• Corpus ID: 236088088

Elliptic Curve Fast Fourier Transform (ECFFT) Part I: Fast Polynomial Algorithms over all Finite Fields

@article{BenSasson2021EllipticCF,
  title={Elliptic Curve Fast Fourier Transform (ECFFT) Part I: Fast Polynomial Algorithms over all Finite Fields},
  author={Eli Ben-Sasson and Dan Carmon and Swastik Kopparty and David Levit},
  journal={Electron. Colloquium Comput. Complex.},
  year={2021},
  volume={28},
  pages={103}
}
Over finite fields F q containing a root of unity of smooth order n (smoothness means n is the product of small primes), the Fast Fourier Transform (FFT) leads to the fastest known algebraic algorithms for many basic polynomial operations, such as multiplication, division, interpolation and multi-point evaluation. These operations can be computed by constant fan-in arithmetic circuits over F q of quasi-linear size; specifically, O ( n log n ) for multiplication and division, and O ( n log 2 n… 
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