# galois-fft: FFTs over finite fields

[ cryptography, library, mit ] [ Propose Tags ]

Finite field polynomial arithmetic based on fast Fourier transforms

Versions [faq] 0.1.0 ChangeLog.md base (>=4.10 && <5), elliptic-curve (==0.3.*), galois-field (==1.*), poly (>=0.3.2), protolude (==0.2.*), vector (==0.12.*) [details] MIT Adjoint Inc (info@adjoint.io) Cryptography https://github.com/adjoint-io/galois-fft#readme https://github.com/adjoint-io/galois-fft/issues head: git clone https://github.com/adjoint-io/galois-fft by sdiehl at Wed Nov 27 09:42:32 UTC 2019 NixOS:0.1.0 131 total (35 in the last 30 days) (no votes yet) [estimated by Bayesian average] λ λ λ Docs available Last success reported on 2019-11-27

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## Readme for galois-fft-0.1.0

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# 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 ()


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