Arithmetic in finite fields based on the Chudnovsky-Chudnovsky multiplication algorithm
Kévin Atighehchi, Stéphane Ballet, Alexis Bonnecaze, Robert Rolland · Mathematics of Computation · 2017
Thanks to a new construction of the so-called Chudnovsky- Chudnovsky multiplication algorithm, we design efficient algorithms for both the exponentiation and the multiplication in finite fields. They are tailored to hardware implementation and they allow computations to be parallelized while maintaining a low number of bilinear multiplications. We give an example with the finite field F 16 13 \mathbb {F}_{16^{13}} .