# 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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