Thesis (Ph. D.)--University of Texas at Austin, 2005. / Supervisor: César Salgado. Vita. Includes bibliographical references.

Thesis (MSc (Mathematics))--Stellenbosch University, 2008. / This is an exposition of the explicit approach to Local Class Field Theory due to J. Tate and J. Lubin. We mainly follow the treatment given in [15] and [25]. We start with an informal introduction to p-adic numbers. We then review the standard theory of valued elds and completion of those elds. The complete discrete valued elds with nite residue eld known as local elds are our main focus. Number theoretical aspects for local elds are considered. The standard facts about Hensel's lemma, Galois and rami cation theory for local elds are treated. This being done, we continue our discussion by introducing the key notion of relative Lubin-Tate formal groups and modules. The torsion part of a relative Lubin-Tate module is then used to generate a tower of totally rami ed abelian extensions of a local eld. Composing this tower with the maximal unrami ed extension gives the maximal abelian extension: this is the local Kronecker-Weber theorem. What remains then is to state and prove the theorems for explicit local class eld theory and end our discussion.

A collection of poems by Kimberly Abruzzo.

Five resorts in East Tennessee--Montvale Springs and the Wonderland Hotel in the Smokies, Tate Spring in the Holston River Valley, Unaka Springs on the Nolichucky River, and the Cloudland Hotel at the summit of Roan Mountain--stand testament to the proposition that their region engaged fully with areas outside southern Appalachia. Their origins, clientele, and health and leisure offerings followed those of other resorts of the same time period. Moreover, the effects of national socioeconomic trends on the hotels serve as a contradiction to the stereotype of southern Appalachia as an isolated region barricaded from the outside world by mountainous topography. The East Tennessee resorts covered in this thesis indicate that the region as a whole was emblematic of national socioeconomic and cultural trends.

Denna studie handlar om Andrew Tates uttalanden på TikTok och vilka ideer han sprider om män och kvinnor. Syftet var att undersöka Tates idealbild av både män och kvinnor. De teoretiska ramverk som studien är uppbyggd av är femininitets- och maskulinitetsteorier, samt en socialkonstruktionistisk idetradition. För att få en djupare bild av Tates uttalanden har både en tematisk- och DHA analys utförts. Genom den tematiska analysen kunde orden och meningarna brytas ner i teman som visade på tydliga mönster i Tates uttalanden om män och kvinnor och vad han ansåg vara maskulint respektive feminint. DHA analysen möjliggjorde en djupare analys av vilka värden Tate tillsätter män och kvinnor samt hur diskursen byggs upp. Resultatet av den tematiska analysen utmynnade i fyra huvudteman. Dessa var misogyni, mansideal, kvinnoideal, könsroller och Tate försöker visa medkänsla för kvinnor. Resultaten av DHA analysen påvisar att Tate tycker det är viktigt att skilja på könen och gör detta genom att belysa skillnaderna på män och kvinnor.

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Abstract.  The purpose of this study is to investigate connections between Andrew Tate and right-wing extreme ideologies through fascist and feminist theories and how they spread in a digitalized globalization. The material is gathered from interviews and podcasts on YouTube where Andrew Tate shares his opinions. I have used theories and concepts that discuss sex, gender and heteronormativity as a social construction, as well as a theoretical framework that identifies tactics used by fascist movements to spread their ideas and increase their influence. The result of my study shows that there are distinct connections between Andrew Tate opinions and right-wing extreme ideologies. Tate uses the same tactical method as fascism to spread his message and gain followers. They also share the traditional conservative view on gender and gender roles where everything is based on masculinity and femininity in relation to one's biology. Both ideologies are based on a heteronormativity that lacks intersectional analysis and stigmatizes those who break the norm.

Mikroprimstellen wurden eingeführt von J. Neukirch im Rahmen der abstrakten Klassenkörpertheorie. Eine Verallgemeinerung der Zerlegungsgruppen von Primstellen globaler Körper motivierte die rein gruppentheoretische Definition der Mikroprimstellen als gewisse Äquivalenzklassen von Frobeniuselementen. Auf den Fall der Galoisgruppen lokaler oder globaler Körper angewendet, ergibt diese Theorie eine Beschreibung spezieller Konjugationsklassen. Die Hauptaufgabe von J. Neukirch ist, die zahlentheoretische Bedeutung der Mikroprimstellen zu verstehen, das heißt, sie in Termen des Grundkörpers anzugeben. J. Mehlig und E.-W. Zink fanden eine Bijektion zwischen Mikroprimstellen und normverträglichen Folgen von Primelementen in Körpertürmen. Diese Türme entstehen durch die Fixkörper der abgeleiteten Untergruppen der Trägheitsgruppe. Auf diese Weise betrachtet man Mikroprimstellen für die entsprechenden Faktorgruppen der absoluten Galoisgruppe, um dann einen projektive Limes zu bilden. Im ersten Schritt ist eine Bijektion zwischen relativen Mikroprimstellen und Konjugationsklassen von Primelementen gezeigt worden. Das Hauptergebnis dieser Arbeit ist eine vollständige Antwort auf die Frage von J. Neukirch im zweiten Schritt. Es wird eine Normabbildung für Lubin-Tate-Potenzreihen verschiedener Höhe angegeben und der projektive Limes bezüglich dieser Normabbildungen gebildet. Dazu werden Ergebnisse der Klassenkörpertheorie auf einen ''''fastabelschen'''' Fall übertragen. Schließlich können die Mikroprimstellen als Galoisorbits von normverträglichen Abfolgen normischer Lubin-Tate-Potenzreihen beschrieben werden. Die Koeffizienten aller dieser Lubin-Tate-Potenzreihen sind in einer endlichen unverzweigten Erweiterung des Grundkörpers. Also kann man zu einer gegebenen normverträglichen Abfolge normischer Lubin-Tate-Potenzreihen den Koeffizientenkörper definieren. Der Grad dieses Körpers bzw. die Länge des Galoisorbits entspricht dem Grad der zugehörigen Mikroprimstelle. / Micro primes were introduced by J. Neukirch in the context of abstract class field theory. A generalization of decomposition groups of primes of global fields led him to a purely group theoretical definition of micro primes as certain equivalence classes of Frobenius elements. Applied to the case of Galois groups of local or global fields this theory yields a description of special conjugacy classes. The main problem already posed by J. Neukirch is to understand the number theoretical meaning of micro primes, that is to describe them in terms of the base field. J. Mehlig and E.-W. Zink established a bijection between micro primes and norm compatible sequences of prime elements in field towers. These towers arise as fixed point fields for the sequence of derived subgroups of the inertia group. So one has to study micro primes for the corresponding factor groups of the absolute Galois group and then to form a projective limit. In the first step, a bijection between relative micro primes and conjugacy classes of prime elements has been obtained. The main result of this project is a complete answer to the problem of J. Neukirch for the second step. One has to introduce norm maps between Lubin-Tate power series of different height and the projective limit has to be taken with respect to these norm maps. For this purpose results from class field theory are transferred to an ''''almost abelian'''' case. In the end micro primes can be described as Galois orbits of norm compatible sequences of normic Lubin-Tate power series. The coefficients of all the Lubin-Tate power series are in finite unramified extensions of the base field. Therefore one can define a field of coefficients for a given norm compatible sequence of normic Lubin-Tate power series. The degree of that field respectively the length of the Galois orbit is at the same time the degree of the corresponding micro prime.

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 curve point multiplication is the most computationally expensive component. Similarly, Tate pairing is also quite computationally expensive. Therefore, it is more attractive to implement the ECC and Tate pairing using hardware than using software. The bases of both ECC and Tate pairing are Galois field arithmetic units. In this thesis, I propose the FPGA implementations of the elliptic curve point multiplication in GF (2283) as well as Tate pairing computation on supersingular elliptic curve in GF (2283). I have designed and synthesized the elliptic curve point multiplication and Tate pairing module using Xilinx's FPGA, as well as synthesized all the Galois arithmetic units used in the designs. Experimental results demonstrate that the FPGA implementation can speedup the elliptic curve point multiplication by 31.6 times compared to software based implementation. The results also demonstrate that the FPGA implementation can speedup the Tate pairing computation by 152 times compared to software based implementation.

Identity based cryptography was first proposed by Shamir in 1984. Rather than deriving a public key from private information, which would be the case in traditional public key encryption schemes, in identity based schemes a user's identity plays the role of the public key. This reduces the amount of computations required for authentication, and simplifies key-management. Efficient and strong implementations of identity based schemes are based around easily computable bilinear mappings of two points on an elliptic curve onto a multiplicative subgroup of a field, also called pairing. The idea of utilizing the identity of the user simplifies the public key infrastructure. However, since pairing computations are expensive for both area and timing, the proposed identity based cryptosystem are hard to implement. In order to be able to efficiently utilize the idea of identity based cryptography, there is a strong need for an efficient pairing implementations. Pairing computations could be realized in multiple fields. Since the main building block and the bottleneck of the algorithm is multiplication, we focused our research on building a fast and small arithmetic core that can work on multiple fields. This would allow a single piece of hardware to realize a wide spectrum of cryptographic algorithms, including pairings, with minimal amount of software coding. We present a novel unified core design which is extended to realize Montgomery multiplication in the fields GF(2^n), GF(3^m), and GF(p). Our unified design supports RSA and elliptic curve schemes, as well as identity based encryption which requires a pairing computation on an elliptic curve. The architecture is pipelined and is highly scalable. The unified core utilizes the redundant signed digit representation to reduce the critical path delay. While the carry-save representation used in classical unified architectures is only good for addition and multiplication operations, the redundant signed digit representation also facilitates efficient computation of comparison and subtraction operations besides addition and multiplication. Thus, there is no need for transformation between the redundant and non-redundant representations of field elements, which would be required in classical unified architectures to realize the subtraction and comparison operations. We also quantify the benefits of unified architectures in terms of area and critical path delay. We provide detailed implementation results. The metric shows that the new unified architecture provides an improvement over a hypothetical non-unified architecture of at least 24.88 % while the improvement over a classical unified architecture is at least 32.07 %. Until recently there has been no work covering the security of pairing based cryptographic hardware in the presence of side-channel attacks, despite their apparent suitability for identity-aware personal security devices, such as smart cards. We present a novel non-linear error coding framework which incorporates strong adversarial fault detection capabilities into identity based encryption schemes built using Tate pairing computations. The presented algorithms provide quantifiable resilience in a well defined strong attacker model. Given the emergence of fault attacks as a serious threat to pairing based cryptography, the proposed technique solves a key problem when incorporated into software and hardware implementations. In this dissertation, we also present an efficient accelerator for computing the Tate Pairing in characteristic 3, based on the Modified Duursma Lee algorithm.