Safe Haskell	Safe-Inferred
Language	Haskell2010

Factor.Ec

Description

Documentation

data Curve Source #

Constructors

Curve
Fields kCurve :: Prime aCurve :: Gfp bCurve :: Gfp

Instances

Instances details

Eq Curve Source #
Instance details Defined in Factor.Ec Methods (==) :: Curve -> Curve -> Bool # (/=) :: Curve -> Curve -> Bool #
Ord Curve Source #
Instance details Defined in Factor.Ec Methods compare :: Curve -> Curve -> Ordering # (<) :: Curve -> Curve -> Bool # (<=) :: Curve -> Curve -> Bool # (>) :: Curve -> Curve -> Bool # (>=) :: Curve -> Curve -> Bool # max :: Curve -> Curve -> Curve # min :: Curve -> Curve -> Curve #
Show Curve Source #
Instance details Defined in Factor.Ec Methods showsPrec :: Int -> Curve -> ShowS # show :: Curve -> String # showList :: [Curve] -> ShowS #

data Point Source #

Constructors

Point
Fields xPoint :: Gfp yPoint :: Gfp
Infinity

Instances

Instances details

Eq Point Source #
Instance details Defined in Factor.Ec Methods (==) :: Point -> Point -> Bool # (/=) :: Point -> Point -> Bool #
Ord Point Source #
Instance details Defined in Factor.Ec Methods compare :: Point -> Point -> Ordering # (<) :: Point -> Point -> Bool # (<=) :: Point -> Point -> Bool # (>) :: Point -> Point -> Bool # (>=) :: Point -> Point -> Bool # max :: Point -> Point -> Point # min :: Point -> Point -> Point #
Show Point Source #
Instance details Defined in Factor.Ec Methods showsPrec :: Int -> Point -> ShowS # show :: Point -> String # showList :: [Point] -> ShowS #

rhs :: Curve -> Gfpx Source #

rhsEvaluate :: Curve -> Gfp -> Gfp Source #

onCurve :: Curve -> Point -> Bool Source #

xPoints :: Curve -> Gfp -> [Point] Source #

points :: Curve -> [Point] Source #

discriminant :: Curve -> Gfp Source #

singular :: Curve -> Bool Source #

uniformCurve :: RandomGen r => Prime -> r -> ((Curve, Point), r) Source #

uniformPoint :: RandomGen r => Curve -> r -> (Point, r) Source #

negate :: Curve -> Point -> Point Source #

addLambdaF :: Curve -> Gfp -> Gfp -> Gfp -> Gfp -> Gfp -> Factor Integer Point Source #

doubleF :: Curve -> Point -> Factor Integer Point Source #

double :: Curve -> Point -> Point Source #

addF :: Curve -> Point -> Point -> Factor Integer Point Source #

add :: Curve -> Point -> Point -> Point Source #

addMultiplyF :: Curve -> Point -> Point -> Integer -> Factor Integer Point Source #

addMultiply :: Curve -> Point -> Point -> Integer -> Point Source #

multiplyF :: Curve -> Point -> Integer -> Factor Integer Point Source #

multiply :: Curve -> Point -> Integer -> Point Source #

data TargetConfig Source #

Constructors

CurvePointTargetConfig Int
PrimeTargetConfig Int

Instances

Instances details

Eq TargetConfig Source #
Instance details Defined in Factor.Ec Methods (==) :: TargetConfig -> TargetConfig -> Bool # (/=) :: TargetConfig -> TargetConfig -> Bool #
Ord TargetConfig Source #
Instance details Defined in Factor.Ec Methods compare :: TargetConfig -> TargetConfig -> Ordering # (<) :: TargetConfig -> TargetConfig -> Bool # (<=) :: TargetConfig -> TargetConfig -> Bool # (>) :: TargetConfig -> TargetConfig -> Bool # (>=) :: TargetConfig -> TargetConfig -> Bool # max :: TargetConfig -> TargetConfig -> TargetConfig # min :: TargetConfig -> TargetConfig -> TargetConfig #
Show TargetConfig Source #
Instance details Defined in Factor.Ec Methods showsPrec :: Int -> TargetConfig -> ShowS # show :: TargetConfig -> String # showList :: [TargetConfig] -> ShowS #

data Config Source #

Constructors

Config
Fields targetConfig :: [TargetConfig]

Instances

Instances details

Eq Config Source #
Instance details Defined in Factor.Ec Methods (==) :: Config -> Config -> Bool # (/=) :: Config -> Config -> Bool #
Ord Config Source #
Instance details Defined in Factor.Ec Methods compare :: Config -> Config -> Ordering # (<) :: Config -> Config -> Bool # (<=) :: Config -> Config -> Bool # (>) :: Config -> Config -> Bool # (>=) :: Config -> Config -> Bool # max :: Config -> Config -> Config # min :: Config -> Config -> Config #
Show Config Source #
Instance details Defined in Factor.Ec Methods showsPrec :: Int -> Config -> ShowS # show :: Config -> String # showList :: [Config] -> ShowS #

defaultConfig :: Config Source #

limitPrimesConfig :: Maybe Int -> Config -> Config Source #

factorPrime :: [(Curve, Point)] -> Prime -> Factor Integer [(Curve, Point)] Source #

factorPrimes :: [(Curve, Point)] -> [Prime] -> Factor Integer [(Curve, Point)] Source #

factorTargets :: RandomGen r => Integer -> ([(Curve, Point)], Int) -> [TargetConfig] -> r -> Verbose (Maybe Integer, r) Source #

factor :: RandomGen r => Config -> Integer -> r -> Verbose (Maybe Integer, r) Source #

data DivisionPolynomial Source #

Constructors

DivisionPolynomial
Fields psiDivisionPolynomial :: Gfpx phiDivisionPolynomial :: Gfpx omegaDivisionPolynomial :: Gfpx

Instances

Instances details

Eq DivisionPolynomial Source #
Instance details Defined in Factor.Ec Methods (==) :: DivisionPolynomial -> DivisionPolynomial -> Bool # (/=) :: DivisionPolynomial -> DivisionPolynomial -> Bool #
Ord DivisionPolynomial Source #
Instance details Defined in Factor.Ec Methods compare :: DivisionPolynomial -> DivisionPolynomial -> Ordering # (<) :: DivisionPolynomial -> DivisionPolynomial -> Bool # (<=) :: DivisionPolynomial -> DivisionPolynomial -> Bool # (>) :: DivisionPolynomial -> DivisionPolynomial -> Bool # (>=) :: DivisionPolynomial -> DivisionPolynomial -> Bool # max :: DivisionPolynomial -> DivisionPolynomial -> DivisionPolynomial # min :: DivisionPolynomial -> DivisionPolynomial -> DivisionPolynomial #
Show DivisionPolynomial Source #
Instance details Defined in Factor.Ec Methods showsPrec :: Int -> DivisionPolynomial -> ShowS # show :: DivisionPolynomial -> String # showList :: [DivisionPolynomial] -> ShowS #

psiDivisionPolynomials :: Curve -> [Gfpx] Source #

divisionPolynomials :: Curve -> [DivisionPolynomial] Source #

data End Source #

Constructors

End Gfpx Gfpx

Instances

Instances details

Eq End Source #
Instance details Defined in Factor.Ec Methods (==) :: End -> End -> Bool # (/=) :: End -> End -> Bool #
Ord End Source #
Instance details Defined in Factor.Ec Methods compare :: End -> End -> Ordering # (<) :: End -> End -> Bool # (<=) :: End -> End -> Bool # (>) :: End -> End -> Bool # (>=) :: End -> End -> Bool # max :: End -> End -> End # min :: End -> End -> End #
Show End Source #
Instance details Defined in Factor.Ec Methods showsPrec :: Int -> End -> ShowS # show :: End -> String # showList :: [End] -> ShowS #

evaluateEnd :: Curve -> End -> Point -> Point Source #

identityEnd :: Curve -> Gfpx -> End Source #

composeEnd :: Curve -> Gfpx -> End -> End -> End Source #

negateEnd :: Curve -> End -> End Source #

addLambdaEnd :: Curve -> Gfpx -> Gfpx -> Gfpx -> Gfpx -> Gfpx -> Gfpx -> Factor Gfpx End Source #

doubleEnd :: Curve -> Gfpx -> End -> Factor Gfpx End Source #

addEnd :: Curve -> Gfpx -> End -> End -> Factor Gfpx End Source #

addMultiplyEnd :: Curve -> Gfpx -> End -> End -> Integer -> Factor Gfpx End Source #

multiplyEnd :: Curve -> Gfpx -> End -> Integer -> Factor Gfpx End Source #

frobeniusEnd :: Curve -> Gfpx -> End Source #

traceOfFrobeniusMod2 :: Curve -> Integer Source #

traceOfFrobeniusModOddPrime :: Curve -> Prime -> Gfpx -> Integer Source #

traceOfFrobenius :: Curve -> Integer Source #

supersingular :: Curve -> Bool Source #

order :: Curve -> Integer Source #