秘密影像分享系統之研究

A Study of Secret Image Sharing Schemes

李青芬(Ching-Fen Lee)

指導教授 ： 阮夙姿

國立暨南國際大學/科技學院/資訊工程學系/碩士(2009年)

摘要

秘密影像分享系統(Secret Image Sharing Scheme) 可以有效地解決數位資料、軍事文件及重要影像被偽造、竄改及竊取等問題。迄今, 已有許多學者建構各種秘密影像分享系統。然而, 多數皆有其缺點與限制或可改進的空間, 如: 計算過於複雜、每位參與者所持有的部分秘密(Share) 過多、只能運行於特殊的授權者集合(Access Structure)、無法同時分享多重機秘影像、無法多次使用、無法達到可驗證與偵測欺騙者的能力等問題。鑒於前述多項缺失, 本篇論文的目的為提出更具完整性與多功能的秘密影像分享系統。此篇論文可分為三大部份: 第一部份, 在2008年徐等學者所提出的多重秘密影像分享系統中, 針對一般授權者集合所設計的分享系統, 其秘密影像可能會被一群不合法的參與者子集合中的所有參與者解出, 導致系統的不安全。因此, 我們提出二個改進的多重秘密影像分享系統(t, n)-MSISS1 與GMSISS1, 在公佈影像的大小與時間複雜度上皆勝於徐等學者所提出的系統。同時, GMSISS1使得不合法的參與者子集合無法解出不該解出的秘密影像。第二部份, 在2008年施等學者提出(t, n)-門檻值秘密影像分享系統。但在施等學者的系統中, 任何人皆可能從公佈影像經簡單計算得到秘密影像的輪廓, 而且此系統所分享的秘密影像之寬必須等於高。另外, 施等學者的系統在分享多重秘密影像時, 所有秘密影像的大小必須一致。因此我們提出了兩個多重秘密影像分享系統(t, n)-MSISS2 與GMSISS2; 同時解決了洩密的問題及秘密影像的寬與高不可彈性決定的問題。同時, (t, n)-MSISS2 與GMSISS2 可達到分享多重秘密影像、多次使用, 以及分享多重秘密影像時, 每個參與者只持有一個部份秘密。其中GMSISS2 可適用於一般授權者集合。第三部份, 在2009年趙等學者提出可識別欺騙者之秘密影像分享系統, 但在趙等學者的系統中, 可能存在偽裝的問題及無法永久達到多次使用的功能。因此我們提出了一個針對一般授權者集合所設計之可驗證及偵測的多重秘密影像分享系統VDGMSISS。不但提供了可驗證有效參與者的身分、與其所提出的部分秘密之正確性; 此外, VDGMSISS 達到一些特性, 諸如可分享多重秘密影像、可多次使用與無須存在秘密通道等。最後我們針對本文所提出的各種方法進行分析與比較。

關鍵字

秘密影像分享系統 ； 授權者集合 ； 多重秘密影像 ； 多次使用 ； 可驗證與偵測

並列摘要

Secret image sharing scheme can efficiently solve the problems that are digit materials, military documents and important images could be forged, falsified and stolen, etc. Up to now, there are many scholars to design various secret image sharing schemes. However, most of the schemes have many drawbacks and limits or still can be improved. For example: the computation is too complex; each participant holds too many shares; those schemes only can be applied in specified access structure; cannot share multi-secret images, achieve the capabilities of the multi-use, verification and detection at the same time. Based on the above defects, the goal of this thesis presents secret image sharing schemes with more integrity and multi-function. Therefore, we will divide thesis into three parts: In first part, Shyu and Chen proposed multiple secret images sharing schemes in 2008, but the secret images could be found by a set of unqualified participants in their general access structure sharing scheme. Therefore, we propose two multi-secret images sharing schemes (t, n)-MSISS1 and GMSISS1. The sizes of the public image and time complexity of these two schemes are better than Shyu and Chen’s schemes. Moreover, any set of the unqualified participants cannot found the secret images in these two schemes. In second part, Shi et al. proposed a (t, n)-threshold secret sharing scheme for image encryption in 2008, but there are some drawbacks in this scheme: the phenomenon shapes of the secret image could be found by using the public image, the width must be equal to the height, and the size of the secret images must be the same upon sharing multi-secret images. Therefore, we propose two multi-secret images sharing schemes (t, n)-MSISS2 and GMSISS2 to solve these problems. Furthermore, the proposed (t, n)-MSISS2 and GMSISS2 can respectively achieve sharing multi-secret images, multi-use, and each participant only holds one share, and GMSISS2 can be used for any general access structure. In third part, Zhao et al. proposed image secret sharing scheme to identify cheaters in 2009. But these exists the problem of disguise, and cannot achieve multi-use forever in Zhao et al.’s scheme. Therefore, we propose a verifiable and detectable multi-secret images sharing scheme with general access structure VDGMSISS to provide a verifiable procedure to authenticate identity of valid participants and a detectable method to check accuracy of the share. In addition, the proposed VDGMSISS can achieve some properties, such as sharing multi-secret images, multi-use, without security channel and be used for any access structure.

並列關鍵字

secret image sharing scheme ； access structure ； multi-secret images ； multi-use ； verifiable and detectable

參考文獻

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