Pairing.Fq

Prime field with characteristic _q, over which the elliptic curve is defined and the other finite field extensions. First field in the tower:

• Fq
• Fq2 := Fq[u]/u^2 + 1
• Fq6 := Fq2[v]/v^3 - (9 + u)
• Fq12 := Fq6[w]/w^2 - v

Documentation

newtype Fq

Prime field with characteristic _q

Constructors

Fq Integer

Use new instead of this constructor

Instances

Eq Fq

Defined in Pairing.Fq

Methods

(==) :: Fq -> Fq -> Bool

(/=) :: Fq -> Fq -> Bool

Fractional Fq

Defined in Pairing.Fq

Methods

(/) :: Fq -> Fq -> Fq

recip :: Fq -> Fq

fromRational :: Rational -> Fq

Num Fq

Defined in Pairing.Fq

Methods

(+) :: Fq -> Fq -> Fq

(-) :: Fq -> Fq -> Fq

(*) :: Fq -> Fq -> Fq

negate :: Fq -> Fq

abs :: Fq -> Fq

signum :: Fq -> Fq

fromInteger :: Integer -> Fq

Ord Fq

Defined in Pairing.Fq

Methods

compare :: Fq -> Fq -> Ordering

(<) :: Fq -> Fq -> Bool

(<=) :: Fq -> Fq -> Bool

(>) :: Fq -> Fq -> Bool

(>=) :: Fq -> Fq -> Bool

max :: Fq -> Fq -> Fq

min :: Fq -> Fq -> Fq

Show Fq

Defined in Pairing.Fq

Methods

showsPrec :: Int -> Fq -> ShowS

show :: Fq -> String

showList :: [Fq] -> ShowS

Generic Fq

Defined in Pairing.Fq

Associated Types

type Rep Fq :: Type -> Type

Methods

from :: Fq -> Rep Fq x

to :: Rep Fq x -> Fq

Semigroup G1

Defined in Pairing.Group

Methods

(<>) :: G1 -> G1 -> G1

sconcat :: NonEmpty G1 -> G1

stimes :: Integral b => b -> G1 -> G1

Monoid G1

Defined in Pairing.Group

Methods

mempty :: G1

mappend :: G1 -> G1 -> G1

mconcat :: [G1] -> G1

Bits Fq

Defined in Pairing.Fq

Methods

(.&.) :: Fq -> Fq -> Fq

(.|.) :: Fq -> Fq -> Fq

xor :: Fq -> Fq -> Fq

complement :: Fq -> Fq

shift :: Fq -> Int -> Fq

rotate :: Fq -> Int -> Fq

zeroBits :: Fq

bit :: Int -> Fq

setBit :: Fq -> Int -> Fq

clearBit :: Fq -> Int -> Fq

complementBit :: Fq -> Int -> Fq

testBit :: Fq -> Int -> Bool

bitSizeMaybe :: Fq -> Maybe Int

bitSize :: Fq -> Int

isSigned :: Fq -> Bool

shiftL :: Fq -> Int -> Fq

unsafeShiftL :: Fq -> Int -> Fq

shiftR :: Fq -> Int -> Fq

unsafeShiftR :: Fq -> Int -> Fq

rotateL :: Fq -> Int -> Fq

rotateR :: Fq -> Int -> Fq

popCount :: Fq -> Int

NFData Fq

Defined in Pairing.Fq

Methods

rnf :: Fq -> ()

ByteRepr Fq

Defined in Pairing.Fq

Methods

mkRepr :: Fq -> Maybe ByteString

fromRepr :: Fq -> ByteString -> Maybe Fq

reprLength :: Fq -> Int

Validate G1

Defined in Pairing.Group

Methods

isValidElement :: G1 -> Bool

FromX Fq

Defined in Pairing.Fq

Methods

yFromX :: Fq -> LargestY -> Maybe Fq

isLargestY :: Fq -> Bool

CyclicGroup G1

Defined in Pairing.Group

Methods

generator :: G1

order :: Proxy G1 -> Integer

expn :: AsInteger e => G1 -> e -> G1

inverse :: G1 -> G1

random :: MonadRandom m => G1 -> m G1

AsInteger Fq

Defined in Pairing.Fq

Methods

asInteger :: Fq -> Integer

ToUncompressedForm G1

Defined in Pairing.Group

Methods

serializeUncompressed :: G1 -> Maybe ByteString

ToCompressedForm G1

Defined in Pairing.Group

Methods

serializeCompressed :: G1 -> Maybe ByteString

Arbitrary (Point Fq)

Defined in Pairing.Group

Methods

arbitrary :: Gen (Point Fq)

shrink :: Point Fq -> [Point Fq]

type Rep Fq

Defined in Pairing.Fq

type Rep Fq = D1 (MetaData "Fq" "Pairing.Fq" "pairing-0.3.1-JhhvluXyNup3CB27ybng3m" True) (C1 (MetaCons "Fq" PrefixI False) (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 Integer)))

new :: Integer -> Fq

Turn an integer into an Fq number, should be used instead of the Fq constructor.

fqInv :: Fq -> Fq

Multiplicative inverse

fqZero :: Fq

Additive identity

fqOne :: Fq

Multiplicative identity

fqNqr :: Fq

Quadratic non-residue

fqPow :: Integral e => Fq -> e -> Fq

fqSqrt :: Bool -> Fq -> Maybe Fq

random :: MonadRandom m => m Fq

fqYforX :: Fq -> Bool -> Maybe Fq

fromBytesToInteger :: ByteString -> Integer