logos-storage/plonky2-verifier
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use the same multiplicative generators as Plonky2

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Balazs Komuves 2024-12-12 12:33:24 +01:00
parent 7ed7cfe2d7
commit e593049dce
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1 changed files with 17 additions and 40 deletions
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57
Goldilocks.hs
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@ -34,51 +34,28 @@ toF = mkGoldilocks . fromIntegral
rndF :: IO F
rndF = Goldilocks <$> randomRIO ( 0 , 0xffff_ffff_0000_0000 )
-- | The generator of the multiplicative subgroup of F used by Plonky2
multGen :: F
multGen = 0xc65c18b67785d900
-- | The generator of the largest 2-adic subgroup of F used by Plonky2
twoAdicGen :: F
twoAdicGen = 0x64fdd1a46201e246
-- | Sage code:
--
-- > p = 2^64-2^32+1
-- > F = GF(p)
-- > g = F(7)
-- > g = F(0xc65c18b67785d900)
-- > print( g.multiplicative_order() == p-1 )
-- > a = g ^ ( (p-1) / 2^32 )
-- > [ a^(2^(32-k)) for k in range(33) ]
-- > h = g ^ ( (p-1) / 2^32 )
-- > print( h == F(0x64fdd1a46201e246) )
-- > [ h^(2^(32-k)) for k in range(33) ]
--
rootsOfUnity :: Array Int Goldilocks
rootsOfUnity = listArray (0,32) $ map toF
[ 1
, 18446744069414584320
, 281474976710656
, 18446744069397807105
, 17293822564807737345
, 70368744161280
, 549755813888
, 17870292113338400769
, 13797081185216407910
, 1803076106186727246
, 11353340290879379826
, 455906449640507599
, 17492915097719143606
, 1532612707718625687
, 16207902636198568418
, 17776499369601055404
, 6115771955107415310
, 12380578893860276750
, 9306717745644682924
, 18146160046829613826
, 3511170319078647661
, 17654865857378133588
, 5416168637041100469
, 16905767614792059275
, 9713644485405565297
, 5456943929260765144
, 17096174751763063430
, 1213594585890690845
, 6414415596519834757
, 16116352524544190054
, 9123114210336311365
, 4614640910117430873
, 1753635133440165772
]
rootsOfUnity = listArray (0,32) $ reverse $ go twoAdicGen where
go 1 = [1]
go x = x : go (x*x)
--------------------------------------------------------------------------------
@ -90,8 +67,8 @@ asInteger :: Goldilocks -> Integer
asInteger (Goldilocks x) = x
instance Show Goldilocks where
-- show (Goldilocks x) = printf "0x%016x" x
show (Goldilocks x) = show x
show (Goldilocks x) = printf "0x%016x" x
-- show (Goldilocks x) = show x
--------------------------------------------------------------------------------