視覺機密分享機制之像素擴張最佳化研究

Optimization of Pixel Expansion in Visual Secret Sharing Schemes

陳明江(Ming-Chiang Chen)

指導教授 ： 趙坤茂

共同指導教授 ： 徐熊健(Shyong-Jian Shyu)

國立臺灣大學/電機資訊學院/資訊工程學研究所/博士(2010年)

https://doi.org/10.6342/NTU.2010.01277

摘要

在這篇論文中，我們探討了兩個研究課題，分別為視覺機密分享以及視覺機密顯示，其目的都在保護機密的設計中結合了人類視覺能力。本論文針對視覺機密分享研究提出像素擴張最佳化的設計方法，而針對視覺機密顯示研究提出同時保護多個機密的設計方法。
對於視覺機密分享研究，加密技術將機密加密後產生多張分享影像並列印輸出在投影片，每位參與者都會拿到一張投影片，在參與者中，只有合法群組才能利用投影片解密辨識出機密。視覺機密分享的特色在於解密技術僅利用人類視覺系統來解密，不需使用任何擁有計算能力的設備、複雜精細的光學儀器或是密碼學技巧。針對不同存取結構、不同機密個數或是不同機密顏色等考量，視覺機密分享研究已經發展出一系列相關課題；其中，視覺機密分享研究的目標之一是設計擁有最少像素擴張的視覺機密分享方法。本論文針對不同存取結構考量探討兩個基本視覺機密分享課題：門檻存取結構以及一般化存取結構。本論文針對這些課題建立線性規劃模型進而設計像素擴張最佳化的視覺機密分享方法，提出的線性規劃模型不僅成功地達到像素擴張最佳化的視覺機密分享，改進了現有最好的像素擴張數值，也可以根據不同考量的視覺機密分享課題輕易地修改建立對應的線性規劃模型。
對於視覺機密顯示研究，目標是在基於螢幕與遮罩架構下利用人類視覺系統來保護在螢幕顯示的機密以防止窺看。在螢幕與遮罩架構下，只有站在預先訂定的限制範圍內，合法瀏覽者利用手上的遮罩才能瀏覽螢幕顯示的機密。探討的課題包含了多個機密、多個遮罩、黑白機密、彩色機密以及螢幕與遮罩的數個關係等考量。本論文首先將視覺機密分享方法應用在視覺機密顯示，達到視覺機密顯示目的和有效的機密大小擴張。本論文也根據人類視覺系統對於調控顏色的視覺反應設計一系列視覺機密顯示方法，即使在螢幕顯示完整機密狀態下，仍能成功地達到在不同考量下的視覺機密顯示。

關鍵字

視覺機密分享 ； 線性規劃 ； 像素擴張

並列摘要

This dissertation studies both the problems of visual secret sharing and visual secret display which integrate the human visual intelligence into the design of securing the secret. We aim at designing the schemes for visual secret sharing with an efficient pixel expansion and the schemes for visual secret display with respect to multiple binary secrets as well as color secrets.
Visual secret sharing is a cryptographic technique for distributing the secret image among the participants in such a way that the secret is encrypted into the shares of transparencies which are distributed into the participants and is decrypted by the qualified groups of participants by superimposing their shares. The innovative feature of visual secret sharing is that the decoding process relies only on human visual system without any computing device, complicated optical equipment, nor cryptographic knowledge. Many sub-problems concerning the various types of access structures, different number of secrets, particular colors of the secret, etc. are studied. With regard to design of the visual secret sharing scheme, one of the most important factors is the pixel expansion which enlarges the size of the secret in the shares and is expected as small as possible. We study two fundamental problems of visual secret sharing: threshold visual secret sharing and visual secret sharing for general access structures, and propose the approaches to design the schemes achieving the optimization of the pixel expansion. The existing best pixel expansion of both fundamental visual secret sharing problems has never been improved since 1996. The computational studies demonstrate that our approaches are not only effective for minimizing the pixel expansion but also flexible for different considerations of visual secret sharing.
On the other hand, visual secret display is to protect the secret information that is displayed on the screen against the unauthorized peeping attack. Based on the mechanism of the display and the masks, the authorized participant is able to visually perceive the secret from the screen by using their own transparencies while standing within a limited viewing zone. We apply the approaches devised for visual secret sharing to achieve visual secret display on securing one secret with an efficient expanding size. We also examine the visual effects on the binary images as well as the color images and conclude several primitive color features to the human visual system. By utilizing these valuable and interesting features, we provide the schemes for the visual secret display problem under various considerations such as different number of secrets and particular relationships among the display and the masks. Even the display keeps showing the secrets without losing any information; we effectively secure the displayed secrets among the display and the masks and recover the secrets to our eyes from the display through the corresponding masks. Moreover, the experimental results indicate that our schemes successfully achieve the visual secret display for secreting multiple secrets including the binary secret images as well as the color secret images.

並列關鍵字

Visual Cryptography ； Linear Programming ； Pixel Expansion

參考文獻

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