Thesis (Ph. D.)--University of Texas at Austin, 1999. / Vita. Includes bibliographical references (leaves 160-162). Available also in a digital version from Dissertation Abstracts.

No description available.

No description available.

Thesis (M.S.)--Ohio State University, 2008. / Title from first page of PDF file. Includes bibliographical references (p. 41-42).

Thesis (M.S. in Computer Science)--Naval Postgraduate School, March 2010. / Thesis Advisor: Volpano, Dennis. Second Reader: Fredricksen, Harold. "March 2010." Author(s) subject terms: Discrete logarithms, analysis of algorithms, advice strings, Diffie-Hellman Key Exchange. Includes bibliographical references (p. 51-53). Also available in print.

Logaritmos são partes integrantes de muitas formas de tecnologia, e sua história e desenvolvimento ajudam a ver sua importância e relevância. Os logaritmos têm sido parte da matemática há vários séculos, mas o conceito de logaritmo mudou notavelmente ao longo dos anos. O logaritmo tem sido uma ferramenta para matemáticos, físicos e engenheiros ao redor do mundo, simplificando seus cálculos. A ideia de logaritmo existe desde o início do século XVII, como uma forma de facilitar a divissão e a multiplicação de números grandes. O logaritmo tomou diferentes formas em sua jornada para se tornar o que é hoje e houve muitos matemáticos, tais como John Napier, Henry Briggs e Leonhard Euler que fizeram contribuições significativas para o assunto. Este trabalho aborda as origens dos logaritmos e sua utilidade nos tempos antigos e modernos. / Logarithms are an integral part of many forms of technology, and their history and development help to see their importance and relevance. Logarithms have been part of mathematics for several centuries, but the concept of logarithm has changed markedly over the years. The logarithm has been a tool for mathematicians, physicists and engineers around the world, simplifying your calculations . Having existed since the early seventeenth century, the logarithm changed a lot since its introduction into the world of mathematics, it began as a way to make multiplication and division of large numbers an easier way to look up values in a table. and then adding them for its addition and sustenance to the division and from there it evolved into the logarithm today known as the inverse of the exponential. The logarithm took different forms on its journey to become what it is today and there were many mathematicians, such as John Napier, Henry Briggs and Leonhard Euler who made significant contributions to the matter. This paper addresses the origins of logarithms and their usefulness in ancient and modern times.

by Chan Hing Che. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2000. / Includes bibliographical references (leaves 59-[61]). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Background --- p.8 / Chapter 2.1 --- Abstract Algebra --- p.8 / Chapter 2.1.1 --- Group --- p.9 / Chapter 2.1.2 --- Ring --- p.10 / Chapter 2.1.3 --- Field --- p.11 / Chapter 2.1.4 --- Useful Theorems in Number Theory --- p.12 / Chapter 2.2 --- Discrete Logarithm --- p.13 / Chapter 2.3 --- Solving Discrete Logarithm --- p.14 / Chapter 2.3.1 --- Exhaustive Search --- p.14 / Chapter 2.3.2 --- Baby Step Giant Step --- p.15 / Chapter 2.3.3 --- Pollard's rho --- p.16 / Chapter 2.3.4 --- Pohlig-Hellman --- p.18 / Chapter 2.3.5 --- Index Calculus --- p.23 / Chapter 3 --- Forging ElGamal Signature --- p.26 / Chapter 3.1 --- ElGamal Signature Scheme --- p.26 / Chapter 3.2 --- ElGamal signature without hash function --- p.29 / Chapter 3.3 --- Security of ElGamal signature scheme --- p.32 / Chapter 3.4 --- Bleichenbacher's Attack --- p.34 / Chapter 3.4.1 --- Constructing trapdoor --- p.36 / Chapter 3.5 --- Extension to Bleichenbacher's attack --- p.37 / Chapter 3.5.1 --- Attack on variation 3 --- p.38 / Chapter 3.5.2 --- Attack on variation 5 --- p.39 / Chapter 3.5.3 --- Attack on variation 6 --- p.39 / Chapter 3.6 --- Digital Signature Standard(DSS) --- p.40 / Chapter 4 --- Quadratic Field Sieve --- p.47 / Chapter 4.1 --- Quadratic Field --- p.47 / Chapter 4.1.1 --- Integers of Quadratic Field --- p.48 / Chapter 4.1.2 --- Primes in Quadratic Field --- p.49 / Chapter 4.2 --- Number Field Sieve --- p.50 / Chapter 4.3 --- Solving Sparse Linear Equations Over Finite Fields --- p.53 / Chapter 4.3.1 --- Lanczos and conjugate gradient methods --- p.53 / Chapter 4.3.2 --- Structured Gaussian Elimination --- p.54 / Chapter 4.3.3 --- Wiedemann Algorithm --- p.55 / Chapter 5 --- Conclusion --- p.57 / Bibliography --- p.59

Thesis (Ph. D.)--Lehigh University, 2004. / Includes vita. Includes bibliographical references (leaves 153-167).

No description available.

Since Mclntosh's introduction of the H^∞-calculus for sectorial operators, the topic has been studied by many authors. Haase has constructed a similar functional calculus for strip-type operators, and has also developed an abstract framework which unifies both of these examples and more. In this thesis we use this abstract functional calculus setting to study two particular problems in operator theory. The first of these is concerned with operator sums. We ask the question of when the sum log A+log B is closed, where A and B are a pair of injective sectorial operators whose resolvents commute. We show that the sum is always closable and, when A and B are invertible, we determine sufficient conditions for the sum to be closed. These conditions are of Kalton-Weis type, and in fact ensure that AB is sectorial and that the identity log A + log B = log(AB) holds. We then identify an interpolation space on which these conditions are automatically satisfied. Our second problem is connected to the exponential of a strip-type operator B</e>, specifically the question of whether e^B is sectorial. When -1 ∈ p(e^B), the spectrum of e^B lies in a sector, and we obtain an estimate on the resolvent outside this sector. This estimate becomes closer to sectoriality as more restrictions are placed on the resolvents of B itself. This leads us to introduce the ideas of F-sectorial and F-strong strip-type operators, whose spectra are contained in a sector or strip, but which satisfy a different resolvent estimate from that of a sectorial or strong striptype operator. In some cases it is possible to define the logarithm of an F-sectorial operator or the exponential of an F-strong strip-type operator. We prove resolvent estimates for the resulting logarithms and exponentials, and explore the relationships between the various classes of operators considered.