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研究生: 許峻瑜
Hsu, Chun-Yu
論文名稱: 利用對稱偶合條件下的兩個相互耦合注入半導體雷射光學系統進行亂數產生
Chaos in Two mutually delay-coupled semiconductor lasers with symmetric coupling strength for random number generation
指導教授: 黃勝廣
Hwang, Sheng-Kwang
學位類別: 碩士
Master
系所名稱: 理學院 - 光電科學與工程學系
Department of Photonics
論文出版年: 2022
畢業學年度: 110
語文別: 中文
論文頁數: 118
中文關鍵詞: 半導體雷射相互耦合系統隨機亂數位元產生信號處理亂度資料安全
外文關鍵詞: Random number generation, Random bit generation, Nonlinear dynamics, Entropy, Encryption, Data Security, Semiconductor lasers
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  • 資料存儲、傳遞方式的改變,使通訊加密變成一項至關重要的環節,蒙地卡羅的隨機模擬,到虛擬貨幣的加密安全,這些領域都是隨機亂數/隨機位元產生的應用,這也使高效的亂數產生系統為競逐的目標,本研究將嘗試利用半導體雷射的物理機制產生加密數位資料所需的隨機亂數。

    亂數產生的分類可大致分為兩種,第一種傳統的作法為給定起始值,再利用演算法所形成的序列,稱作偽隨機亂數/位元(pseudo random number/bit),第二種方式為例用物理機制產生混沌序列,稱作真隨機亂數/位元(true random number/bit),在傳統的對稱式加密當中,資料的傳送端以及接受端會需要同一種私鑰來加、解密資料,當私鑰在網路上由傳遞方遞交給接受方的過程當中,駭客會有機會截取到私鑰的加密演算法,以演算法所構成的傳統的加密方式一旦被破解,所有以此演算法加密的資料皆暴露在風險當中,為降低加密方式被破解的風險,將採取和以往傳統利用數學演算法產生的不同的方式,以半導體雷射相互耦合系統來產生隨機位元,利用本身的物理機制的不可被預測性,降低了截取資料被破解的風險,大大提升了安全性,另外其產生信號的大頻寬對於隨機位元產生的高效率也有著決定性的因素。

    本研究先透過對光類比混沌信號的初步檢測,評測出混沌信號的品質,在確保類比混沌的品質下再對信號進行數位化,最後由美國國家中央標準技術研究所提出的NIST SP 800-90b將數位資料進行亂度測試。本研究提出了一系列檢測類比光信號混沌特性的工具 如: 信號時序動態分析、0-1test、自相關性測試、有效頻寬測試…等等,加以篩選出最佳的系統組成和最佳的操作條件,使雷射系統產生趨近理想化的光類比混沌信號,以達到最高亂度。

    本研究成功利用半導體雷射相互耦合系統,經過初步的類比信號評測工具篩選出最佳的系統以及操作條件,產生出60GHZ大頻寬的混沌訊號,經過取樣成功通過NIST SP 80090B的測試,其中NIST SP 800-90B是一項檢測系統亂度的指標測試,用以檢測系統的輸出,確保產生出來的隨機數位位元的安全性,此研究當中將完整呈現隨機亂數/數位位元產生的流程、分類、搭配各套件的分析,搭配信號亂度評估,超過60GHz大頻寬的互相耦合系統成功達成高效率的隨機亂數位元產生,為之後的應用提供了另一項優異的選擇。

    In this study, the whole conception of random number generation will be introduced, the random source’s category, scheme, and the result of the NIST SP 800-90b random test from the physical source will also be demonstrated, followed by the main physical system to generate the broadband microwaves using mutually symmetric optically-injected semiconductor laser system. The bandwidth of the high-frequency microwave chaos is greater than 60 GHz and tends to overwhelm the low-frequency microwave chaos generated by optical feedback, optical injection, and another optical system, a efficient random bit generator is then successfully achieved, giving a new choice for random number generation applying in data security.

    摘要 I Extended Abstract II 表目錄 VIII 圖目錄 IX 第一章 前言 14 1.1 研究背景 & 動機 14 1.2 大綱介紹 (點選word上方工作列檢視中的功能窗格打開文章架構) 16 第二章 雷射模擬數值模型以及基本亂數產生介紹 17 2.1雷射基本原理 17 2.2非線性機制 19 2.3相互耦合雷射模型 20 2.3.1光場的單位正規化 (Field Normalization) 22 2.3.2參數的替換及單位正規化 23 2.3.3合併結論 24 2.4相互耦合系統的非線性動態 26 2.5亂數產生基本介紹 30 第三章 亂數產生 31 3.1 基本架構 31 3.2 操作條件的分析與選擇 (承接Fig3-1) 32 3.2-1 Resample處理 33 3.3 Quantization(類比轉數位的量化) (接續Fig3-1總流程圖) 34 3.3-1 Nyquist Sampling Theorem (奈奎斯特取樣定理) 35 3.4亂度測試 (Entropy Testing)(Fig3-1的最後測試) 36 3.4-1關於隨機數位位元產生速率 (About Entropy Rate) 36 3.4-2 關於NIST SP 800-90B測試 37 3.4-3 綜合討論 39 第四章 模擬實驗結果討論 40 4.1 挑選操作條件 & 現象討論 41 4.2 獨立系統亂度趨勢討論 57 4.2.1 Mutual long delay (40.15 ns) Entropy Test (相互耦合系統長延遲的亂度測試) 58 4.2.2 Mutual short delay (22.4 ps) Entropy Test (相互耦合系統短延遲的亂度測試) 67 4.2.3 Entropy Test for Feedback System (光回饋系統的亂度測試) 74 4.2.4 Injection Entropy Test (光注入系統的亂度測試) 76 4.3 系統亂度綜合比較 78 4.3.1 相互耦合系統的長延遲以及短延遲比較 79 4.3.2 短延遲的綜合比較 80 4.3.3 全系統比較 81 4.4 相互耦合信號輸出回饋週期性討論 84 4.4.1信號擷取範圍對於亂度的影響比較 87 4.5 隨機亂數位元產生速率比較表 (Entropy rate Comparison) 99 第五章 附錄(分析用套件以及NIST90b補充說明) 101 5.1自相關性測試 (Time delay signature) 101 5.2 0-1 Test 102 5.3 頻寬量測 103 5.4 系統發散程度測試 (Lyapunov Exponent) 104 5.5 NIST 90b 補充說明 106 5.5-1眾數分析(most common value) 106 5.5-2 Repeated group discussion ( t-tuple & long repeated substring) 107 第六章 補充資料(後處理的應用以及資料呈現) 108 6.1 XOR 法 108 6.2 Derivative微分法 112 6.3 總結 114 參考文獻 115

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