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研究生:陳盈如
研究生(外文):Ying-ru Chen
論文名稱:一些新的機密影像分享機制
論文名稱(外文):New Secret Image Sharing Schemes
指導教授:徐熊健徐熊健引用關係何祖鳳何祖鳳引用關係
指導教授(外文):Shyong-Jian ShyuTsu-Feng Ho
學位類別:碩士
校院名稱:銘傳大學
系所名稱:資訊工程學系碩士班
學門:工程學門
學類:電資工程學類
論文種類:學術論文
論文出版年:2008
畢業學年度:96
語文別:中文
論文頁數:80
中文關鍵詞:機密分享機密影像分享一般化存取結構門檻機制中國餘式定理固定私鑰
外文關鍵詞:Secret sharingGeneral access structureConstant-size keyChinese remainder theoremSecret image sharingThreshold scheme
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  • 被引用被引用:0
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  • 下載下載:29
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  此論文共提出三個數位影像機密分享方法,分別對以下三個問題進行考量:(1) 一般化存取結構分享多張機密影像;(2) 以大小固定的私鑰分享多張機密影像;(3) 利用中國餘式定理於門檻機制之單張機密影像分享。我們分別對這些問題提出創新的機密影像分享機制。
  本文所提的第一個機制,以 Shamir 的 (n, n) 門檻式機密分享機制為基礎,可在一般化存取結構下,對多張數位影像進行機密分享;此機制可能在某些存取結構下,使每一位參與者拿到大小不同的分享圖。第二個問題即盼改善這個分享者拿到大小不同分享圖的缺點。我們分別對門檻式和一般化存取結構設計其機密分享機制,使每一位參與者只需持有大小固定的私鑰,即可分享多張影像。此機制使每一位參與者所需持有的資訊變小且易於攜帶(甚至可以直接記憶腦中),確為機密影像分享的研究帶來新的思考方向。
  針對第三個問題,我們運用中國餘式定理,提出了兩個門檻式的機密影像分享機制,有別於諸多機密影像分享之研究大多沿用 Shamir 以多項式建構機密分享的概念,中國餘式定理的引入,可為機密影像分享研究領域拓展出新的視野。
  文章中亦對於所提出的機制,個別分析其安全性;並進行實作實驗。實驗結果驗證了所提方法的可行性與實用性。
  In this thesis we study three problems in secret image sharing: (1) sharing multiple images in general access structures, (2) sharing multiple images using constant-size keys, and (3) sharing one image in a threshold structure by Chinese remainder theorem. We design novel schemes for these three problems.
  For the first problem, our scheme, which is based on Shamir’s (n, n) threshold scheme, is the first result for sharing more than one secret image among participants with any given general access structure. One major disadvantage for this approach is that the sizes of the shadows for all participants may be different for a certain access structure. The second problem is meant to deals with this disadvantage so that each participant only takes a constant-size key, instead of various-size shadows. We propose schemes for threshold and general structures, respectively. This is a new development in secret image sharing in the view that the size of information distributed to each participant is so small that it is very easy to carry (or just to memorize).
  Regarding the third problem, we devise two new threshold secret image sharing schemes. Applying Chinese remainder theorem, instead of following Shamir’s idea of using polynomial interpolation for secret sharing, reveal new possibilities in the area of secret image sharing.
  The secrecy analyses of these schemes are discussed. We also implement our designs and the experimental results demonstrate the feasibility and applicability of the proposed schemes.
摘 要 ii
Abstract iii
致 謝 iv
目 錄 v
表目錄 vi
圖目錄 vii
第一章 簡介 1
1.1 研究背景與動機 1
1.2 研究問題 2
1.3 研究目的 2
第二章 文獻探討 4
2.1 機密分享及其發展概況 4
2.2 Shamir (r, n) 門檻機制 7
2.3 一般化存取結構 10
2.4 機密影像分享 12
2.5 中國餘式定理與機密分享 13
2.5.1 Mignotte 的門檻式機密分享機制 14
2.5.2 Asmuth-Bloom 的門檻式機密分享機制 15
第三章 研究成果與討論 17
3.1 一般化存取結構分享多張機密影像 17
3.2 以大小固定的私鑰分享多張機密影像 24
3.2.1 在門檻機制下之多張機密影像分享 25
3.2.2 一般化存取結構下之機密影像分享 29
3.3 利用中國餘式定理於門檻機制之單張機密影像分享 37
3.3.1 基於 Miggto之 (r, n) 機密影像分享機制 37
3.3.2 基於 Asmuth-Bloom之 (r, n) 機密影像分享機制 41
第四章 實驗結果 46
4.1 一般化存取結構依群組考量之多張機密影像分享實作 46
4.2 利用大小固定私鑰之多張機密影像分享實作 51
4.3 利用中國餘式定理之機密影像分享實作 55
第五章 結論 60
參考文獻 63
附錄A、解多項式展開係數 66
附錄B、GF(p) 與GF(2n) 70
附錄C、互質模數表 73
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