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Thesis (M.S.) -- Central Connecticut State University, 2008. / Thesis advisor: Louise Gould. "... in partial fulfillment of the requirements for the degree of Master of Science in Mathematics." Includes bibliographical references (leaves 30-31). Also available via the World Wide Web.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1965. / Typescript. Abstracted in Dissertation abstracts, v, 27, no. 3A (1966) p. 602-03. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliography.

Thesis (M.S.)--Central Connecticut State University, 2000. / Thesis advisor: Philip Halloran. " ... in partial fulfillment of the requirements for the degree of Master of Science [in Mathematical Sciences]." Includes bibliographical references (leaves 28-32).

Thesis (Ph. D.)--University of Wisconsin--Madison, 1975. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 170-171).

The study was designed to determine the effect delay of knowledge of results has on the acquisition and retention of novel multiplication facts presented in a classroom situation. Nine third grade classed, divided into three groups, were presented the task of learning fourteen novel facts. For group 1, a novel problem was read followed by a three second response interval during which the students recorded their answers. Knowledge of results, a reading of the problem and correct answer, was presented immediately after the response interval. For group 2, knowledge of results was provided after completion of all the problems and corresponding response intervals. For group 3, no knowledge of results was presented. The treatments were administered on each of five consecutive days. A criterion test, consisting of a tape-recording of a reading of all the multiplication problems, was administered before the treatments, immediately after completion of the treatments, and six days after completion of the treatments. The difference between the number of novel problems answered correctly on the first and second administrations of the criterion test was defined as the measure of acquisition. Retention was defined as the corresponding difference between the first and third administrations of the criterion test. The one-tailed test for correlated samples was used to test the significance of the acquisition and the retention within each group. Analysis of covariance and Scheffe's test for multiple comparisons were used to test the significance of the differences in acquisition and in retention between the groups. An ancillary problem investigated concerned the relationship between delay of knowledge of results during the acquisition of the novel multiplication facts and the possible effects on performance on the non-novel facts. The differences between the number of non-novel problems answered correctly on the first and second administrations of the criterion test and between the number of non-novel problems answered correctly on the first and third administrations of the criterion test were analyzed using the same statistical tests as for acquisition and retention. The acquisition and retention of the novel multiplication facts were statistically, but not educationally, significant. The educational insignificance of these findings was attributed to the short period over which the experiment was conducted. In comparing groups the acquisition and retention of the novel facts were significantly greater for the two groups provided with knowledge of results than for the group provided with no knowledge of results. No significant difference existed between the group provided with immediate knowledge of results and the group provided with delayed knowledge of results. This apparent lack in difference was likely due to the small gains made by both groups. The number of non-novel problems answered correctly was significantly greater on the second and third administrations of the criterion test than on the first for the group provided with immediate knowledge of results during the acquisition of the novel facts. The number of non-novel problems answered correctly was significantly greater on the third administration of the criterion test than on the first for the group provided with delayed knowledge of results. All other differences were found to be insignificant. / Education, Faculty of / Graduate

La première partie de cette thèse est dévolue à l’étude d’une conjecture combinatoire dont la validité assure l’existence de familles infinies de fonctions booléennes dotées de propriétés cryptographiques intéressantes. Quoique particulièrement innocente au premier abord, la validité de cette conjecture reste un problème ouvert. Néanmoins, l’auteur espère que les résultats théoriques et expérimentaux présentés ici permettront au lecteur d’acquérir un tant soit peu de familiarité avec la conjecture. Dans la seconde partie de ce manuscrit, des liens entre fonctions (hyper-)courbes — une classe particulière de fonctions booléennes —, sommes exponentielles et courbes (hyper)elliptiques sont présentés. Les fonctions (hyper-)courbes sont en effet particulièrement difficiles à classifier et à construire. L’étude des liens mentionnés ci-dessus permet de résoudre de façon élégante des problèmes d’ordre tout aussi bien théorique que pratique. La troisième et dernière partie pousse plus avant l’étude des courbes (hyper)elliptiques d’un point de vue sensiblement différent. De nombreuses constructions cryptographiques reposent en effet sur l’utilisation de classes particulières de telles courbes qui ne peuvent être construites en utilisant des méthodes classiques. Cependant, la méthode CM permet de donner une réponse positive à ce problème. Les polynômes de classes sont des objets fondamentaux de cette méthode. Habituellement, leur construction n’est envisagée que pour des ordres maximaux. La modeste contribution de l’auteur est d’expliciter comment une telle construction — la méthode analytique complexe — s’étend aux ordres non-maximaux. / The first part is devoted to the study of a combinatorial conjecture whose validity entails the existence of infinite classes of Boolean functions with good cryptographic properties. Although the conjecture seems quite innocuous, its validity remains an open question. Nonetheless, the author sincerely hopes that the theoretical and experimental results presented here will give the reader a good insight into the conjecture. In the second part, some connections between (hyper-)bent functions — a subclass of Boolean functions —, exponential sums and point counting on (hyper)elliptic curves are presented. Bent functions and hyper-bent functions are known to be difficult to classify and to build explicitly. However, exploring the links between these different worlds makes possible to give beautiful answers to theoretical questions and to design efficient algorithms addressing practical problems. The third and last part investigates the theory of (hyper)elliptic curves in a different direction. Several constructions in cryptography indeed rely on the use of highly specific classes of such curves which can not be constructed by classical means. Nevertheless, the so-called “complex multiplication” method solves some of these problems. Class polynomials are fundamental objects for that method, but their construction is usually considered only for maximal orders. The modest contribution of the author is to clarify how a specific flavor of their construction — the complex analytic method — extends to non-maximal orders.

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This thesis addresses concepts of implementing a RSA cryptosystem on a passive RFID tag. With a limited number of public key cryptosystems on passive RFID platforms, the proposed algorithm makes use of Montgomery multiplication primitives to reduce the amount of computation required on the power constrained tag therefore making the proposition viable. Public key cryptography is being suggested for next generation RFID systems to reduce the number of possible attack vectors native to this type of technology. By estimating the area, power and time constraints of the RFID platform, it was determined that the area constraint was the critical variable in determining the maximum implementable security variable. Although the application of this algorithm has been targeted for passive HF RFID platforms, the algorithm could be used in other low power, sized constrained applications.

This thesis addresses concepts of implementing a RSA cryptosystem on a passive RFID tag. With a limited number of public key cryptosystems on passive RFID platforms, the proposed algorithm makes use of Montgomery multiplication primitives to reduce the amount of computation required on the power constrained tag therefore making the proposition viable. Public key cryptography is being suggested for next generation RFID systems to reduce the number of possible attack vectors native to this type of technology. By estimating the area, power and time constraints of the RFID platform, it was determined that the area constraint was the critical variable in determining the maximum implementable security variable. Although the application of this algorithm has been targeted for passive HF RFID platforms, the algorithm could be used in other low power, sized constrained applications.