Progressive Visual Cryptography With Unexpanded Shares

Abstract

The basic ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> , <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> )-threshold visual cryptography (VC) scheme is to share a secret image with <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> participants. The secret image can be recovered while stacking <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> or more shares obtained; but we will get nothing if there are less than <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> pieces of shares being overlapped. On the contrary, progressive VC can be utilized to recover the secret image gradually by superimposing more and more shares. If we only have a few pieces of shares, we could get an outline of the secret image; by increasing the number of the shares being stacked, the details of the hidden information can be revealed progressively. Previous research, such as Jin in 2005, and Fang and Lin in 2006, 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 and Lin's research had a severe security problem that will disclose the secret information on each share. In this letter, we proposed a brand new sharing scheme of progressive VC to produce pixel-unexpanded shares. In our research, the possibility for either black or white pixels of the secret image to appear as black pixels on the shares is the same, which approximates to 1/ <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> . Therefore, no one can obtain any hidden information from a single share, hence ensures the security. When superimposing <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> (sheets of share), the possibility for the white pixels being stacked into black pixels remains 1/ <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> , while the possibility rises to <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> / <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> for the black pixels, which sharpens the contrast of the stacked image and the hidden information, therefore, become more and more obvious. After superimposing all of the shares, the contrast rises to ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> -1)/ <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> which is apparently better than the traditional ways that can only obtain 50% of contrast, consequently, a clearer recovered image can be achieved.