous results.