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17x bits elliptic curve scalar multiplication over GF(2M) using optimal normal basis.January 2001 (has links)
Tang Ko Cheung, Simon. / Thesis (M.Phil.)Chinese University of Hong Kong, 2001. / Includes bibliographical references (leaves 8991). / 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  Highspeed 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

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Trace forms and selfdual normal bases in Galois field extensions /Kang, Dong Seung. January 1900 (has links)
Thesis (Ph. D.)Oregon State University, 2003. / Typescript (photocopy). Includes bibliographical references (leaves 4346). Also available on the World Wide Web.

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