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Student Number 88521071
Author Zh-Qiang Zhuang(莊志強)
Author's Email Address No Public.
Statistics This thesis had been viewed 2029 times. Download 1287 times.
Department Electrical Engineering
Year 2000
Semester 2
Degree Master
Type of Document Master's Thesis
Language zh-TW.Big5 Chinese
Title 應用於橢圓曲線密碼系統之低複雜性有限場乘法器設計
Date of Defense 2001-06-28
Page Count 77
Keyword
  • 乘法器
  • 密碼
  • 有限場
  • 橢圓曲線
  • Abstract none
    Table of Content Contents
    Contents II
    List of Figures V
    List of Tables VIII
    CHAPTER 1INTRODUCTION1
    1.1OVERVIEW OF CRYPTOGRAPHY1
    1.2OVERVIEW OF ECC CRYPTOGRAPHY2
    1.3MOTIVATION AND GOAL5
    1.4CONTRIBUTION OF THE THESIS7
    1.5THESIS ORGANIZATION8
    CHAPTER 2ELLIPTIC CURVE CRYPTOSYSTEMS10
    2.1HISTORY OF ELLIPTIC CURVES10
    2.2MATHEMATIC BACKGROUND ON ELLIPTIC CURVES12
    2.2.1THE GROUP LAW14
    2.2.2ELLIPTIC CURVE ADDITION15
    2.2.3ELLIPTIC CURVES OVER GF(2M)19
    2.2.4POINT MULTIPLICATION ON ELLIPTIC CURVES21
    2.2.5GROUP OPERATION WITH PROJECTIVE COORDINATES22
    2.3SUMMARY OF ENCRYPTION/DECRYPTION IN ECC25
    CHAPTER 3FINITE FIELD ARITHMETIC26
    3.1CHOOSING A FIELD27
    3.2REPRESENTATION OF FINITE FIELD ELEMENTS28
    3.3COMPUTER ARITHMETIC IN FINITE FIELDS30
    3.3.1FINITE FIELD ADDITION (FFA)30
    3.3.2SQUARING IN GF(2M)32
    3.3.3FINITE FIELD MULTIPLICATION (FFM)33
    CHAPTER 4DESIGN OF LOW-COMPLEXITY COMPOSITE FIELDS GF((2N)M) MULTIPLIERS38
    4.1PROPOSED NORMAL BASIS TYPE-II MULTIPLIER39
    4.1.1IMPROVED MULTIPLICATION ALGORITHM41
    4.1.2MULTIPLICATION EXAMPLE43
    4.1.3COMPARISON OF MULTIPLICATION ALGORITHMS45
    4.2DESIGN OF EFFICIENT NORMAL BASIS MULTIPLIER IN COMPOSITE FIELDS48
    4.2.1REVIEW OF TYPE-I ONB MULTIPLIER48
    4.2.2PROPOSED TYPE-II COMPOSITE FIELDS MULTIPLIER49
    4.2.3COMPARISON OF OTHER MULTIPLIERS53
    CHAPTER 5THE DESIGN OF ECC PROCESSOR AND SIMULATION57
    5.1ARCHITECTURAL DESIGN OF ECC PROCESSOR58
    5.1.1DESIGN OF POINT MULTIPLICATION UNIT58
    5.1.2DESIGN OF CONTROL UNIT61
    5.1.3ECC PROCESSOR DESIGN63
    5.2SIMULATION RESULT67
    5.2.1VERIFICATION OF OUR ARCHITECTURE67
    5.2.2OTHER TESTING CASES70
    CHAPTER 6CONCLUSION73
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    [30]C. Paar, P. Fleischmann, and P. Poelse. Efficient Mulitplier Architecture for Galois Fields. IEEE Trans Computers, vol. 47, no. 2, pp.162-170, Feb. 1998.
    [31]AMERICAN NATIONAL STANDARD X9.62-1998. public key cryptography for the financial services industry. The Elliptic Curve Digital Signature Alogorithm (ECDSA).
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    [33]M.A. Hasan, M.Z. Wang, and V.K. Bhargava. Modular Construction of Low Complexity Parallel Multipliers for a Class of Finite Fileds GF(2^m). IEEE Trans Comput., vol. 41, no.8,pp. 962-971, Aug. 1992.
    Advisor
  • Shyh-Jye Jou(周世傑)
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    Date of Submission 2001-06-28

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