{-# LANGUAGE RecordWildCards, NamedFieldPuns, MultiWayIf, ScopedTypeVariables #-}
module Bulletproofs.InnerProductProof.Verifier (
verifyProof,
) where
import Protolude
import qualified Data.List as L
import qualified Data.Map as Map
import Data.Curve.Weierstrass.SECP256K1 (PA, Fr, mul)
import Bulletproofs.Utils
import Bulletproofs.InnerProductProof.Internal
verifyProof
:: Integer
-> InnerProductBase PA
-> PA
-> InnerProductProof Fr PA
-> Bool
verifyProof n productBase@InnerProductBase{..} commitmentLR productProof@InnerProductProof{ l, r }
= c == cProof
where
(challenges, _invChallenges, c) = mkChallenges productProof commitmentLR
otherExponents = mkOtherExponents n challenges
cProof
= (gsCommit `mul` l)
<>
(hsCommit `mul` r)
<>
(bH `mul` (l * r) )
gsCommit = sumExps otherExponents bGs
hsCommit = sumExps (reverse otherExponents) bHs
mkChallenges
:: InnerProductProof Fr PA
-> PA
-> ([Fr], [Fr], PA)
mkChallenges InnerProductProof{ lCommits, rCommits } commitmentLR
= foldl'
(\(xs, xsInv, accC) (li, ri)
-> let x = shamirX' accC li ri
xInv = recip x
c = (li `mul` (x ^ 2)) <> (ri `mul` (xInv ^ 2)) <> accC
in (x:xs, xInv:xsInv, c)
)
([], [], commitmentLR)
(zip lCommits rCommits)
mkOtherExponents :: Integer -> [Fr] -> [Fr]
mkOtherExponents n challenges
= Map.elems $ foldl'
f
(Map.fromList [(0, recip $ product challenges)])
[0..n'-1]
where
n' = n `div` 2
f acc i = foldl' (f' i) acc [0..logBase2 n-1]
f' :: Integer -> Map.Map Integer Fr -> Integer -> Map.Map Integer Fr
f' i acc' j
= let i1 = (2^j) + i in
if | i1 >= n -> acc'
| Map.member i1 acc' -> acc'
| otherwise -> Map.insert
i1
(acc' Map.! i * ((challenges L.!! fromIntegral j) ^ 2))
acc'