A Characterization of the Fermat Number Transform on Different Hardware Platforms
Katherine Jean Olsen · Bucknell Digital Commons (Bucknell University) · 2015
This thesis will provide a characterization of the computation of the Fermat number transform (FNT) implemented on three different hardware platforms, a typical desktop computer, a graphics processing unit, and a field programmable gate array. This characterization will investigate the latency, throughput, and resource requirements of an optimized implementation of this transform. The FNT, which is a specific type of numeric theoretic transform that operates within finite fields defined by Fermat primes, is typically used in applications such as fast multiplication and digital filtering. Instead of focusing on a single application of this transform, this study will evaluate optimizations of the FNT on each platform thoroughly with reference to these three metrics, where the architecture of each hardware platform necessitated unique optimization strategies. Developers looking to use the FNT in their applications may use this characterization as an aid in selecting the most appropriate hardware and implementation best suited for their particular application.