Optimizing scalar multiplication for koblitz curves using hybrid FPGAs

Elliptic curve cryptography (ECC) is a type of public-key cryptosystem which uses the additive group of points on a nonsingular elliptic curve as a cryptographic medium. Koblitz curves are special elliptic curves that have unique properties which allow scalar multiplication, the bottleneck operation in most ECC cryptosystems, to be performed very efficiently. Optimizing the scalar multiplication operation on Koblitz curves is an active area of research with many proposed algorithms for FPGA and software implementations. As of yet little to no research has been reported on using the capabilities of hybrid FPGAs, such as the Xilinx Virtex-4 FX series, which would allow for the design of a more flexible single-chip system that performs scalar multiplication and is not constrained by high communication costs between hardware and software. While the results obtained in this thesis were competitive with many other FPGA implementations, the most recent research efforts have produced significantly faster FPGA based systems. These systems were created by utilizing new and interesting approaches to improve the runtime of performing scalar multiplication on Koblitz curves and thus significantly outperformed the results obtained in this thesis. However, this thesis also functioned as a comparative study of the usage of different basis representations and proved that strict polynomial basis approaches can compete with strict normal basis implementations when performing scalar multiplication on Koblitz curves

Unravelling Phanerozoic evolution of radial to rosette trace fossils

Feeding trace fossils, produced by either deposit or detritus feeders and showing radial to rosetted morphology, are all included in the same architectural category. These radial to rosette ichnofossils are widely recorded worldwide throughout the Phanerozoic and have attracted the attention of numerous ichnologists for decades. Construction of a database summarizing occurrences of radial to rosette trace fossils through the Phanerozoic shows that representatives of this category occurred for the first time during the Fortunian, which accounts for the appearance of at least 12% of the total number of ichnogenera in this category. Overall, 32% of all known rosette ichnogenera resulted from the Cambrian Explosion. A second ichnodiversity increase took place (20%) during the Ordovician. Subsequent to the Great Ordovician Biodiversification Event, this architectural category shows minor fluctuations in ichnodiversity resulting in a long-term plateau. The apparent decline in ichnodiversity by the end of the Cenozoic could reflect a taphonomic artefact resulting from the difficulties of identifying cumulative trace fossils in highly bioturbated modern sediments. Our data set indicates that several radial to rosette ichnogenera (e.g. Arenituba, Dactylophycus, Gyrophyllites, Phoebichnus, Volkichnium) occurred first in shallow-marine settings and then migrated to either deeper-water or marginal-marine environments, while others (e.g. Asterichnus, Cladichnus, Dactyloidites) apparently first occurred in deep-sea environments and then migrated to shallower waters.Fil: Muñoz, Diego Fernando. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigaciones en Ciencias de la Tierra. Universidad Nacional de Córdoba. Facultad de Ciencias Exactas Físicas y Naturales. Centro de Investigaciones en Ciencias de la Tierra; ArgentinaFil: Mangano, Maria Gabriela. University of Saskatchewan; Canadá. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Buatois, Luis Alberto. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. University of Saskatchewan; Canad