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研究生:邱迺軒
研究生(外文):Chiu, Nai-Hsuan
論文名稱:利用叢集運算提升RSA加解密系統之模指數運算速度
論文名稱(外文):Using the cluster computing to improve the speed of the modular exponentiation in RSA system
指導教授:張德仁張德仁引用關係
指導教授(外文):Chang, Te-Jen
口試委員:張德仁陳子和江豐光吳清揚鍾隆維
口試委員(外文):Chang, Te-JenChen,Zih-HeJiang,Fong-GuangWu,Cing-YangJhong,Long-Wei
口試日期:2011-05-06
學位類別:碩士
校院名稱:國防大學理工學院
系所名稱:電子工程碩士班
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:2011
畢業學年度:99
語文別:中文
論文頁數:92
中文關鍵詞:叢集運算模指數
外文關鍵詞:Cluster computingmodular exponentiation
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生活在數位時代中,資訊安全議題逐漸成為資訊產業的研究主流,為確保學術、商業的機密,密碼學扮演非常重要的角色。其中RSA密碼系統對於編碼、加密有很大的貢獻,其加、解密原理源於模指數的運算,必須使用多位元指數達到安全性。本論文改進C語言整數類別變數,其儲存空間不足的缺點,透過陣列方式儲存並計算,達到「大數運算」之功能。
大數運算對於中央處理器是一項很沉重的負擔,計算時間會因數字變大而更加耗時。對於增加計算速度方面,除在演算法上的改進,如二元法、滑動視窗法、加法鏈法等演算法,還可以透過叢集運算來幫助計算。撰寫有效的平行演算法於各個叢集計算節點中,利用此方法將會提升模指數的計算速度。
因此除C語言之外,本論文還會使用到MPICH2軟體,將實驗室電腦組成叢集電腦,由滑動視窗法、加法鏈法兩種演算法,延伸出兩套適合平行處理的模指數法,大幅減少高位數模指數的計算時間,並有效利用每節點的計算能力。利用叢集電腦有兩點好處,第一利用現有資源達到高效能計算,節省硬體的研發成本,第二提升計算效能,可使用閒置的電腦,避免閒置電腦(計算資源)的情況發生。
近年來,雲端計算成為主流的研究發展目標,而叢集運算屬於雲端計算的開端,本研究將資訊安全與雲端計算兩議題相互結合,在往後將有助於雲端計算的安全性。

In the digital times, information security becomes gradually popular research in IT (Information Technology) industry. Cryptography plays an important role in science and commerce. In many cryptography systems, RSA system is a great contribution to code. Its method is based on modular exponentiation. We should use more bits to promote the security. In this paper, we improve the size of the variables in C language. The computer can store and compute the higher bits through the array. We call this method as “a large number calculation”.
The operation of a large number is a very heavy burden for CPU. The larger the number becomes, the longer the computation time is. For increasing the computing speed, in addition to improve the algorithm, such as the binary method, the sliding window method, the addition chain method, and so on, the cluster computer can be used to advance computing speed. Write an effective parallel algorithm in each node of the cluster. This method will promote the speed of the modular exponentiation.
Therefore, apart from C language, it uses MPICH2 software in this paper. The cluster is composed of laboratory computers by MPICH2. Extending two modes suits the parallel processes of the modular exponentiation by combining the sliding window method with the addition chain method. It significantly reduces the computation time of the modular exponentiation which more digits effectively use computing power per node. There are two advantages for using the cluster. Firstly, we use current resources to achieve high computing performance and reduce the cost of the research. Then, we improve the efficiency of computation to use the idle computers and avoid idle computers (idle computing resources) to be happened.
In recent years, the cloud computing becomes the main research and the cluster computing is the beginning of the cloud computing. This paper combines the security issue with the cloud computing. In the future, it will contribute to the security of the cloud computing.

誌謝 ii
摘要 iii
ABSTRACT iv
目錄 vi
表目錄 ix
圖目錄 x
1. 緒論 1
1.1 研究背景 1
1.2 研究方向與方法 1
1.3 論文架構 2
2. 資訊安全 3
2.1 對稱式金鑰與非對稱式金鑰 3
2.2 RSA加密法 3
2.3 快速模指數運算 5
2.3.1 二元法(Binary Method) 5
2.3.2 m位數法(m-ary Method) 8
2.3.3 滑動視窗法(Sliding Window Method) 9
2.3.4 加法鏈(Addition Chain Method) 15
3. 叢集運算 17
3.1 分散式作業系統概論 17
3.2 叢集運算的演進 19
3.3 叢集運算工作原理 23
3.3.1 叢集運算的網路標準 23
3.3.2 叢集運算的硬體資源 24
3.3.3 常見的平行處理輸出方式 26
4. 實驗 30
4.1 實驗環境 30
4.1.1 硬體架構 30
4.1.2 軟體架構 31
4.2 軟體安裝及使用 33
4.2.1 軟體安裝 33
4.2.2 匯入MPI函式庫 34
4.2.3 MPICH2軟體 37
4.3 平行檔案系統 42
4.3.1 檔案階層式結構 42
4.3.2 絕對路徑與相對路徑 42
4.3.3 程式與檔案的互動 44
4.3.4 實驗程式的檔案 44
4.4 實驗程式 45
4.4.1 程式語言 45
4.4.2 圖形使用者介面(GUI)設計 45
4.5 演算法程式設計 48
4.5.1 大數運算構想與設計 48
4.5.2 陣列法程式設計 51
4.5.3 二元法程式設計 52
4.5.4 滑動視窗法程式設計 54
4.5.5 加法鏈法程式設計 56
4.5.6 平行滑動視窗模指數運算程式設計 57
4.5.7 平行加法鏈模指數運算程式設計 60
4.6 實驗結果 63
4.6.1 單機運算實驗數據 63
4.6.2 叢集運算實驗數據 69
5. 結論與未來研究方向 72
5.1 結論 72
5.2 未來研究方向 72
參考文獻 74
自傳 77


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