像素不擴展之漸進式視覺密碼

Progressive Visual Cryptography with Unexpanded Shares

視覺密碼的（k, n）-threshold機制，是將機密影像分給n個參與者，當取得k張以上的分享影像時，透過分享影像的疊合就可以顯示出機密影像，如果小於k張分享影像，則無法獲得機密影像的資訊。在這個機制之下，就算你已經取得k-1張的分享影像，也無法得知任何機密影像的蛛絲馬跡，這樣無形中降低了資訊分享的便利性。漸進式視覺密碼則是在疊合分享影像時，隨著疊合的分享影像數目增加，可以逐步地還原機密影像。在較少張分享影像的情況下，只能疊合出機密資訊的輪廓，隨著疊合的分享影像增加，即可逐漸獲得機密資訊的細部內容。 以往的漸進式視覺密碼研究都是以像素擴展為基礎，所以造成儲存空間與傳輸時間的浪費，並且針對機密影像上的黑點部分，在還原影像上並不保證是產生全黑，這將會造成機密影像的還原品質不佳。因此本研究將提出一個新的漸進式視覺密碼分享方法，我們的分享矩陣可以產生不擴展的分享影像，隨著疊合的分享影像數目增加，機密資訊的輪廓將愈來愈清晰，並且機密影像中黑點部分在疊合的還原影像上將是全黑，藉此產生良好的色差對比、提升還原影像的視覺品質。 根據實驗結果可以發現，無論機密影像的像素內容是黑點或白點，分享影像上出現黑點的機率皆相同，都是1/n，因此無法從單張分享影像中獲得機密影像的資訊，可以確保視覺密碼的安全性。當疊合k張分享影像後，機密影像中的白色部分被疊合出黑點的機率仍然是1/n，而黑色部份的機率則漸增為k/n，使得色差對比加大，機密影像愈來愈清晰。當疊合所有的分享影像後，在疊合影像上的黑白色差增加為（n-1）/n，優於傳統視覺密碼中50％的色差，因此可以產生更清晰的疊合影像。

The basic (k, n)-threshold visual cryptography scheme is to share a secret image with n participators. The secret image can be recovered while stacking k or more shares obtained; but you will get nothing if there are less than k shares being overlapped. Based on this concept, even though we get k-1 shares, we still do not know anything about the secret, which may cause the inconvenience of sharing information. Progressive visual cryptography can be utilized to recover the secret image gradually by superimposing more and more shares. In other words, if we only have a few pieces of shares, we get an outline of the secret; but by increasing the number of the shares being stacked, the details of the secret information can be revealed progressively. Previous researches of progressive visual cryptography were all based upon pixel-expansion, which not only causes the waste of storage space and transmission time but also gets a poor visual quality on the stacked image. Furthermore, Fang & Lin's research had a severe security problem that will disclose the secret information on each shares. In this paper we proposed a brand new sharing scheme of progressive visual cryptography to produce pixel- unexpanded shares. When stacking more shares, the contour of the secret image will get much clearer on the stacked shares. The objectives we have achieved in this paper include secure, better visual quality on the stacked image, smaller size of shares, and progressive transmission. In our research, the possibility for either black or white pixels of the secret image to appear as black pixels on the shares are the same, which equals to 1/n, therefore no one can obtain any secret information from a single share, which ensures the security. When superimposing k sheets of share, the possibility for the white pixels being stacked into black pixels remains 1/n, while for the black pixels the possibility are raised to k/n, which sharpens the contrast of the stacked image and the recovered secret image will become more and more obvious. After superimposing all shares, the color contrast rises to (n-1)/n which is better than the traditional ways of 50%, consequently a clearer recovered image can be achieved.