新視覺化密碼編碼法的分析

Abstract

視覺化密碼（visual cryptography）是指一種把秘密圖像編碼成秘密圖像分享的編碼法，在每個參與者擁有一份印有秘密圖像分享的投影片時，讓某些合乎資格（qualified）的參與者，可以透過「視覺」直接地回復秘密圖像，而無需擁有任何密碼學相關的知識，也無需任何的運算；但是，對於限制資格（forbidden）的參與者來說，不管透過任何方法，都無法從手中的秘密圖像分享，得到任何關於秘密圖像的資訊。 由於先前視覺化密碼的定義，幾乎都侷限於單調（monotone）的情況，而且，定義上也有不合理的地方，舉例來說，在疊合投影片後，秘密圖像都比周圍背景的顏色為深。而實際上，只要有對比存在，不管秘密圖像是比周圍背景的顏色深或淺，我們都可以透過視覺系統分辨出來。而新的定義便修正了上述不合理的地方，也較原先的定義更適用於一般的情況。 本篇論文就基於新視覺化密碼的定義，對新的定義做性質方面的討論，提出一套能讓建構的過程更有效率的編碼方法，並在兩種定義下，比較其對於相同的存取結構（access structure）的編碼效果。

Visual cryptography is a method to encode a secret image into some secret image shares. Each participant receives a transparency that is printed some secret image share. Certain qualified subsets of participants can “visually” recover the secret image directly without knowing any knowledge of cryptography and performing any computations, but other sets, called forbidden sets, of participants have no information about the secret image, even to any cryptanalyst. The conventional definition of visual cryptography is limited to monotonic situation, and it is unreasonable about the part of “contrast”, for example, the recovered secret image is always darker than background after stacking transparencies, but we know that this is not necessary. No matter the recovered secret image is darker or lighter than background, we can recover the secret image by human visual system. New definition corrects this and makes it more general than conventional one. Based on the new definition, in this paper, we study the properties of new definition, propose a more efficient construction method, and show some results about comparison of two definitions.