(k, n) 秘密分享(Secret Sharing; SS)是一種將秘密數據分為n個子秘密的方法，其中k表示重建秘密時所需要的最少子秘密數量也就是門檻值、n則是所有子秘密的數目。(k, n)-SS只需要k個子秘密就能使用Lagrange interpolation多項式插值的方法恢復原始數據達到保護秘密的功能。但是，任何(k 1)個或更少的子秘密都無法解回原始秘密數據。(k, n)-SS最初的目的是保護密碼系統中的秘密鑰，現在它已被擴展並廣泛應用於許多應用情境，例如秘密影像分享(Secret Image Sharing; SIS)、和秘密文件分享(Secret Document Sharing; SIS)。把SS擴展至SIS、和SDS時，並不只是簡單地把秘密替換成影像、文件。而是要考慮秘密的樣式(隨機或有意義)、有限域的選擇、嵌入秘密的多項式係數位置、以及子影像和子文件的樣式。
當我們想要通過SS在分散式網路中分享秘密數據時，有時候不適合以原始數據格式傳輸分享，因為某些應用、或協議(例如加密、電子郵件、和HTML)的保留字元或者控制字元會造成通信協議中斷。植基於這個想法，給了我們研究秘密Base64數據分享機制(簡稱SBS)的動機。如同將SS擴展到SIS、和SDS時有其考量的條件，我們研究將SS擴展到SBS時也需考慮和處理使用Base64資料作為秘密時的一些問題。在本論文“使用簡單模除運算的Base64資料分享機制”，我們使用了無損秘密資料的模運算而不用比較複雜的GF(2N)有限域，其中N是6的倍數以配合Base64碼。我們對N=6、12、18、和24，選了不同的模除運算。另外，也對檔案長時間儲存放置(所謂的靜態數據)時，設計使用霍夫曼編碼具低複雜度、高壓縮率的SBS機制。本文做了三種不同類型秘密資料，文件文字、影像、與加密影像的實驗模擬。實驗結果呈現了我們的SBS機制確實可以正常運作。

A (k, n) Secret Sharing (SS) is a threshold scheme to share secret data into n sub secrets (referred to as shares). The value of k is the minimum number of shares required to reconstruct the secret and n represents the total number of share. For recovery, (k, n)-SS could k shares to recover secret via Lagrange interpolation. However, any (k 1) or fewer shares cannot be used for recovering secret data. The (k, n)-SS is first presented to safeguard a key in cryptosystem. Now, the approach of SS is extended to the secret image sharing (SIS) and secret document sharing. The extension of SS to SIS (or SDS) is not trivial and just using “image” and “document” as secret. We should carefully think about some key issues of extending SS to SIS, e.g., type of secret (random or meaningful), choice of finite field, positions of coefficients in a polynomial for embedding secret, and patterns on shares.
When we want to share secret data in a distributed network using SS approach, it is not suitable to use the files of shares directly. Because some applications and communication protocols (for example using ciphertext, e-mail and HTML) may have control character or non-printing character, and this will result in interruption. Base on this notion, we take the lead to study secret Base64 data sharing (SBS) scheme. Same as designing SIS and SDS, when extending SS to SBS some critical issues should be carefully addressed. In this thesis, we propose a (k, n)-SBS by using simple modular arithmetic instead of complicated finite field instead GF(2N), where N is a multiple of 6. For N=6, 12, 18 and 24, we choose various modular arithmetic operations. Consider the case “data at rest, we also design a Huffman code based low-complexity and high-compress compressing method for SBS. Three type of secrets: document, image and encrypted image, are used for testing SBS. Experiments our SBS performs correctly.

Chapter 1 Introduction 1
1.1 Background 1
1.2 Organization of The Thesis 3
Chapter 2 Previous Works 7
2.1 Shamir’s (k, n)-SS 7
2.2 The (k, n)-SIS 8
2.3 Base64 Codes 9
Chapter 3 The Proposed (k, n)-SBS 11
3.1 Design Concept 11
3.2 Generation and Recovery of (k, n)-SBS 24
Chapter 4 Experiment and Discussion 35
4.1 The (k, n)-SBS using (mod PG) 35
4.2 Comparison of using (mod PG) and (mod PS) for N = 6~24 41
4.3 Discussion 44
Chapter 5 Conclusion and Future Work 49
References 53

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