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Finite field polynomial arithmetic based on fast Fourier transforms

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sdiehl/galois-fft

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galois-fft

The library provides Fast Fourier Transforms over finite fields with functionality for polynomial evaluation, polynomial interpolation, and computation of Lagrange polynomials.

In a finite field with elements. We can define a discrete Fourier transform by selecting roots of unity .

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

Copyright (c) 2018-2020 Adjoint Inc.

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