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## A novel high speed GF (2173) elliptic curve crypto-processor.

Leung Pak Keung. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2003. / Includes bibliographical references (leaves 69-70). / Abstracts in English and Chinese. / Chapter Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Introduction to Elliptic Curve Crypto-processor --- p.1 / Chapter 1.2 --- Aims --- p.2 / Chapter 1.3 --- Contributions --- p.2 / Chapter 1.4 --- Thesis Outline --- p.3 / Chapter Chapter 2 --- Cryptography --- p.5 / Chapter 2.1 --- Introduction to Cryptography --- p.5 / Chapter 2.2 --- Public-key Cryptosystems --- p.6 / Chapter 2.3 --- Secret-key Cryptosystems --- p.9 / Chapter 2.4 --- Discrete Logarithm Problem --- p.9 / Chapter 2.5 --- Comparison between ECC and RSA --- p.10 / Chapter 2.6 --- Summary --- p.13 / Chapter Chapter 3 --- Mathematical Background in Number Systems --- p.14 / Chapter 3.1 --- Introduction to Number Systems --- p.14 / Chapter 3.2 --- "Groups, Rings and Fields" --- p.14 / Chapter 3.3 --- Finite Fields --- p.15 / Chapter 3.4 --- Modular Arithmetic --- p.16 / Chapter 3.5 --- Optimal Normal Basis --- p.16 / Chapter 3.5.1 --- What is a Normal Basis? --- p.17 / Chapter 3.5.2 --- Addition --- p.17 / Chapter 3.5.3 --- Squaring --- p.18 / Chapter 3.5.4 --- Multiplication --- p.19 / Chapter 3.5.5 --- Optimal Normal Basis --- p.19 / Chapter 3.5.6 --- Generation of the Lambda Matrix --- p.20 / Chapter 3.5.7 --- Inversion --- p.22 / Chapter 3.6 --- Summary --- p.24 / Chapter Chapter 4 --- Introduction to Elliptic Curve Mathematics --- p.26 / Chapter 4.1 --- Introduction --- p.26 / Chapter 4.2 --- Mathematical Background of Elliptic Curves --- p.26 / Chapter 4.3 --- Elliptic Curve over Real Number System --- p.27 / Chapter 4.3.1 --- Order of the Elliptic Curves --- p.28 / Chapter 4.3.2 --- Negation of Point P --- p.28 / Chapter 4.3.3 --- Point at Infinity --- p.28 / Chapter 4.3.4 --- Elliptic Curve Addition --- p.29 / Chapter 4.3.5 --- Elliptic Curve Doubling --- p.30 / Chapter 4.3.6 --- Equations of Curve Addition and Curve Doubling --- p.31 / Chapter 4.4 --- Elliptic Curve over Finite Fields Number System --- p.32 / Chapter 4.4.1 --- Elliptic Curve Operations in Optimal Normal Basis Number System --- p.32 / Chapter 4.4.2 --- Elliptic Curve Operations in Projective Coordinates --- p.33 / Chapter 4.4.3 --- Elliptic Curve Equations in Projective Coordinates --- p.34 / Chapter 4.5 --- Curve Multiplication --- p.36 / Chapter 4.6 --- Elliptic Curve Discrete Logarithm Problem --- p.37 / Chapter 4.7 --- Public-key Cryptography in Elliptic Curve Cryptosystem --- p.38 / Chapter 4.8 --- Diffie-Hellman Key Exchange in Elliptic Curve Cryptosystem --- p.38 / Chapter 4.9 --- Summary --- p.39 / Chapter Chapter 5 --- Design Architecture --- p.40 / Chapter 5.1 --- Introduction --- p.40 / Chapter 5.2 --- Criteria for the Low Power System Design --- p.40 / Chapter 5.3 --- Simplification in ONB Curve Addition Equations over Projective Coordinates --- p.41 / Chapter 5.4 --- Finite Field Adder Architecture --- p.43 / Chapter 5.5 --- Finite Field Squaring Architecture --- p.43 / Chapter 5.6 --- Finite Field Multiplier Architecture --- p.44 / Chapter 5.7 --- 3-way Parallel Finite Field Multiplier --- p.46 / Chapter 5.8 --- Finite Field Arithmetic Logic Unit --- p.47 / Chapter 5.9 --- Elliptic Curve Crypto-processor Control Unit --- p.50 / Chapter 5.10 --- Register Unit --- p.52 / Chapter 5.11 --- Summary --- p.53 / Chapter Chapter 6 --- Specifications and Communication Protocol of the IC --- p.54 / Chapter 6.1 --- Introduction --- p.54 / Chapter 6.2 --- Specifications --- p.54 / Chapter 6.3 --- Communication Protocol --- p.57 / Chapter Chapter 7 --- Results --- p.59 / Chapter 7.1 --- Introduction --- p.59 / Chapter 7.2 --- Results of the Public-key Cryptography --- p.59 / Chapter 7.3 --- Results of the Session-key Cryptography --- p.62 / Chapter 7.4 --- Comparison with the Existing Crypto-processor --- p.65 / Chapter 7.5 --- Power Consumption --- p.66 / Chapter Chapter 8 --- Conclusion --- p.68 / Bibliography --- p.69 / Appendix --- p.71 / 173-bit Type II ONB Multiplication Table --- p.71 / Layout View of the Elliptic Curve Crypto-processor --- p.76 / Schematics of the Elliptic Curve Crypto-processor --- p.77 / Schematics of the System Level Design --- p.78 / Schematics of the I/O Control Interface --- p.79 / Schematics of the Curve Multiplication Module --- p.80 / Schematics of the Curve Addition Module --- p.81 / Schematics of the Curve Doubling Module --- p.82 / Schematics of the Field Inversion Module --- p.83 / Schematics of the Register Unit --- p.84 / Schematics of the Datapath --- p.85 / Schematics of the Finite Field ALU --- p.86 / Schematics of the 3-way Parallel Multiplier --- p.87 / Schematics of the Multiplier Elements --- p.88 / Schematics of the Field Adder --- p.89 / Schematics of Demultiplexer --- p.90 / Schematics of the Control of the Demultiplexer --- p.91

Identifer | oai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_324253 |

Date | January 2003 |

Contributors | Leung, Pak Keung., Chinese University of Hong Kong Graduate School. Division of Electronic Engineering. |

Source Sets | The Chinese University of Hong Kong |

Language | English, Chinese |

Detected Language | English |

Type | Text, bibliography |

Format | print, xi, 91 leaves : ill. ; 30 cm. |

Rights | Use of this resource is governed by the terms and conditions of the Creative Commons â€śAttribution-NonCommercial-NoDerivatives 4.0 Internationalâ€ť License (http://creativecommons.org/licenses/by-nc-nd/4.0/) |

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