FFTs over finite fields.

Finite field polynomial arithmetic based on fast Fourier transforms

galois-fft

Fast Fourier Transforms over finite fields. Provides functionality for polynomial evaluation, polynomial interpolation, and computation of Lagrange polynomials.

In a finite field F with 2^m elements. We can define a discrete Fourier transform by selecting 2^m - 1 roots of unity ω ∈ F.

Example

import Protolude

import Data.Curve.Weierstrass.BN254 (Fr)
import Data.Pairing.BN254           (getRootOfUnity)

import FFT

k :: Int
k = 5

polySize :: Int
polySize = 2^k

leftCoeffs, rightCoeffs :: [Fr]
leftCoeffs = map fromIntegral [1..polySize]
rightCoeffs = map fromIntegral (reverse [1..polySize])

main :: IO ()
main = do
  print $ interpolate getRootOfUnity leftCoeffs
  print $ fftMult getRootOfUnity leftCoeffs rightCoeffs
  pure ()

License

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