Big Prime Field FFT on the GPU

Liangyu Chen (1) , Svyatoslav Covanov (2) , Davood Mohajerani (3) , Marc Moreno Maza (3)

1 ECNU - East China Normal University [Shangaï]
2 CARAMBA - Cryptology, arithmetic : algebraic methods for better algorithms
3 ORCCA - Ontario Research Center for Computer Algebra

We consider prime fields of large characteristic, typically fitting on k machine words, where k is a power of 2. When the characteristic of these fields is restricted to a subclass of the generalized Fermat numbers, we show that arithmetic operations in such fields offer attractive performance both in terms of algebraic complexity and parallelism. In particular , these operations can be vectorized, leading to efficient implementation of fast Fourier transforms on graphics processing units.

Mots clés: Graphics processing units; Analysis of algorithms; Experimentation; Algorithms; Finite fields; CUDA; Algebraic algorithms; Fast Fourier transforms; Generalized Fermat numbers

Domaines: Calcul formel [cs.SC]; Calcul parallèle, distribué et partagé [cs.DC]

Liangyu Chen, Svyatoslav Covanov, Davood Mohajerani, Marc Moreno Maza. Big Prime Field FFT on the GPU. ISSAC 2017, Jul 2017, Kaiserslautern, Germany. pp.85-92, ⟨10.1145/3087604.3087657⟩. ⟨hal-01518830⟩