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Fast Fourier Transforms Over Prime Fields Of Large Characteristic And Their Implementation On Graphics Processing Units, Davood Mohajerani

Electronic Thesis and Dissertation Repository

Prime field arithmetic plays a central role in computer algebra and supports computation in Galois fields which are essential to coding theory and cryptography algorithms. The prime fields that are used in computer algebra systems, in particular in the implementation of modular methods, are often of small characteristic, that is, based on prime numbers that fit on a machine word. Increasing precision beyond the machine word size can be done via the Chinese Remaindering Theorem or Hensel Lemma. In this thesis, we consider prime fields of large characteristic, typically fitting on n machine words, where n is a power of …