Crypto.Lol.Types

Exports concrete types needed to instantiate cryptographic applications. Specifically:

• Crypto.Lol.Types.Complex
• Crypto.Lol.Types.IrreducibleChar2
• Crypto.Lol.Types.Random
• Crypto.Lol.Types.RRq
• Crypto.Lol.Types.ZqBasic

Documentation

module Crypto.Lol.Types.Random

data Complex a

Newtype wrapper (with slightly different instances) for Number.Complex.

Instances

Transcendental a => CRTrans Maybe (Complex a)

For testing ergonomics, we also have a Maybe instance of CRTrans for complex numbers.

Defined in Crypto.Lol.CRTrans

Methods

crtInfo :: Reflects m Int => TaggedT m Maybe (CRTInfo (Complex a))

Transcendental a => CRTrans Identity (Complex a)

Complex numbers have CRTrans for any index \(m\)

Defined in Crypto.Lol.CRTrans

Methods

crtInfo :: Reflects m Int => TaggedT m Identity (CRTInfo (Complex a))

Eq a => Eq (Complex a)

Defined in Crypto.Lol.Types.Unsafe.Complex

Methods

(==) :: Complex a -> Complex a -> Bool

(/=) :: Complex a -> Complex a -> Bool

Show a => Show (Complex a)

Defined in Crypto.Lol.Types.Unsafe.Complex

Methods

showsPrec :: Int -> Complex a -> ShowS

show :: Complex a -> String

showList :: [Complex a] -> ShowS

Random a => Random (Complex a)

Defined in Crypto.Lol.Types.Unsafe.Complex

Methods

randomR :: RandomGen g => (Complex a, Complex a) -> g -> (Complex a, g)

random :: RandomGen g => g -> (Complex a, g)

randomRs :: RandomGen g => (Complex a, Complex a) -> g -> [Complex a]

randoms :: RandomGen g => g -> [Complex a]

randomRIO :: (Complex a, Complex a) -> IO (Complex a)

randomIO :: IO (Complex a)

NFData a => NFData (Complex a)

Defined in Crypto.Lol.Types.Unsafe.Complex

Methods

rnf :: Complex a -> ()

C a => C (Complex a)

Defined in Crypto.Lol.Types.Unsafe.Complex

Methods

(/) :: Complex a -> Complex a -> Complex a

recip :: Complex a -> Complex a

fromRational' :: Rational -> Complex a

(^-) :: Complex a -> Integer -> Complex a

Field a => C (Complex a)

Custom instance replacing the one provided by numeric prelude: it always returns 0 as the remainder of a division. (The NP instance sometimes has precision issues, because it yields nonzero remainders, which is a problem for divG methods.)

Defined in Crypto.Lol.Types.Unsafe.Complex

Methods

div :: Complex a -> Complex a -> Complex a

mod :: Complex a -> Complex a -> Complex a

divMod :: Complex a -> Complex a -> (Complex a, Complex a)

C a => C (Complex a)

Defined in Crypto.Lol.Types.Unsafe.Complex

Methods

(*) :: Complex a -> Complex a -> Complex a

one :: Complex a

fromInteger :: Integer -> Complex a

(^) :: Complex a -> Integer -> Complex a

C a => C (Complex a)

Defined in Crypto.Lol.Types.Unsafe.Complex

Methods

isZero :: Complex a -> Bool

C a => C (Complex a)

Defined in Crypto.Lol.Types.Unsafe.Complex

Methods

zero :: Complex a

(+) :: Complex a -> Complex a -> Complex a

(-) :: Complex a -> Complex a -> Complex a

negate :: Complex a -> Complex a

Transcendental a => CRTEmbed (Complex a)

Self-embed

Defined in Crypto.Lol.CRTrans

Associated Types

type CRTExt (Complex a) :: Type

Methods

toExt :: Complex a -> CRTExt (Complex a)

fromExt :: CRTExt (Complex a) -> Complex a

ApproxEqual (Complex Double)

Defined in Crypto.Lol.Utils.Tests

Methods

(=~=) :: Complex Double -> Complex Double -> Bool

Show (ArgType (Complex Double))

Defined in Crypto.Lol.Utils.ShowType

Methods

showsPrec :: Int -> ArgType (Complex Double) -> ShowS

show :: ArgType (Complex Double) -> String

showList :: [ArgType (Complex Double)] -> ShowS

type CRTExt (Complex a)

Defined in Crypto.Lol.CRTrans

type CRTExt (Complex a) = Complex a

roundComplex :: (RealRing a, ToInteger b) => Complex a -> (b, b)

Rounds the real and imaginary components to the nearest integer.

cis :: Transcendental a => a -> Complex a

cis \(t\) is a complex value with magnitude 1 and phase \(t \bmod 2\cdot\pi\)).

real :: Complex a -> a

Real component of a complex number.

imag :: Complex a -> a

Imaginary component of a complex number.

fromReal :: Additive a => a -> Complex a

Embeds a scalar as the real component of a complex number.

data RRq q r

The additive group \( \R/(q\Z) \) of reals modulo q, using underlying floating-point type r.

Instances

(Reflects q r, RealField r) => Reduce r (RRq q r)

Defined in Crypto.Lol.Types.Unsafe.RRq

Methods

reduce :: r -> RRq q r

TensorPowDec t (RRq q r) => UnCyc t (RRq q r)

Defined in Crypto.Lol.Cyclotomic.Cyc

Methods

cycPow :: Fact m => CycRep t P m (RRq q r) -> Cyc t m (RRq q r)

cycDec :: Fact m => CycRep t D m (RRq q r) -> Cyc t m (RRq q r)

unCycPow :: Fact m => Cyc t m (RRq q r) -> CycRep t P m (RRq q r)

unCycDec :: Fact m => Cyc t m (RRq q r) -> CycRep t D m (RRq q r)

TensorPowDec t (RRq q r) => ExtensionCyc (Cyc t) (RRq q r)

Defined in Crypto.Lol.Cyclotomic.Cyc

Methods

embed :: Divides m m' => Cyc t m (RRq q r) -> Cyc t m' (RRq q r)

twace :: Divides m m' => Cyc t m' (RRq q r) -> Cyc t m (RRq q r)

powBasis :: Divides m m' => Tagged m [Cyc t m' (RRq q r)]

coeffsCyc :: Divides m m' => Basis -> Cyc t m' (RRq q r) -> [Cyc t m (RRq q r)]

(Protoable (IZipVector m (RRq q Double)), ProtoType (IZipVector m (RRq q Double)) ~ KqProduct, Protoable (IZipVector m b), ProtoType (IZipVector m b) ~ KqProduct) => Protoable (IZipVector m (RRq q Double, b))

Defined in Crypto.Lol.Types.IZipVector

Associated Types

type ProtoType (IZipVector m (RRq q Double, b)) :: Type

Methods

toProto :: IZipVector m (RRq q Double, b) -> ProtoType (IZipVector m (RRq q Double, b))

fromProto :: MonadError String m0 => ProtoType (IZipVector m (RRq q Double, b)) -> m0 (IZipVector m (RRq q Double, b))

(Fact m, Reflects q Double) => Protoable (IZipVector m (RRq q Double))

Defined in Crypto.Lol.Types.IZipVector

Associated Types

type ProtoType (IZipVector m (RRq q Double)) :: Type

Methods

toProto :: IZipVector m (RRq q Double) -> ProtoType (IZipVector m (RRq q Double))

fromProto :: MonadError String m0 => ProtoType (IZipVector m (RRq q Double)) -> m0 (IZipVector m (RRq q Double))

(Fact m, UnCyc t Int64, UnCyc t (RRq q r), IFunctor t, IFElt t Int64, IFElt t (RRq q r)) => FunctorCyc (Cyc t m) Int64 (RRq q r)

Defined in Crypto.Lol.Cyclotomic.Cyc

Methods

fmapCyc :: Maybe Basis -> (Int64 -> RRq q r) -> Cyc t m Int64 -> Cyc t m (RRq q r)

(Fact m, UnCyc t Double, UnCyc t (RRq q r), IFunctor t, IFElt t Double, IFElt t (RRq q r)) => FunctorCyc (Cyc t m) Double (RRq q r)

Defined in Crypto.Lol.Cyclotomic.Cyc

Methods

fmapCyc :: Maybe Basis -> (Double -> RRq q r) -> Cyc t m Double -> Cyc t m (RRq q r)

(Fact m, UnCyc t (a, b), UnCyc t (RRq q r), IFunctor t, IFElt t (a, b), IFElt t (RRq q r)) => FunctorCyc (Cyc t m) (a, b) (RRq q r)

Defined in Crypto.Lol.Cyclotomic.Cyc

Methods

fmapCyc :: Maybe Basis -> ((a, b) -> RRq q r) -> Cyc t m (a, b) -> Cyc t m (RRq q r)

(Fact m, TensorPowDec t (RRq q r), Foldable (t m)) => FoldableCyc (Cyc t m) (RRq q r)

Defined in Crypto.Lol.Cyclotomic.Cyc

Methods

foldrCyc :: Maybe Basis -> (RRq q r -> b -> b) -> b -> Cyc t m (RRq q r) -> b

(Fact m, UnCyc t (RRq q r), UnCyc t Int64, IFunctor t, IFElt t (RRq q r), IFElt t Int64) => FunctorCyc (Cyc t m) (RRq q r) Int64

Defined in Crypto.Lol.Cyclotomic.Cyc

Methods

fmapCyc :: Maybe Basis -> (RRq q r -> Int64) -> Cyc t m (RRq q r) -> Cyc t m Int64

(Fact m, UnCyc t (RRq q r), UnCyc t Double, IFunctor t, IFElt t (RRq q r), IFElt t Double) => FunctorCyc (Cyc t m) (RRq q r) Double

Defined in Crypto.Lol.Cyclotomic.Cyc

Methods

fmapCyc :: Maybe Basis -> (RRq q r -> Double) -> Cyc t m (RRq q r) -> Cyc t m Double

(Fact m, Functor (t m), UnCyc t (RRq q r)) => FunctorCyc (Cyc t m) (RRq q r) Integer

Defined in Crypto.Lol.Cyclotomic.Cyc

Methods

fmapCyc :: Maybe Basis -> (RRq q r -> Integer) -> Cyc t m (RRq q r) -> Cyc t m Integer

(Fact m, UnCyc t (RRq q r), UnCyc t (a, b), IFunctor t, IFElt t (RRq q r), IFElt t (a, b)) => FunctorCyc (Cyc t m) (RRq q r) (a, b)

Defined in Crypto.Lol.Cyclotomic.Cyc

Methods

fmapCyc :: Maybe Basis -> (RRq q r -> (a, b)) -> Cyc t m (RRq q r) -> Cyc t m (a, b)

(Fact m, Rescale (RRq q r) (RRq p r), TensorPowDec t (RRq q r), TensorPowDec t (RRq p r)) => RescaleCyc (Cyc t m) (RRq q r) (RRq p r)

rescale from one modulus to another

Defined in Crypto.Lol.Cyclotomic.Cyc

Methods

rescaleCyc :: Basis -> Cyc t m (RRq q r) -> Cyc t m (RRq p r)

(Fact m, UnCyc t (ZqBasic q z), UnCyc t (RRq q r), IFunctor t, IFElt t (ZqBasic q z), IFElt t (RRq q r)) => FunctorCyc (Cyc t m) (ZqBasic q z) (RRq q r)

Defined in Crypto.Lol.Cyclotomic.Cyc

Methods

fmapCyc :: Maybe Basis -> (ZqBasic q z -> RRq q r) -> Cyc t m (ZqBasic q z) -> Cyc t m (RRq q r)

(Fact m, UnCyc t (RRq q r), UnCyc t (ZqBasic q z), IFunctor t, IFElt t (RRq q r), IFElt t (ZqBasic q z)) => FunctorCyc (Cyc t m) (RRq q r) (ZqBasic q z)

Defined in Crypto.Lol.Cyclotomic.Cyc

Methods

fmapCyc :: Maybe Basis -> (RRq q r -> ZqBasic q z) -> Cyc t m (RRq q r) -> Cyc t m (ZqBasic q z)

(Fact m, UnCyc t (RRq q r), UnCyc t (RRq q r), IFunctor t, IFElt t (RRq q r), IFElt t (RRq q r)) => FunctorCyc (Cyc t m) (RRq q r) (RRq q r)

Defined in Crypto.Lol.Cyclotomic.Cyc

Methods

fmapCyc :: Maybe Basis -> (RRq q r -> RRq q r) -> Cyc t m (RRq q r) -> Cyc t m (RRq q r)

Eq r => Eq (RRq q r)

Defined in Crypto.Lol.Types.Unsafe.RRq

Methods

(==) :: RRq q r -> RRq q r -> Bool

(/=) :: RRq q r -> RRq q r -> Bool

Show r => Show (RRq q r)

Defined in Crypto.Lol.Types.Unsafe.RRq

Methods

showsPrec :: Int -> RRq q r -> ShowS

show :: RRq q r -> String

showList :: [RRq q r] -> ShowS

Show (t m (RRq q r)) => Show (Cyc t m (RRq q r))

Defined in Crypto.Lol.Cyclotomic.Cyc

Methods

showsPrec :: Int -> Cyc t m (RRq q r) -> ShowS

show :: Cyc t m (RRq q r) -> String

showList :: [Cyc t m (RRq q r)] -> ShowS

Random (RRq q Double)

Defined in Crypto.Lol.Types.Unsafe.RRq

Methods

randomR :: RandomGen g => (RRq q Double, RRq q Double) -> g -> (RRq q Double, g)

random :: RandomGen g => g -> (RRq q Double, g)

randomRs :: RandomGen g => (RRq q Double, RRq q Double) -> g -> [RRq q Double]

randoms :: RandomGen g => g -> [RRq q Double]

randomRIO :: (RRq q Double, RRq q Double) -> IO (RRq q Double)

randomIO :: IO (RRq q Double)

Random (t m (RRq q r)) => Random (Cyc t m (RRq q r))

Defined in Crypto.Lol.Cyclotomic.Cyc

Methods

randomR :: RandomGen g => (Cyc t m (RRq q r), Cyc t m (RRq q r)) -> g -> (Cyc t m (RRq q r), g)

random :: RandomGen g => g -> (Cyc t m (RRq q r), g)

randomRs :: RandomGen g => (Cyc t m (RRq q r), Cyc t m (RRq q r)) -> g -> [Cyc t m (RRq q r)]

randoms :: RandomGen g => g -> [Cyc t m (RRq q r)]

randomRIO :: (Cyc t m (RRq q r), Cyc t m (RRq q r)) -> IO (Cyc t m (RRq q r))

randomIO :: IO (Cyc t m (RRq q r))

NFData r => NFData (RRq q r)

Defined in Crypto.Lol.Types.Unsafe.RRq

Methods

rnf :: RRq q r -> ()

(Fact m, forall (m' :: Factored). Fact m' => NFData (t m' (RRq q r))) => NFData (Cyc t m (RRq q r))

Defined in Crypto.Lol.Cyclotomic.Cyc

Methods

rnf :: Cyc t m (RRq q r) -> ()

C r => C (RRq q r)

Defined in Crypto.Lol.Types.Unsafe.RRq

Methods

isZero :: RRq q r -> Bool

ZeroTestable (t m (RRq q r)) => C (Cyc t m (RRq q r))

Defined in Crypto.Lol.Cyclotomic.Cyc

Methods

isZero :: Cyc t m (RRq q r) -> Bool

RealField r => C (RRq q r)

Defined in Crypto.Lol.Types.Unsafe.RRq

Methods

zero :: RRq q r

(+) :: RRq q r -> RRq q r -> RRq q r

(-) :: RRq q r -> RRq q r -> RRq q r

negate :: RRq q r -> RRq q r

(Additive (RRq q r), TensorPowDec t (RRq q r), IFunctor t, Fact m) => C (Cyc t m (RRq q r))

Defined in Crypto.Lol.Cyclotomic.Cyc

Methods

zero :: Cyc t m (RRq q r)

(+) :: Cyc t m (RRq q r) -> Cyc t m (RRq q r) -> Cyc t m (RRq q r)

(-) :: Cyc t m (RRq q r) -> Cyc t m (RRq q r) -> Cyc t m (RRq q r)

negate :: Cyc t m (RRq q r) -> Cyc t m (RRq q r)

(Reflects q r, Field r, Reduce r (RRq q r)) => Lift' (RRq q r)

Defined in Crypto.Lol.Types.Unsafe.RRq

Methods

lift :: RRq q r -> LiftOf (RRq q r)

(Fact m, CRTElt t Double, TensorPowDec t (RRq q Double), Protoable (CycRep t D m (RRq q Double))) => Protoable (Cyc t m (RRq q Double))

Defined in Crypto.Lol.Cyclotomic.Cyc

Associated Types

type ProtoType (Cyc t m (RRq q Double)) :: Type

Methods

toProto :: Cyc t m (RRq q Double) -> ProtoType (Cyc t m (RRq q Double))

fromProto :: MonadError String m0 => ProtoType (Cyc t m (RRq q Double)) -> m0 (Cyc t m (RRq q Double))

(Additive (RRq q r), Additive (RRq p r)) => Rescale (RRq q r) (RRq p r)

Defined in Crypto.Lol.Types.Unsafe.RRq

Methods

rescale :: RRq q r -> RRq p r

(Reflects q Double, FunctorCyc (Cyc t m) Double (RRq q Double)) => Reduce (Cyc t m Double) (Cyc t m (RRq q Double))

Defined in Crypto.Lol.Cyclotomic.Cyc

Methods

reduce :: Cyc t m Double -> Cyc t m (RRq q Double)

(ToInteger z, RealField r, Reflects q z, Reflects q r) => Subgroup (ZqBasic q z) (RRq q r)

Defined in Crypto.Lol.Types.Unsafe.RRq

Methods

fromSubgroup :: ZqBasic q z -> RRq q r

data Cyc t m (RRq q r)

additive group \( K/qR \), limited to powerful- or decoding-basis representation

Defined in Crypto.Lol.Cyclotomic.Cyc

data Cyc t m (RRq q r)

• = PowRRq !(CycRep t P m (RRq q r))
• | DecRRq !(CycRep t D m (RRq q r))

type ProtoType (IZipVector m (RRq q Double, b))

Defined in Crypto.Lol.Types.IZipVector

type ProtoType (IZipVector m (RRq q Double, b)) = KqProduct

type ProtoType (IZipVector m (RRq q Double))

Defined in Crypto.Lol.Types.IZipVector

type ProtoType (IZipVector m (RRq q Double)) = KqProduct

type LiftOf (RRq q r)

Defined in Crypto.Lol.Types.Unsafe.RRq

type LiftOf (RRq q r) = r

type ProtoType (Cyc t m (RRq q Double))

Defined in Crypto.Lol.Cyclotomic.Cyc

type ProtoType (Cyc t m (RRq q Double))

data ZqBasic q z

The ring \(\Z_q\) of integers modulo q, using underlying integer type z.

Instances

Correct gad (CycG t m (ZqBasic q Int64)) => Correct (gad :: k2) (Cyc t m (ZqBasic q Int64))

Defined in Crypto.Lol.Cyclotomic.Cyc

Methods

correct :: [Cyc t m (ZqBasic q Int64)] -> (Cyc t m (ZqBasic q Int64), [LiftOf (Cyc t m (ZqBasic q Int64))])

(Decompose gad (CycG t m (ZqBasic q Int64)), Reduce (Cyc t m Int64) (Cyc t m (ZqBasic q Int64))) => Decompose (gad :: k2) (Cyc t m (ZqBasic q Int64))

Defined in Crypto.Lol.Cyclotomic.Cyc

Associated Types

type DecompOf (Cyc t m (ZqBasic q Int64)) :: Type

Methods

decompose :: Cyc t m (ZqBasic q Int64) -> [DecompOf (Cyc t m (ZqBasic q Int64))]

Gadget gad (CycG t m (ZqBasic q z)) => Gadget (gad :: k2) (Cyc t m (ZqBasic q z))

Defined in Crypto.Lol.Cyclotomic.Cyc

Methods

gadget :: [Cyc t m (ZqBasic q z)]

encode :: Cyc t m (ZqBasic q z) -> [Cyc t m (ZqBasic q z)]

(Reflects q z, ToInteger z) => Reduce Integer (ZqBasic q z)

Defined in Crypto.Lol.Types.Unsafe.ZqBasic

Methods

reduce :: Integer -> ZqBasic q z

(Reflects q z, IntegralDomain z) => Reduce z (ZqBasic q z)

Defined in Crypto.Lol.Types.Unsafe.ZqBasic

Methods

reduce :: z -> ZqBasic q z

(Reflects q z, ToInteger z, PID z, Enum z, NFData z) => CRTrans Maybe (ZqBasic q z)

Defined in Crypto.Lol.Types.Unsafe.ZqBasic

Methods

crtInfo :: Reflects m Int => TaggedT m Maybe (CRTInfo (ZqBasic q z))

CRTElt t (ZqBasic q z) => UnCyc t (ZqBasic q z)

Defined in Crypto.Lol.Cyclotomic.Cyc

Methods

cycPow :: Fact m => CycRep t P m (ZqBasic q z) -> Cyc t m (ZqBasic q z)

cycDec :: Fact m => CycRep t D m (ZqBasic q z) -> Cyc t m (ZqBasic q z)

unCycPow :: Fact m => Cyc t m (ZqBasic q z) -> CycRep t P m (ZqBasic q z)

unCycDec :: Fact m => Cyc t m (ZqBasic q z) -> CycRep t D m (ZqBasic q z)

(Reflects q z, ToInteger z, Ring z) => Correct TrivGad (ZqBasic q z)

Defined in Crypto.Lol.Types.Unsafe.ZqBasic

Methods

correct :: [ZqBasic q z] -> (ZqBasic q z, [LiftOf (ZqBasic q z)])

(Reflects q z, ToInteger z) => Decompose TrivGad (ZqBasic q z)

Defined in Crypto.Lol.Types.Unsafe.ZqBasic

Associated Types

type DecompOf (ZqBasic q z) :: Type

Methods

decompose :: ZqBasic q z -> [DecompOf (ZqBasic q z)]

(Reflects q z, ToInteger z) => Gadget TrivGad (ZqBasic q z)

Defined in Crypto.Lol.Types.Unsafe.ZqBasic

Methods

gadget :: [ZqBasic q z]

encode :: ZqBasic q z -> [ZqBasic q z]

(Reflects q z, ToInteger z, Reflects b z) => Correct (BaseBGad b :: Type) (ZqBasic q z)

Defined in Crypto.Lol.Types.Unsafe.ZqBasic

Methods

correct :: [ZqBasic q z] -> (ZqBasic q z, [LiftOf (ZqBasic q z)])

(Reflects q z, ToInteger z, Reflects b z) => Decompose (BaseBGad b :: Type) (ZqBasic q z)

Defined in Crypto.Lol.Types.Unsafe.ZqBasic

Associated Types

type DecompOf (ZqBasic q z) :: Type

Methods

decompose :: ZqBasic q z -> [DecompOf (ZqBasic q z)]

(Reflects q z, ToInteger z, RealIntegral z, Reflects b z) => Gadget (BaseBGad b :: Type) (ZqBasic q z)

Defined in Crypto.Lol.Types.Unsafe.ZqBasic

Methods

gadget :: [ZqBasic q z]

encode :: ZqBasic q z -> [ZqBasic q z]

CRTSetCyc (CycG t) (ZqBasic q z) => CRTSetCyc (Cyc t) (ZqBasic q z)

Defined in Crypto.Lol.Cyclotomic.Cyc

Methods

crtSet :: Divides m m' => Tagged m [Cyc t m' (ZqBasic q z)]

ExtensionCyc (CycG t) (ZqBasic q z) => ExtensionCyc (Cyc t) (ZqBasic q z)

Defined in Crypto.Lol.Cyclotomic.Cyc

Methods

embed :: Divides m m' => Cyc t m (ZqBasic q z) -> Cyc t m' (ZqBasic q z)

twace :: Divides m m' => Cyc t m' (ZqBasic q z) -> Cyc t m (ZqBasic q z)

powBasis :: Divides m m' => Tagged m [Cyc t m' (ZqBasic q z)]

coeffsCyc :: Divides m m' => Basis -> Cyc t m' (ZqBasic q z) -> [Cyc t m (ZqBasic q z)]

(Mod (ZqBasic q z), Show z) => Show (ArgType (ZqBasic q z))

Defined in Crypto.Lol.Utils.ShowType

Methods

showsPrec :: Int -> ArgType (ZqBasic q z) -> ShowS

show :: ArgType (ZqBasic q z) -> String

showList :: [ArgType (ZqBasic q z)] -> ShowS

(Protoable (IZipVector m (ZqBasic q Int64)), ProtoType (IZipVector m (ZqBasic q Int64)) ~ RqProduct, Protoable (IZipVector m b), ProtoType (IZipVector m b) ~ RqProduct) => Protoable (IZipVector m (ZqBasic q Int64, b))

Defined in Crypto.Lol.Types.IZipVector

Associated Types

type ProtoType (IZipVector m (ZqBasic q Int64, b)) :: Type

Methods

toProto :: IZipVector m (ZqBasic q Int64, b) -> ProtoType (IZipVector m (ZqBasic q Int64, b))

fromProto :: MonadError String m0 => ProtoType (IZipVector m (ZqBasic q Int64, b)) -> m0 (IZipVector m (ZqBasic q Int64, b))

(Fact m, Reflects q Int64) => Protoable (IZipVector m (ZqBasic q Int64))

Defined in Crypto.Lol.Types.IZipVector

Associated Types

type ProtoType (IZipVector m (ZqBasic q Int64)) :: Type

Methods

toProto :: IZipVector m (ZqBasic q Int64) -> ProtoType (IZipVector m (ZqBasic q Int64))

fromProto :: MonadError String m0 => ProtoType (IZipVector m (ZqBasic q Int64)) -> m0 (IZipVector m (ZqBasic q Int64))

(Fact m, Reflects q z, Reduce z b, ZeroTestable z, CRTElt t (ZqBasic q z), C b (Cyc t m b)) => RescaleCyc (Cyc t m) b (ZqBasic q z, b)

rescale up by one additional modulus

Defined in Crypto.Lol.Cyclotomic.Cyc

Methods

rescaleCyc :: Basis -> Cyc t m b -> Cyc t m (ZqBasic q z, b)

(Fact m, UnCyc t Int64, UnCyc t (ZqBasic q z), IFunctor t, IFElt t Int64, IFElt t (ZqBasic q z)) => FunctorCyc (Cyc t m) Int64 (ZqBasic q z)

Defined in Crypto.Lol.Cyclotomic.Cyc

Methods

fmapCyc :: Maybe Basis -> (Int64 -> ZqBasic q z) -> Cyc t m Int64 -> Cyc t m (ZqBasic q z)

(Fact m, UnCyc t Double, UnCyc t (ZqBasic q z), IFunctor t, IFElt t Double, IFElt t (ZqBasic q z)) => FunctorCyc (Cyc t m) Double (ZqBasic q z)

Defined in Crypto.Lol.Cyclotomic.Cyc

Methods

fmapCyc :: Maybe Basis -> (Double -> ZqBasic q z) -> Cyc t m Double -> Cyc t m (ZqBasic q z)

(ToInteger z, Reflects q z, Reduce z b, Field b, FunctorCyc (Cyc t m) (ZqBasic q z) z, FunctorCyc (Cyc t m) z b, Additive (Cyc t m b), Module b (Cyc t m b)) => RescaleCyc (Cyc t m) (ZqBasic q z, b) b

specialized (faster) rescale-down by a single \(\Z_q\)

Defined in Crypto.Lol.Cyclotomic.Cyc

Methods

rescaleCyc :: Basis -> Cyc t m (ZqBasic q z, b) -> Cyc t m b

(Fact m, UnCyc t (a, b), UnCyc t (ZqBasic q z), IFunctor t, IFElt t (a, b), IFElt t (ZqBasic q z)) => FunctorCyc (Cyc t m) (a, b) (ZqBasic q z)

Defined in Crypto.Lol.Cyclotomic.Cyc

Methods

fmapCyc :: Maybe Basis -> ((a, b) -> ZqBasic q z) -> Cyc t m (a, b) -> Cyc t m (ZqBasic q z)

FoldableCyc (CycG t m) (ZqBasic q z) => FoldableCyc (Cyc t m) (ZqBasic q z)

Defined in Crypto.Lol.Cyclotomic.Cyc

Methods

foldrCyc :: Maybe Basis -> (ZqBasic q z -> b -> b) -> b -> Cyc t m (ZqBasic q z) -> b

(Fact m, UnCyc t (ZqBasic q z), UnCyc t Int64, IFunctor t, IFElt t (ZqBasic q z), IFElt t Int64) => FunctorCyc (Cyc t m) (ZqBasic q z) Int64

Defined in Crypto.Lol.Cyclotomic.Cyc

Methods

fmapCyc :: Maybe Basis -> (ZqBasic q z -> Int64) -> Cyc t m (ZqBasic q z) -> Cyc t m Int64

(Fact m, UnCyc t (ZqBasic q z), UnCyc t Double, IFunctor t, IFElt t (ZqBasic q z), IFElt t Double) => FunctorCyc (Cyc t m) (ZqBasic q z) Double

Defined in Crypto.Lol.Cyclotomic.Cyc

Methods

fmapCyc :: Maybe Basis -> (ZqBasic q z -> Double) -> Cyc t m (ZqBasic q z) -> Cyc t m Double

(Fact m, Functor (t m), UnCyc t (ZqBasic q z)) => FunctorCyc (Cyc t m) (ZqBasic q z) Integer

Defined in Crypto.Lol.Cyclotomic.Cyc

Methods

fmapCyc :: Maybe Basis -> (ZqBasic q z -> Integer) -> Cyc t m (ZqBasic q z) -> Cyc t m Integer

(Fact m, UnCyc t (ZqBasic q z), UnCyc t (a, b), IFunctor t, IFElt t (ZqBasic q z), IFElt t (a, b)) => FunctorCyc (Cyc t m) (ZqBasic q z) (a, b)

Defined in Crypto.Lol.Cyclotomic.Cyc

Methods

fmapCyc :: Maybe Basis -> (ZqBasic q z -> (a, b)) -> Cyc t m (ZqBasic q z) -> Cyc t m (a, b)

RescaleCyc (CycG t m) (ZqBasic q z) (ZqBasic p z) => RescaleCyc (Cyc t m) (ZqBasic q z) (ZqBasic p z)

rescale from one modulus to another

Defined in Crypto.Lol.Cyclotomic.Cyc

Methods

rescaleCyc :: Basis -> Cyc t m (ZqBasic q z) -> Cyc t m (ZqBasic p z)

(Fact m, UnCyc t (ZqBasic q z), UnCyc t (ZqBasic q z), IFunctor t, IFElt t (ZqBasic q z), IFElt t (ZqBasic q z)) => FunctorCyc (Cyc t m) (ZqBasic q z) (ZqBasic q z)

Defined in Crypto.Lol.Cyclotomic.Cyc

Methods

fmapCyc :: Maybe Basis -> (ZqBasic q z -> ZqBasic q z) -> Cyc t m (ZqBasic q z) -> Cyc t m (ZqBasic q z)

(Fact m, UnCyc t (ZqBasic q z), UnCyc t (RRq q r), IFunctor t, IFElt t (ZqBasic q z), IFElt t (RRq q r)) => FunctorCyc (Cyc t m) (ZqBasic q z) (RRq q r)

Defined in Crypto.Lol.Cyclotomic.Cyc

Methods

fmapCyc :: Maybe Basis -> (ZqBasic q z -> RRq q r) -> Cyc t m (ZqBasic q z) -> Cyc t m (RRq q r)

(Fact m, UnCyc t (RRq q r), UnCyc t (ZqBasic q z), IFunctor t, IFElt t (RRq q r), IFElt t (ZqBasic q z)) => FunctorCyc (Cyc t m) (RRq q r) (ZqBasic q z)

Defined in Crypto.Lol.Cyclotomic.Cyc

Methods

fmapCyc :: Maybe Basis -> (RRq q r -> ZqBasic q z) -> Cyc t m (RRq q r) -> Cyc t m (ZqBasic q z)

Eq z => Eq (ZqBasic q z)

Defined in Crypto.Lol.Types.Unsafe.ZqBasic

Methods

(==) :: ZqBasic q z -> ZqBasic q z -> Bool

(/=) :: ZqBasic q z -> ZqBasic q z -> Bool

Eq (CycG t m (ZqBasic q z)) => Eq (Cyc t m (ZqBasic q z))

Defined in Crypto.Lol.Cyclotomic.Cyc

Methods

(==) :: Cyc t m (ZqBasic q z) -> Cyc t m (ZqBasic q z) -> Bool

(/=) :: Cyc t m (ZqBasic q z) -> Cyc t m (ZqBasic q z) -> Bool

Ord z => Ord (ZqBasic q z)

Defined in Crypto.Lol.Types.Unsafe.ZqBasic

Methods

compare :: ZqBasic q z -> ZqBasic q z -> Ordering

(<) :: ZqBasic q z -> ZqBasic q z -> Bool

(<=) :: ZqBasic q z -> ZqBasic q z -> Bool

(>) :: ZqBasic q z -> ZqBasic q z -> Bool

(>=) :: ZqBasic q z -> ZqBasic q z -> Bool

max :: ZqBasic q z -> ZqBasic q z -> ZqBasic q z

min :: ZqBasic q z -> ZqBasic q z -> ZqBasic q z

Show z => Show (ZqBasic q z)

Defined in Crypto.Lol.Types.Unsafe.ZqBasic

Methods

showsPrec :: Int -> ZqBasic q z -> ShowS

show :: ZqBasic q z -> String

showList :: [ZqBasic q z] -> ShowS

Show (CycG t m (ZqBasic q z)) => Show (Cyc t m (ZqBasic q z))

Defined in Crypto.Lol.Cyclotomic.Cyc

Methods

showsPrec :: Int -> Cyc t m (ZqBasic q z) -> ShowS

show :: Cyc t m (ZqBasic q z) -> String

showList :: [Cyc t m (ZqBasic q z)] -> ShowS

(Reflects q z, Ring z, Random z) => Random (ZqBasic q z)

Defined in Crypto.Lol.Types.Unsafe.ZqBasic

Methods

randomR :: RandomGen g => (ZqBasic q z, ZqBasic q z) -> g -> (ZqBasic q z, g)

random :: RandomGen g => g -> (ZqBasic q z, g)

randomRs :: RandomGen g => (ZqBasic q z, ZqBasic q z) -> g -> [ZqBasic q z]

randoms :: RandomGen g => g -> [ZqBasic q z]

randomRIO :: (ZqBasic q z, ZqBasic q z) -> IO (ZqBasic q z)

randomIO :: IO (ZqBasic q z)

Random (CycG t m (ZqBasic q z)) => Random (Cyc t m (ZqBasic q z))

Defined in Crypto.Lol.Cyclotomic.Cyc

Methods

randomR :: RandomGen g => (Cyc t m (ZqBasic q z), Cyc t m (ZqBasic q z)) -> g -> (Cyc t m (ZqBasic q z), g)

random :: RandomGen g => g -> (Cyc t m (ZqBasic q z), g)

randomRs :: RandomGen g => (Cyc t m (ZqBasic q z), Cyc t m (ZqBasic q z)) -> g -> [Cyc t m (ZqBasic q z)]

randoms :: RandomGen g => g -> [Cyc t m (ZqBasic q z)]

randomRIO :: (Cyc t m (ZqBasic q z), Cyc t m (ZqBasic q z)) -> IO (Cyc t m (ZqBasic q z))

randomIO :: IO (Cyc t m (ZqBasic q z))

NFData z => NFData (ZqBasic q z)

Defined in Crypto.Lol.Types.Unsafe.ZqBasic

Methods

rnf :: ZqBasic q z -> ()

NFData (CycG t m (ZqBasic q z)) => NFData (Cyc t m (ZqBasic q z))

Defined in Crypto.Lol.Cyclotomic.Cyc

Methods

rnf :: Cyc t m (ZqBasic q z) -> ()

(Reflects q z, ToInteger z, PID z, Show z) => C (ZqBasic q z)

Defined in Crypto.Lol.Types.Unsafe.ZqBasic

Methods

(/) :: ZqBasic q z -> ZqBasic q z -> ZqBasic q z

recip :: ZqBasic q z -> ZqBasic q z

fromRational' :: Rational -> ZqBasic q z

(^-) :: ZqBasic q z -> Integer -> ZqBasic q z

(Reflects q z, ToInteger z, PID z, Show z) => C (ZqBasic q z)

Defined in Crypto.Lol.Types.Unsafe.ZqBasic

Methods

div :: ZqBasic q z -> ZqBasic q z -> ZqBasic q z

mod :: ZqBasic q z -> ZqBasic q z -> ZqBasic q z

divMod :: ZqBasic q z -> ZqBasic q z -> (ZqBasic q z, ZqBasic q z)

(Reflects q z, ToInteger z) => C (ZqBasic q z)

Defined in Crypto.Lol.Types.Unsafe.ZqBasic

Methods

(*) :: ZqBasic q z -> ZqBasic q z -> ZqBasic q z

one :: ZqBasic q z

fromInteger :: Integer -> ZqBasic q z

(^) :: ZqBasic q z -> Integer -> ZqBasic q z

Ring (CycG t m (ZqBasic q z)) => C (Cyc t m (ZqBasic q z))

Defined in Crypto.Lol.Cyclotomic.Cyc

Methods

(*) :: Cyc t m (ZqBasic q z) -> Cyc t m (ZqBasic q z) -> Cyc t m (ZqBasic q z)

one :: Cyc t m (ZqBasic q z)

fromInteger :: Integer -> Cyc t m (ZqBasic q z)

(^) :: Cyc t m (ZqBasic q z) -> Integer -> Cyc t m (ZqBasic q z)

C z => C (ZqBasic q z)

Defined in Crypto.Lol.Types.Unsafe.ZqBasic

Methods

isZero :: ZqBasic q z -> Bool

ZeroTestable (CycG t m (ZqBasic q z)) => C (Cyc t m (ZqBasic q z))

Defined in Crypto.Lol.Cyclotomic.Cyc

Methods

isZero :: Cyc t m (ZqBasic q z) -> Bool

(Reflects q z, IntegralDomain z) => C (ZqBasic q z)

Defined in Crypto.Lol.Types.Unsafe.ZqBasic

Methods

zero :: ZqBasic q z

(+) :: ZqBasic q z -> ZqBasic q z -> ZqBasic q z

(-) :: ZqBasic q z -> ZqBasic q z -> ZqBasic q z

negate :: ZqBasic q z -> ZqBasic q z

Additive (CycG t m (ZqBasic q z)) => C (Cyc t m (ZqBasic q z))

Defined in Crypto.Lol.Cyclotomic.Cyc

Methods

zero :: Cyc t m (ZqBasic q z)

(+) :: Cyc t m (ZqBasic q z) -> Cyc t m (ZqBasic q z) -> Cyc t m (ZqBasic q z)

(-) :: Cyc t m (ZqBasic q z) -> Cyc t m (ZqBasic q z) -> Cyc t m (ZqBasic q z)

negate :: Cyc t m (ZqBasic q z) -> Cyc t m (ZqBasic q z)

(Reflects q z, Ring z, Ord z, IntegralDomain z) => Lift' (ZqBasic q z)

Defined in Crypto.Lol.Types.Unsafe.ZqBasic

Methods

lift :: ZqBasic q z -> LiftOf (ZqBasic q z)

(Reflects q z, ToInteger z) => Mod (ZqBasic q z)

Defined in Crypto.Lol.Types.Unsafe.ZqBasic

Associated Types

type ModRep (ZqBasic q z) :: Type

Methods

modulus :: ModRep (ZqBasic q z)

(Reflects q z, Ring z, Enum z) => Enumerable (ZqBasic q z)

Defined in Crypto.Lol.Types.Unsafe.ZqBasic

Methods

values :: [ZqBasic q z]

CosetGaussianCyc (CycG t m (ZqBasic q Int64)) => CosetGaussianCyc (Cyc t m (ZqBasic q Int64))

uses Double for the intermediate Gaussian samples

Defined in Crypto.Lol.Cyclotomic.Cyc

Methods

cosetGaussian :: (ToRational v, MonadRandom rnd) => v -> Cyc t m (ZqBasic q Int64) -> rnd (LiftOf (Cyc t m (ZqBasic q Int64)))

Cyclotomic (CycG t m (ZqBasic q z)) => Cyclotomic (Cyc t m (ZqBasic q z))

Defined in Crypto.Lol.Cyclotomic.Cyc

Methods

mulG :: Cyc t m (ZqBasic q z) -> Cyc t m (ZqBasic q z)

divG :: Cyc t m (ZqBasic q z) -> Maybe (Cyc t m (ZqBasic q z))

advisePow :: Cyc t m (ZqBasic q z) -> Cyc t m (ZqBasic q z)

adviseDec :: Cyc t m (ZqBasic q z) -> Cyc t m (ZqBasic q z)

adviseCRT :: Cyc t m (ZqBasic q z) -> Cyc t m (ZqBasic q z)

(Reflects q z, ToInteger z, Ring (ZqBasic q z)) => CRTEmbed (ZqBasic q z)

Embeds into the complex numbers \( \C \).

Defined in Crypto.Lol.Types.Unsafe.ZqBasic

Associated Types

type CRTExt (ZqBasic q z) :: Type

Methods

toExt :: ZqBasic q z -> CRTExt (ZqBasic q z)

fromExt :: CRTExt (ZqBasic q z) -> ZqBasic q z

Eq r => ApproxEqual (ZqBasic q r)

Defined in Crypto.Lol.Utils.Tests

Methods

(=~=) :: ZqBasic q r -> ZqBasic q r -> Bool

(Fact m, CRTElt t Double, Protoable (CycG t m (ZqBasic q z))) => Protoable (Cyc t m (ZqBasic q z))

Defined in Crypto.Lol.Cyclotomic.Cyc

Associated Types

type ProtoType (Cyc t m (ZqBasic q z)) :: Type

Methods

toProto :: Cyc t m (ZqBasic q z) -> ProtoType (Cyc t m (ZqBasic q z))

fromProto :: MonadError String m0 => ProtoType (Cyc t m (ZqBasic q z)) -> m0 (Cyc t m (ZqBasic q z))

(Module (ZqBasic q z) (CycG t m (ZqBasic q z)), Ring (ZqBasic q z)) => C (ZqBasic q z) (Cyc t m (ZqBasic q z))

Defined in Crypto.Lol.Cyclotomic.Cyc

Methods

(*>) :: ZqBasic q z -> Cyc t m (ZqBasic q z) -> Cyc t m (ZqBasic q z)

(Ring (GF (ZqBasic q z) d), Module (GF (ZqBasic q z) d) (CycG t m (ZqBasic q z))) => C (GF (ZqBasic q z) d) (Cyc t m (ZqBasic q z))

Defined in Crypto.Lol.Cyclotomic.Cyc

Methods

(*>) :: GF (ZqBasic q z) d -> Cyc t m (ZqBasic q z) -> Cyc t m (ZqBasic q z)

(Reflects p z, Reflects q z, IntegralDomain z, Field (ZqBasic q z), Field (ZqBasic p z)) => Encode (ZqBasic p z) (ZqBasic q z)

Defined in Crypto.Lol.Types.Unsafe.ZqBasic

Methods

lsdToMSD :: (ZqBasic p z, ZqBasic q z)

(Reflects q z, ToInteger z, Reflects q' z, Ring z) => Rescale (ZqBasic q z) (ZqBasic q' z)

Defined in Crypto.Lol.Types.Unsafe.ZqBasic

Methods

rescale :: ZqBasic q z -> ZqBasic q' z

(Reflects q Int64, Functor (t m)) => Reduce (Cyc t m Integer) (Cyc t m (ZqBasic q Int64))

Defined in Crypto.Lol.Cyclotomic.Cyc

Methods

reduce :: Cyc t m Integer -> Cyc t m (ZqBasic q Int64)

Reduce (CycG t m Int64) (CycG t m (ZqBasic q Int64)) => Reduce (Cyc t m Int64) (Cyc t m (ZqBasic q Int64))

Defined in Crypto.Lol.Cyclotomic.Cyc

Methods

reduce :: Cyc t m Int64 -> Cyc t m (ZqBasic q Int64)

(ToInteger z, RealField r, Reflects q z, Reflects q r) => Subgroup (ZqBasic q z) (RRq q r)

Defined in Crypto.Lol.Types.Unsafe.RRq

Methods

fromSubgroup :: ZqBasic q z -> RRq q r

newtype Cyc t m (ZqBasic q z)

Defined in Crypto.Lol.Cyclotomic.Cyc

newtype Cyc t m (ZqBasic q z) = CycZqB {

• unCycZqB :: CycG t m (ZqBasic q z)

}

type CharOf (ZqBasic p z)

Defined in Crypto.Lol.Types.Unsafe.ZqBasic

type CharOf (ZqBasic p z) = p

type ProtoType (IZipVector m (ZqBasic q Int64, b))

Defined in Crypto.Lol.Types.IZipVector

type ProtoType (IZipVector m (ZqBasic q Int64, b)) = RqProduct

type ProtoType (IZipVector m (ZqBasic q Int64))

Defined in Crypto.Lol.Types.IZipVector

type ProtoType (IZipVector m (ZqBasic q Int64)) = RqProduct

type LiftOf (ZqBasic q z)

Defined in Crypto.Lol.Types.Unsafe.ZqBasic

type LiftOf (ZqBasic q z) = z

type ModRep (ZqBasic q z)

Defined in Crypto.Lol.Types.Unsafe.ZqBasic

type ModRep (ZqBasic q z) = z

type DecompOf (ZqBasic q z)

Defined in Crypto.Lol.Types.Unsafe.ZqBasic

type DecompOf (ZqBasic q z) = z

type DecompOf (ZqBasic q z)

Defined in Crypto.Lol.Types.Unsafe.ZqBasic

type DecompOf (ZqBasic q z) = z

type DecompOf (Cyc t m (ZqBasic q Int64))

Defined in Crypto.Lol.Cyclotomic.Cyc

type DecompOf (Cyc t m (ZqBasic q Int64)) = Cyc t m Int64

type CRTExt (ZqBasic q z)

Defined in Crypto.Lol.Types.Unsafe.ZqBasic

type CRTExt (ZqBasic q z) = Complex Double

type ProtoType (Cyc t m (ZqBasic q z))

Defined in Crypto.Lol.Cyclotomic.Cyc

type ProtoType (Cyc t m (ZqBasic q z))

goodQs :: ToInteger a => a -> a -> [a]

An infinite list of primes greater than lower and congruent to 1 mod m.