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Implementation aspects of elliptic curve cryptographySava��, Erkay 20 June 2000 (has links)
As the information-processing and telecommunications revolutions now underway
will continue to change our life styles in the rest of the 21st century, our
personal and economic lives rely more and more on our ability to transact over
the electronic medium in a secure way. The privacy, authenticity, and integrity of
the information transmitted or stored on networked computers must be maintained
at every point of the transaction. Fortunately, cryptography provides algotrithms
and techniques for keeping information secret, for determining that the contents
of a transaction have not been tampered with, for determining who has really authorized
the transaction, and for binding the involved parties with the contents of
the transaction. Since we need security on every piece of digital equipment that
helps conduct transactions over the internet in the near future, space and time performances
of cryptographic algorithms will always remain to be among the most
critical aspects of implementing cryptographic functions.
A major class of cryptographic algorithms comprises public-key schemes which
enable to realize the message integrity and authenticity check, key distribution,
digital signature functions etc. An important category of public-key algorithms is
that of elliptic curve cryptosystems (ECC). One of the major advantages of elliptic
curve cryptosystems is that they utilize much shorter key lengths in comparison to
other well known algorithms such as RSA cryptosystems. However, as do the other
public-key cryptosystems ECC also requires computationally intensive operations.
Although the speed remains to be always the primary concern, other design constraints
such as memory might be of significant importance for certain constrained
platforms.
In this thesis, we are interested in developing space- and time-efficient hardware
and software implementations of the elliptic curve cryptosystems. The main focus
of this work is to improve and devise algorithms and hardware architectures for
arithmetic operations of finite fields used in elliptic curve cryptosystems. / Graduation date: 2001
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An evaluation of the strength characteristics of horizontally curved steel I-girder bridgesCullen, Lauren E. January 2007 (has links)
Thesis (M.S.)--West Virginia University, 2007. / Title from document title page. Document formatted into pages; contains ix, 226 p. : ill. (some col.). Includes abstract. Includes bibliographical references (p. 179-187).
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Tests for equality of curves via wavelets /Guo, Pengfei, January 2005 (has links)
Thesis (M.Sc.)--Memorial University of Newfoundland, 2005. / Bibliography: leaves 81-84.
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The multiple view geometry of implicit curves and surfaces /McKinnon, David N. R. January 2006 (has links) (PDF)
Thesis (Ph.D.) - University of Queensland, 2006. / Includes bibliography.
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Security enhancement on the cryptosystem based on chaotic and elliptic curve cryptography /Man, Kwan Pok. January 2006 (has links) (PDF)
Thesis (M.Phil.)--City University of Hong Kong, 2006. / "Submitted to Department of Electronic Engineering in partial fulfillment of the requirements for the degree of Master of Philosophy" Includes bibliographical references (leaves 93-97)
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Inverse problems of the Darboux theory of integrability for planar polynomial differential systemsPantazi, Chara 16 July 2004 (has links)
No description available.
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An Approach to Quantifying Uncertainty in Estimates of Intensity Duration Frequency (IDF) CurvesAlzahrani, Fahad 13 August 2013 (has links)
Generally urban drainage systems are built to protect urban property and control runoff. Moreover, these systems collect the runoff for storage purposes to serve society through sufficient water supply to meet the needs of demand, irrigation, and drainage. Urban environments are exposed to risks of extreme hydrological events. Therefore, urban water systems and their management are critical. Precipitation data are crucial, but may be prone to errors due to the lack of information e.g., short length of records. In this thesis, a Monte Carlo simulation and regional frequency analysis based on L-moments approach were utilized during the research in order to estimate the uncertainty in the Intensity Duration Frequency (IDF) curves by using historical precipitation data from Environment Canada (EC) weather stations and simulating a new series of data through a weather generator (WG) model. The simulations were then disaggregated from daily into hourly data for extraction of the annual maximum precipitation for different durations in hours (1, 2, 6, 10, 12, and 24). Regional frequency analysis was used to form the sites into groups based on homogeneity test results, and the quantile values were computed for various sites and durations with the return periods (T) in years (2, 10, 20, and 100). As a result, the regional frequency analysis was used to estimate the regional quantile values based on L-moment approach. Moreover, the box and whisker plots were utilized to display the results. When the return periods and durations increased, the uncertainty slightly increased. The historical IDF curves of London site falls within the regional simulated IDF curves. Furthermore, 1000 runs have been generated by using the weather generator.
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Evaluating Large Degree Isogenies between Elliptic CurvesSoukharev, Vladimir 12 1900 (has links)
An isogeny between elliptic curves is an algebraic morphism which is a group homomorphism. Many applications in cryptography require evaluating large degree isogenies between elliptic curves efficiently. For ordinary curves of the same endomorphism ring, the previous fastest algorithm known has a worst case running time which is exponential in the length of the input. In this thesis we solve this problem in subexponential time under reasonable heuristics. We give two versions of our algorithm, a slower version assuming GRH and a faster version assuming stronger heuristics. Our approach is based on factoring the ideal corresponding to the kernel of the isogeny, modulo principal ideals, into a product of smaller prime ideals for which the isogenies can be computed directly. Combined with previous work of Bostan et al., our algorithm yields equations for large degree isogenies in quasi-optimal time given only the starting curve and the kernel.
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Hypergeometric functions over finite fields and relations to modular forms and elliptic curvesFuselier, Jenny G. 15 May 2009 (has links)
The theory of hypergeometric functions over finite fields was developed in the mid-
1980s by Greene. Since that time, connections between these functions and elliptic
curves and modular forms have been investigated by mathematicians such as Ahlgren,
Frechette, Koike, Ono, and Papanikolas. In this dissertation, we begin by giving a
survey of these results and introducing hypergeometric functions over finite fields.
We then focus on a particular family of elliptic curves whose j-invariant gives an
automorphism of P1. We present an explicit relationship between the number of
points on this family over Fp and the values of a particular hypergeometric function
over Fp. Then, we use the same family of elliptic curves to construct a formula for
the traces of Hecke operators on cusp forms in level 1, utilizing results of Hijikata and
Schoof. This leads to formulas for Ramanujan’s -function in terms of hypergeometric
functions.
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Hypergeometric functions over finite fields and their relations to algebraic curves.Vega Veglio, Maria V. 2009 May 1900 (has links)
Classical hypergeometric functions and their relations to counting points on
curves over finite fields have been investigated by mathematicians since the beginnings of 1900. In the mid 1980s, John Greene developed the theory of hypergeometric
functions over finite fi elds. He explored the properties of these functions and found
that they satisfy many summation and transformation formulas analogous to those
satisfi ed by the classical functions. These similarities generated interest in finding
connections that hypergeometric functions over finite fields may have with other objects. In recent years, connections between these functions and elliptic curves and
other Calabi-Yau varieties have been investigated by mathematicians such as Ahlgren,
Frechette, Fuselier, Koike, Ono and Papanikolas. A survey of these results is given at
the beginning of this dissertation. We then introduce hypergeometric functions over
finite fi elds and some of their properties. Next, we focus our attention on a particular
family of curves and give an explicit relationship between the number of points on
this family over Fq and sums of values of certain hypergeometric functions over Fq.
Moreover, we show that these hypergeometric functions can be explicitly related to
the roots of the zeta function of the curve over Fq in some particular cases. Based
on numerical computations, we are able to state a conjecture relating these values
in a more general setting, and advances toward the proof of this result are shown in the last chapter of this dissertation. We nish by giving various avenues for future
study.
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