A microcoded elliptic curve cryptographic processor.

Leung Ka Ho.Thesis (M.Phil.)--Chinese University of Hong Kong, 2001.Includes bibliographical references (leaves [85]-90).Abstracts in English and Chinese.Abstract --- p.iAcknowledgments --- p.iiiList of Figures --- p.ixList of Tables --- p.xiChapter 1 --- Introduction --- p.1Chapter 1.1 --- Motivation --- p.1Chapter 1.2 --- Aims --- p.3Chapter 1.3 --- Contributions --- p.3Chapter 1.4 --- Thesis Outline --- p.4Chapter 2 --- Cryptography --- p.6Chapter 2.1 --- Introduction --- p.6Chapter 2.2 --- Foundations --- p.6Chapter 2.3 --- Secret Key Cryptosystems --- p.8Chapter 2.4 --- Public Key Cryptosystems --- p.9Chapter 2.4.1 --- One-way Function --- p.10Chapter 2.4.2 --- Certification Authority --- p.10Chapter 2.4.3 --- Discrete Logarithm Problem --- p.11Chapter 2.4.4 --- RSA vs. ECC --- p.12Chapter 2.4.5 --- Key Exchange Protocol --- p.13Chapter 2.4.6 --- Digital Signature --- p.14Chapter 2.5 --- Secret Key vs. Public Key Cryptography --- p.16Chapter 2.6 --- Summary --- p.18Chapter 3 --- Mathematical Background --- p.19Chapter 3.1 --- Introduction --- p.19Chapter 3.2 --- Groups and Fields --- p.19Chapter 3.3 --- Finite Fields --- p.21Chapter 3.4 --- Modular Arithmetic --- p.21Chapter 3.5 --- Polynomial Basis --- p.21Chapter 3.6 --- Optimal Normal Basis --- p.22Chapter 3.6.1 --- Addition --- p.23Chapter 3.6.2 --- Squaring --- p.24Chapter 3.6.3 --- Multiplication --- p.24Chapter 3.6.4 --- Inversion --- p.30Chapter 3.7 --- Summary --- p.33Chapter 4 --- Literature Review --- p.34Chapter 4.1 --- Introduction --- p.34Chapter 4.2 --- Hardware Elliptic Curve Implementation --- p.34Chapter 4.2.1 --- Field Processors --- p.34Chapter 4.2.2 --- Curve Processors --- p.36Chapter 4.3 --- Software Elliptic Curve Implementation --- p.36Chapter 4.4 --- Summary --- p.38Chapter 5 --- Introduction to Elliptic Curves --- p.39Chapter 5.1 --- Introduction --- p.39Chapter 5.2 --- Historical Background --- p.39Chapter 5.3 --- Elliptic Curves over R2 --- p.40Chapter 5.3.1 --- Curve Addition and Doubling --- p.41Chapter 5.4 --- Elliptic Curves over Finite Fields --- p.44Chapter 5.4.1 --- Elliptic Curves over Fp with p>〉3 --- p.44Chapter 5.4.2 --- Elliptic Curves over F2n --- p.45Chapter 5.4.3 --- Operations of Elliptic Curves over F2n --- p.46Chapter 5.4.4 --- Curve Multiplication --- p.49Chapter 5.5 --- Elliptic Curve Discrete Logarithm Problem --- p.51Chapter 5.6 --- Public Key Cryptography --- p.52Chapter 5.7 --- Elliptic Curve Diffie-Hellman Key Exchange --- p.54Chapter 5.8 --- Summary --- p.55Chapter 6 --- Design Methodology --- p.56Chapter 6.1 --- Introduction --- p.56Chapter 6.2 --- CAD Tools --- p.56Chapter 6.3 --- Hardware Platform --- p.59Chapter 6.3.1 --- FPGA --- p.59Chapter 6.3.2 --- Reconfigurable Hardware Computing --- p.62Chapter 6.4 --- Elliptic Curve Processor Architecture --- p.63Chapter 6.4.1 --- Arithmetic Logic Unit (ALU) --- p.64Chapter 6.4.2 --- Register File --- p.68Chapter 6.4.3 --- Microcode --- p.69Chapter 6.5 --- Parameterized Module Generator --- p.72Chapter 6.6 --- Microcode Toolkit --- p.73Chapter 6.7 --- Initialization by Bitstream Reconfiguration --- p.74Chapter 6.8 --- Summary --- p.75Chapter 7 --- Results --- p.76Chapter 7.1 --- Introduction --- p.76Chapter 7.2 --- Elliptic Curve Processor with Serial Multiplier (p = 1) --- p.76Chapter 7.3 --- Projective verses Affine Coordinates --- p.78Chapter 7.4 --- Elliptic Curve Processor with Parallel Multiplier (p > 1) --- p.79Chapter 7.5 --- Summary --- p.80Chapter 8 --- Conclusion --- p.82Chapter 8.1 --- Recommendations for Future Research --- p.83Bibliography --- p.85Chapter A --- Elliptic Curves in Characteristics 2 and3 --- p.91Chapter A.1 --- Introduction --- p.91Chapter A.2 --- Derivations --- p.91Chapter A.3 --- "Elliptic Curves over Finite Fields of Characteristic ≠ 2,3" --- p.92Chapter A.4 --- Elliptic Curves over Finite Fields of Characteristic = 2 --- p.94Chapter B --- Examples of Curve Multiplication --- p.95Chapter B.1 --- Introduction --- p.95Chapter B.2 --- Numerical Results --- p.9