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1	Sobre a existência ou não de bases normais auto-duais para extensões galoisianas de corpos / About the existence or not of self-dual normal bases for finite galosian extensions of fields Coutinho, Sávio da Silva 20 March 2009 (has links) Neste trabalho, apresentamos um estudo sobre a existência ou não de bases normais auto-duais para extensões galoisianas finitas de corpos, mostrando que toda extensão galoisiana finita de grau ímpar posui uma base normal auto-dual, enquanto que para extensões galoisianas de grau par, apresentamos algumas condições suficientes que garantem a não existência de bases normais auto-duais / In this work, we present a study about the existence or not of self-dual normal bases for finite galoisian extensions of fields, showing that all the odd degree finite galoisian extension has a self-dual normal base, whereas for even degree galoisian extensions, we present some sufficient conditions that assure the non-existence of self-dual normal bases Bases normais auto-duais Extensions of fields Extensões de corpos Galois theory Self-dual normal bases Teoria de Galois
2	Computational Complexity of Finite Field Multiplication / Beräkningskomplexitet för multiplikation i ändliga kroppar Quttineh, Nils-Hassan January 2003 (has links) <p>The subject for this thesis is to find a basis which minimizes the number of bit operations involved in a finite field multiplication. The number of bases of a finite field increases quickly with the extension degree, and it is therefore important to find efficient search algorithms. Only fields of characteristic two are considered. </p><p>A complexity measure is introduced, in order to compare bases. Different methods and algorithms are tried out, limiting the search in order to explore larger fields. The concept of equivalent bases is introduced. </p><p>A comparison is also made between the Polynomial, Normal and Triangular Bases, referred to as known bases, as they are commonly used in implementations. Tables of the best found known bases for all fields up to GF(2^24) is presented. </p><p>A list of the best found bases for all fields up to GF(2^25) is also given.</p> Datorteknik Finite Field Multiplication Complexity Polynomial Bases Normal Bases Triangular Bases Multiples. Datorteknik Computer engineering Datorteknik
3	Sobre a existência ou não de bases normais auto-duais para extensões galoisianas de corpos / About the existence or not of self-dual normal bases for finite galosian extensions of fields Sávio da Silva Coutinho 20 March 2009 (has links) Neste trabalho, apresentamos um estudo sobre a existência ou não de bases normais auto-duais para extensões galoisianas finitas de corpos, mostrando que toda extensão galoisiana finita de grau ímpar posui uma base normal auto-dual, enquanto que para extensões galoisianas de grau par, apresentamos algumas condições suficientes que garantem a não existência de bases normais auto-duais / In this work, we present a study about the existence or not of self-dual normal bases for finite galoisian extensions of fields, showing that all the odd degree finite galoisian extension has a self-dual normal base, whereas for even degree galoisian extensions, we present some sufficient conditions that assure the non-existence of self-dual normal bases Bases normais auto-duais Extensões de corpos Teoria de Galois Extensions of fields Galois theory Self-dual normal bases
4	Computational Complexity of Finite Field Multiplication / Beräkningskomplexitet för multiplikation i ändliga kroppar Quttineh, Nils-Hassan January 2003 (has links) The subject for this thesis is to find a basis which minimizes the number of bit operations involved in a finite field multiplication. The number of bases of a finite field increases quickly with the extension degree, and it is therefore important to find efficient search algorithms. Only fields of characteristic two are considered. A complexity measure is introduced, in order to compare bases. Different methods and algorithms are tried out, limiting the search in order to explore larger fields. The concept of equivalent bases is introduced. A comparison is also made between the Polynomial, Normal and Triangular Bases, referred to as known bases, as they are commonly used in implementations. Tables of the best found known bases for all fields up to GF(2^24) is presented. A list of the best found bases for all fields up to GF(2^25) is also given. Datorteknik Finite Field Multiplication Complexity Polynomial Bases Normal Bases Triangular Bases Multiples. Datorteknik Computer Engineering Datorteknik
5	Sobre bases normais para extensões galoisianas de corpos / On normal bases for galoisian extensions of fields Mello, Thiago Castilho de 28 February 2008 (has links) Neste trabalho apresentamos várias demonstrações do Teorema da Base Normal para certos tipos de extensões galoisianas de corpos, algumas existenciais e outras construtivas, destacando as diferenças e dificuldades de cada situação. Apresentamos também generalizações de tal teorema e mostramos que toda extensão galoisiana de grau ímpar de corpos admite uma base normal autodual com respeito µa forma bilinear traço / In this work we present several demonstrations of The Normal Basis Theorem for certain kinds of galoisian extensions of fields, some of them existential and others constructive, pointing the diffculties and differences in each situation. We also present generalizations of such theorem and show that every odd degree galoisian extension of fields admits a self-dual normal base with respect to the trace bilinear map Abelian extension Base normal generalizada Bases normal Construção de bases normais Construction of normal bases Cyclic extension Elemento normal Elemento primitivo Extensões abelianas Extensões cíclicas Forma hermitiana Forma traço Galois theory Generalized normal base Hermitian form Normal base Normal element Primitive element Teoria de Galois Trace map
6	Sobre bases normais para extensões galoisianas de corpos / On normal bases for galoisian extensions of fields Thiago Castilho de Mello 28 February 2008 (has links) Neste trabalho apresentamos várias demonstrações do Teorema da Base Normal para certos tipos de extensões galoisianas de corpos, algumas existenciais e outras construtivas, destacando as diferenças e dificuldades de cada situação. Apresentamos também generalizações de tal teorema e mostramos que toda extensão galoisiana de grau ímpar de corpos admite uma base normal autodual com respeito µa forma bilinear traço / In this work we present several demonstrations of The Normal Basis Theorem for certain kinds of galoisian extensions of fields, some of them existential and others constructive, pointing the diffculties and differences in each situation. We also present generalizations of such theorem and show that every odd degree galoisian extension of fields admits a self-dual normal base with respect to the trace bilinear map Base normal generalizada Bases normal Construção de bases normais Elemento normal Elemento primitivo Extensões abelianas Extensões cíclicas Forma hermitiana Forma traço Teoria de Galois Abelian extension Construction of normal bases Cyclic extension Galois theory Generalized normal base Hermitian form Normal base Normal element Primitive element Trace map

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