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17x bits elliptic curve scalar multiplication over GF(2M) using optimal normal basis.

Tang Ko Cheung, Simon. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2001. / Includes bibliographical references (leaves 89-91). / Abstracts in English and Chinese. / Chapter 1 --- Theory of Optimal Normal Bases --- p.3 / Chapter 1.1 --- Introduction --- p.3 / Chapter 1.2 --- The minimum number of terms --- p.6 / Chapter 1.3 --- Constructions for optimal normal bases --- p.7 / Chapter 1.4 --- Existence of optimal normal bases --- p.10 / Chapter 2 --- Implementing Multiplication in GF(2m) --- p.13 / Chapter 2.1 --- Defining the Galois fields GF(2m) --- p.13 / Chapter 2.2 --- Adding and squaring normal basis numbers in GF(2m) --- p.14 / Chapter 2.3 --- Multiplication formula --- p.15 / Chapter 2.4 --- Construction of Lambda table for Type I ONB in GF(2m) --- p.16 / Chapter 2.5 --- Constructing Lambda table for Type II ONB in GF(2m) --- p.21 / Chapter 2.5.1 --- Equations of the Lambda matrix --- p.21 / Chapter 2.5.2 --- An example of Type IIa ONB --- p.23 / Chapter 2.5.3 --- An example of Type IIb ONB --- p.24 / Chapter 2.5.4 --- Creating the Lambda vectors for Type II ONB --- p.26 / Chapter 2.6 --- Multiplication in practice --- p.28 / Chapter 3 --- Inversion over optimal normal basis --- p.33 / Chapter 3.1 --- A straightforward method --- p.33 / Chapter 3.2 --- High-speed inversion for optimal normal basis --- p.34 / Chapter 3.2.1 --- Using the almost inverse algorithm --- p.34 / Chapter 3.2.2 --- "Faster inversion, preliminary subroutines" --- p.37 / Chapter 3.2.3 --- "Faster inversion, the code" --- p.41 / Chapter 4 --- Elliptic Curve Cryptography over GF(2m) --- p.49 / Chapter 4.1 --- Mathematics of elliptic curves --- p.49 / Chapter 4.2 --- Elliptic Curve Cryptography --- p.52 / Chapter 4.3 --- Elliptic curve discrete log problem --- p.56 / Chapter 4.4 --- Finding good and secure curves --- p.58 / Chapter 4.4.1 --- Avoiding weak curves --- p.58 / Chapter 4.4.2 --- Finding curves of appropriate order --- p.59 / Chapter 5 --- The performance of 17x bit Elliptic Curve Scalar Multiplication --- p.63 / Chapter 5.1 --- Choosing finite fields --- p.63 / Chapter 5.2 --- 17x bit test vectors for onb --- p.65 / Chapter 5.3 --- Testing methodology and sample runs --- p.68 / Chapter 5.4 --- Proposing an elliptic curve discrete log problem for an 178bit curve --- p.72 / Chapter 5.5 --- Results and further explorations --- p.74 / Chapter 6 --- On matrix RSA --- p.77 / Chapter 6.1 --- Introduction --- p.77 / Chapter 6.2 --- 2 by 2 matrix RSA scheme 1 --- p.80 / Chapter 6.3 --- Theorems on matrix powers --- p.80 / Chapter 6.4 --- 2 by 2 matrix RSA scheme 2 --- p.83 / Chapter 6.5 --- 2 by 2 matrix RSA scheme 3 --- p.84 / Chapter 6.6 --- An example and conclusion --- p.85 / Bibliography --- p.91

Identiferoai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_323344
Date January 2001
ContributorsTang, Ko Cheung Simon., Chinese University of Hong Kong Graduate School. Division of Information Engineering.
Source SetsThe Chinese University of Hong Kong
LanguageEnglish, Chinese
Detected LanguageEnglish
TypeText, bibliography
Formatprint, ii, 91 leaves : ill. ; 30 cm.
RightsUse of this resource is governed by the terms and conditions of the Creative Commons “Attribution-NonCommercial-NoDerivatives 4.0 International” License (http://creativecommons.org/licenses/by-nc-nd/4.0/)

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