Thesis (Ph. D.)--Oregon State University, 2004. / Typescript (photocopy). Includes bibliographical references (leaves 190-197). Also available on the World Wide Web.

Thesis (Ph. D.)--Ohio University, November, 2003. / Includes bibliographical references (leaves 197-210).

The purpose of the present study was to use an alternate psychoeducational assessment method to examine learning potential of Indian students in an academic domain, specifically Algebra. The study examined six Indian adolescents early in their Year Seven Mathematics. For the purpose of this study, the students were classified as achievers or non-achievers based on Canadian Test of Basic Skills (CTBS) grade equivalent scores, and Grade 7 Mathematics marks on the First Report Card.<p> A cross-case analysis of verbal and nonverbal protocol data gathered from the six Indian achieving and non-achieving Grade Seven students, and reduced through use of a technique developed by Giorgi, yielded information regarding the subjects' internalization processes of algebraic concepts. Vygotsky's zone of proximal development methodology, which was employed in the study, permitted the researcher to investigate processes used by the students during learning, maintenance, and near and far transfer tasks. While verbal and nonverbal communication styles appeared to distinguish achieving from non-achieving students, those same traits did not seem to affect efficiency in problem solving as observed during the present study. Other characteristics such as language usage, questioning techniques, and risk taking were the traits which most clearly affected the students' problem solving skills.<p> During the present study, formal metacognitive data proved hard to collect. This may be attributed to the reluctance of some students to participate in the questioning, and to the difficulty other students experienced In understanding the questions. All students had difficulty at some stage of the study in generating a rule to explain how they had solved the problems.<p> The results of the present study indicated that there were qualitative differences in problem solving between subjects. Those qualitative differences did not follow a pattern of achievement versus non-achievement as delineated by CTBS scores and classroom evaluation in Mathematics. Zone proximal development methodology provided a process assessment which uncovered learning potential profiles that were masked by static standardized tests.

The purpose of the present study was to use an alternate psychoeducational assessment method to examine learning potential of Indian students in an academic domain, specifically Algebra. The study examined six Indian adolescents early in their Year Seven Mathematics. For the purpose of this study, the students were classified as achievers or non-achievers based on Canadian Test of Basic Skills (CTBS) grade equivalent scores, and Grade 7 Mathematics marks on the First Report Card.<p> A cross-case analysis of verbal and nonverbal protocol data gathered from the six Indian achieving and non-achieving Grade Seven students, and reduced through use of a technique developed by Giorgi, yielded information regarding the subjects' internalization processes of algebraic concepts. Vygotsky's zone of proximal development methodology, which was employed in the study, permitted the researcher to investigate processes used by the students during learning, maintenance, and near and far transfer tasks. While verbal and nonverbal communication styles appeared to distinguish achieving from non-achieving students, those same traits did not seem to affect efficiency in problem solving as observed during the present study. Other characteristics such as language usage, questioning techniques, and risk taking were the traits which most clearly affected the students' problem solving skills.<p> During the present study, formal metacognitive data proved hard to collect. This may be attributed to the reluctance of some students to participate in the questioning, and to the difficulty other students experienced In understanding the questions. All students had difficulty at some stage of the study in generating a rule to explain how they had solved the problems.<p> The results of the present study indicated that there were qualitative differences in problem solving between subjects. Those qualitative differences did not follow a pattern of achievement versus non-achievement as delineated by CTBS scores and classroom evaluation in Mathematics. Zone proximal development methodology provided a process assessment which uncovered learning potential profiles that were masked by static standardized tests.

L'objet de cette thèse est l'étude de diverses primitives cryptographiques utiles dans des protocoles Diffie-Hellman. Nous étudions tout d'abord les protocoles Diffie-Helmman sur des structures commutatives ou non. Nous en proposons une formulation unifiée et mettons en évidence les différents problèmes difficiles associés dans les deux contextes. La première partie est consacrée à l'étude de pseudo-paramétrisations de courbes algébriques en temps constant déterministe, avec application aux fonctions de hachage vers les courbes. Les propriétés des courbes algébriques en font une structure de choix pour l'instanciation de protocoles reposant sur le problème Diffie-Hellman. En particulier, ces protocoles utilisent des fonctions qui hachent directement un message vers la courbe. Nous proposons de nouvelles fonctions d'encodage vers les courbes elliptiques et pour de larges classes de fonctions hyperelliptiques. Nous montrons ensuite comment l'étude de la géométrie des tangentes aux points d'inflexion des courbes elliptiques permet d'unifier les fonctions proposées tant dans la littérature que dans cette thèse. Dans la troisième partie, nous nous intéressons à une nouvelle instanciation de l'échange Diffie-Hellman. Elle repose sur la difficulté de résoudre un problème de factorisation dans un anneau de polynômes non-commutatifs. Nous montrons comment un problème de décomposition Diffie-Hellman sur un groupe non-commutatif peut se ramener à un simple problème d'algèbre linéaire pourvu que les éléments du groupe admettent une représentation par des matrices. Bien qu'elle ne soit pas applicable directement au cas des polynômes tordus puisqu'ils n'ont pas d'inverse, nous profitons de l'existence d'une notion de divisibilité pour contourner cette difficulté. Finalement, nous montrons qu'il est possible de résoudre le problème Diffie-Hellman sur les polynômes tordus avec complexité polynomiale. / In this thesis, we study several cryptographic primitives of use in Diffie-Hellman like protocols. We first study Diffie-Hellman protocols on commutative or noncommutative structures. We propose an unified wording of such protocols and bring out on which supposedly hard problem both constructions rely on. The first part is devoted to the study of pseudo-parameterization of algebraic curves in deterministic constant time, with application to hash function into curves. Algebraic curves are indeed particularly interesting for Diffie-Hellman like protocols. These protocols often use hash functions which directly hash into the curve. We propose new encoding functions toward elliptic curves and toward large classes of hyperelliptic curves. We then show how the study of the geometry of flex tangent of elliptic curves unifies the encoding functions as proposed in the litterature and in this thesis. In the third part, we are interested in a new instantiation of the Diffie-Hellman key exchange. It relies on the difficulty of factoring in a non-commutative polynomial ring. We show how to reduce a Diffie-Hellman decomposition problem over a noncommutative group to a simple linear algebra problem, provided that group elements can be represented by matrices. Although this is not directly relevant to the skew polynomial ring because they have no inverse, we use the divisibility to circumvent this difficulty. Finally, we show it's possible to solve the Diffie-Hellman problem on skew polynomials with polynomial complexity.