近年來，在資訊網路爆炸的時代，雲端運算系統被人們廣泛的使用著，然而其
中隱含了不少資訊安全的議題。其中，秘密分享的技術被應用在處理雲端系統關於資
訊隱私性、資料完整性以及資料運算速度的問題。然而，由Shamir所提出的秘密分享
隱含著一些缺陷，當我們將許多檔案使用秘密分享的方式進行上傳時，由每一份秘密
所產生出來欲放置雲端伺服器上的資料量之大小會與檔案大小一樣大，將造成占用許
多雲端上的儲存空間的問題，另外，當計算秘密分享所需要儲存於雲端伺服器資料的
時候，將會耗費許多計算量。
因此，為了解決這兩大由Shamir秘密分享的問題，本文提出一個透過使用者提供
之金鑰，進而產生虛擬亂數的方式，來達到減少雲端儲存空間的方法，並僅採用邏輯
異或的運算方式，來降低生產欲放置雲端伺服器資料之計算量。

In recent years, at an era of information explosion, cloud storage system is wide-spread
used in our daily life. However, cloud storage system include many information security issues.
The technical of secret sharing is applied to solve these problem include data privacy, data
integrity and computational cost. Nevertheless, applying Shamir’s secret sharing scheme to
cloud storage system, there are two fetal problems. When we upload the file to the cloud
storage system, the size of each share equals to the file such that it waste amount of storage to
save these shares; furthermore, a heavy computational cost is required to make shares which is
going to be saved in the cloud servers.
Therefore, we then proposed a secret-sharing-based method by generating pseudo-random
number to replace the real shares such that it reduces the storage cost; in addition, we use
just EXCLUSIVE-OR (XOR) operation to reduce the computational cost when computing the
shares for each cloud servers.

Acknowledgments iii
摘要iv
Abstract v
Chapter 1 Introduction 1
1.1 Motivation and Contribution . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Related Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
Chapter 2 Preliminary 5
2.1 Notations and Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2 Shamir Secret Sharing Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.3 Lagrange Polynomial Interpolation . . . . . . . . . . . . . . . . . . . . . . . . 6
2.4 Ramp Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
Chapter 3 New threshold secret sharing scheme 9
3.1 Satoshi at el.’s Threshold Scheme . . . . . . . . . . . . . . . . . . . . . . . . 10
3.2 Jun Kurihara.at el.’s Threshold Scheme . . . . . . . . . . . . . . . . . . . . . . 11
3.3 Extend Jun Kurihara et al.’s Method to Ramp Scheme . . . . . . . . . . . . . . 15
3.4 Example of Jun Kurihara.at el.’s Threshold Scheme . . . . . . . . . . . . . . . 16
Chapter 4 A Secret-Sharing-Based Method for Cloud Storage System 20
4.1 Notations and Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
4.2 Our Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
4.3 Evaluation of Capacity and Efficiency . . . . . . . . . . . . . . . . . . . . . . 25
Chapter 5 Conclusion and Future Works 27
Bibliography 28

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