Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 20 of 83 for “"Elliptic Curve"”.
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Elliptic Curve Cryptography on Modern Processor Architectures
Abstract Elliptic Curve Cryptography (ECC) has been adopted by the US National Security Agency (NSA) in Suite "B" as part of its "Cryptographic Modernisation Program ". Additionally, it has been favoured by an entire host of mobile devices due to its superior performance characteristics. ECC is …
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Elliptic Curve Cryptography on Heterogeneous Multicore Platform
Elliptic curve cryptography (ECC) is becoming the algorithm of choice for digital signature generation and authentication in embedded context. However, performance of ECC and the underlying modular arithmetic on embedded processors remains a concern. At the same time, more complex system-on-chip …
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Crafting certified elliptic curve cryptography implementations in Coq
Elliptic curve cryptography has become a de-facto standard for protecting the privacy and integrity of internet communications. To minimize the operational cost and enable near-universal adoption, increasingly sophisticated implementation techniques have been developed. While the complete …
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Data storage security for cloud computing using elliptic curve cryptography
… of data stored in Cloud Computing by using Elliptic Curve Integrated Encryption Scheme (ECIES) that provides for confidentiality and integrity. This scheme also uses Identity Based Cryptography (IBC) for more efficient key management. The proposed scheme combines the security of Identity- …
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Computing the trace of an endomorphism of a supersingular elliptic curve
… for computing the trace of an endomorphism of an elliptic curve which is given by a chain of small-degree isogenies. We analyze its complexity, determining that if the length of the chain, the degree of the isogenies, and the log of the field-size are all O(n), the trace of the endomorphism can be …
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FPGA Implementations of Elliptic Curve Cryptography and Tate Pairing over Binary Field
Elliptic curve cryptography (ECC) is an alternative to traditional techniques for public key cryptography. It offers smaller key size without sacrificing security level. Tate pairing is a bilinear map used in identity based cryptography schemes. In a typical elliptic curve cryptosystem, elliptic …
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High Speed and Low-Complexity Hardware Architectures for Elliptic Curve-Based Crypto-Processors
The elliptic curve cryptography (ECC) has been identified as an efficient scheme for public-key cryptography. This thesis studies efficient implementation of ECC crypto-processors on hardware platforms in a bottom-up approach. We first study efficient and low-complexity architectures for finite …
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Securing group communication in dynamic, disadvantaged networks : implementation of an elliptic-curve pairing-based cryptography library
… with the piece de resistance being the elliptic curve-based Collusion-Resistant Broadcast Encryption. The focus of this thesis is primarily the engineering and synthesis of known theoretical schemes; we also present novel extensions to the Boneh-Gentry-Waters encryption scheme. 1. …
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René Schoof's Algorithm for Determining the Order of the Group of Points on an Elliptic Curve over a Finite Field
Elliptic curves have a rich mathematical history dating back to Diophantus (c. 250 C.E.), who used a form of these cubic equations to find right triangles of integer area with rational sides. In more recent times the deep mathematics of elliptic curves was used by Andrew Wiles et. al., to construct …
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L-functions of twisted elliptic curves over function fields
… studied, both theoretically and computationally, elliptic curves and their L-functions over number fields, in particular over the rational numbers. Much less work has been done over function fields, especially computationally, where the underlying geometry of the function field plays an intimate …
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Elliptic curves and their cryptographic applications
<p>"This thesis is a basic overview of elliptic curves and their applications to Cryptography. We begin with basic definitions and a demonstration that, given an elliptic curve addition, the points of an elliptic curve form a mathematical group. We then proceed to delve further into the …
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Expressions for the generating function of the Donaldson invariants for CP²
… phase approximation of a heterotic o-model on an elliptic curve at the boundary of the Coulomb branch with the target space CP1 x U(1). The semi-classical generating function is described in terms of determinant line bundles on the Coulomb branch. We show that in terms of the partition function on …
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Algebraic Curves Over Supersimple Fields
In this work we are concerned with algebraic curves over supersimple fields. First it is proved that an elliptic curve defined over a supersimple field K whose j-invariant is s-generic over empty has a rational point over K which is s-generic over the set of parameters used to define the curve. …
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Self-intersection of Manin-Drinfeld Cycles and Taylor expansion of L-functions
… that the derivative of the L-function of an elliptic curve is equal, up to a constant, to the Néron-Tate height pairing of a special point called a Heegner point on the elliptic curve. A more recent result was proven in the function field case by Yun and Zhang which showed that higher …
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Torus equivariant elliptic cohomology and sigma orientations
… \colon= \mathds{C}/ \Lambda$ be a complex elliptic curve. In this paper, we give a detailed construction of torus equivariant elliptic cohomology, which is a sheaf of $ \mathcal{ O}_{\mathcal{C}^n}$-algebras over $ \mathcal{C}^n$. As applications, we construct global sections for sigma …
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Distribution of Selmer Groups of Quadratic Twists of a Family of Elliptic Curves
As an most interesting example for the elliptic curve E n : y2 = x 3 - n2x, which is closely related with the congruent number problem, we study the distribution of the size of the six Selmer groups arising from the three 2-isogenies and their dual 2-isogenies. We also describe explicit formulas on …
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Correct-by-construction finite field arithmetic in Coq
Elliptic-curve cryptography code, although based on elegant and concise mathematical procedures, often becomes long and complex due to speed optimizations. This statement is especially true for the specialized finite-field libraries used for ECC code, resulting in frequent implementation bugs. I …
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Constructive synthesis of optimized cryptographic primitives
… verified machine-code implementations of Elliptic Curve Cryptography. My implementation outputs Qhasm, a high-level assembly language developed for the implementation of highly optimised cryptography, and maintains platform independence by being totally parametric over the width of system …
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Triangle configurations, and Beilinson's conjecture for $K_{1}^{(2)}$ of the product of a curve with itself
… C)$ where $C$ is a (smooth projective) curve. In particular, it examines whether non-zero integral elements can be obtained from linear combinations of certain special types of elements which I refer to as ``triangle'' configurations. Most of the thesis examines the special case where …
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