Crypto.Lol.Types.Unsafe.ZqBasic

An implementation of the quotient ring \(\Z_q = \Z/(q\Z)\). This module is "unsafe" because it exports the ZqBasic constructor. This module should only be used to make tensor-specific instances for ZqBasic. The safe way to use this type is to import Crypto.Lol.Types.

EAC: It may help GHC do specialization at higher levels of the library if we "simplify" constraints in this module. For example, replace the (Additive (ZqBasic q z)) constraint on the Reduce instance with (Additive z)

Documentation

newtype ZqBasic q z

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

Constructors

ZqB z

Instances

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

Methods

reduce :: Integer -> ZqBasic k q z

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

Methods

reduce :: z -> ZqBasic k q z

(Reflects k q z, ToInteger z, PID z, Enumerable (ZqBasic k q z)) => CRTrans Maybe (ZqBasic k q z)

Methods

crtInfo :: Reflects k1 m Int => TaggedT * k1 m Maybe (CRTInfo (ZqBasic k q z))

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

Methods

correct :: Tagged TrivGad (ZqBasic k q z) [u] -> (u, [LiftOf u])

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

Associated Types

type DecompOf u :: *

Methods

decompose :: u -> Tagged TrivGad (ZqBasic k q z) [DecompOf u]

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

Methods

gadget :: Tagged TrivGad (ZqBasic k q z) [u]

encode :: u -> Tagged TrivGad (ZqBasic k q z) [u]

(Reflects k1 q z, ToInteger z, Reflects k b z) => Correct * (BaseBGad k b) (ZqBasic k1 q z)

Methods

correct :: Tagged (BaseBGad k b) (ZqBasic k1 q z) [u] -> (u, [LiftOf u])

(Reflects k1 q z, ToInteger z, Reflects k b z) => Decompose * (BaseBGad k b) (ZqBasic k1 q z)

Associated Types

type DecompOf u :: *

Methods

decompose :: u -> Tagged (BaseBGad k b) (ZqBasic k1 q z) [DecompOf u]

(Reflects k1 q z, ToInteger z, RealIntegral z, Reflects k b z) => Gadget * (BaseBGad k b) (ZqBasic k1 q z)

Methods

gadget :: Tagged (BaseBGad k b) (ZqBasic k1 q z) [u]

encode :: u -> Tagged (BaseBGad k b) (ZqBasic k1 q z) [u]

(Mod (ZqBasic k q i), Show i) => Show (ArgType * (ZqBasic k q i))

Methods

showsPrec :: Int -> ArgType * (ZqBasic k q i) -> ShowS

show :: ArgType * (ZqBasic k q i) -> String

showList :: [ArgType * (ZqBasic k q i)] -> ShowS

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

Associated Types

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

Methods

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

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

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

Associated Types

type ProtoType (IZipVector m (ZqBasic k q Int64)) :: *

Methods

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

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

Eq z => Eq (ZqBasic k q z)

Methods

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

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

Ord z => Ord (ZqBasic k q z)

Methods

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

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

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

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

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

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

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

Show z => Show (ZqBasic k q z)

Methods

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

show :: ZqBasic k q z -> String

showList :: [ZqBasic k q z] -> ShowS

(Reflects k q z, ToInteger z, Random z) => Random (ZqBasic k q z)

Methods

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

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

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

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

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

randomIO :: IO (ZqBasic k q z)

NFData z => NFData (ZqBasic k q z)

Methods

rnf :: ZqBasic k q z -> ()

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

Methods

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

recip :: ZqBasic k q z -> ZqBasic k q z

fromRational' :: Rational -> ZqBasic k q z

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

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

Methods

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

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

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

C z => C (ZqBasic k q z)

Methods

isZero :: ZqBasic k q z -> Bool

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

Methods

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

one :: ZqBasic k q z

fromInteger :: Integer -> ZqBasic k q z

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

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

Methods

zero :: ZqBasic k q z

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

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

negate :: ZqBasic k q z -> ZqBasic k q z

(Reflects k q z, ToInteger z) => Lift' (ZqBasic k q z)

Methods

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

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

Associated Types

type ModRep (ZqBasic k q z) :: *

Methods

modulus :: Tagged * (ZqBasic k q z) (ModRep (ZqBasic k q z))

(Reflects k q z, ToInteger z, Enum z) => Enumerable (ZqBasic k q z)

Methods

values :: [ZqBasic k q z]

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

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

Associated Types

type CRTExt (ZqBasic k q z) :: *

Methods

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

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

(PPow pp, (~) * zq (ZqBasic PrimePower pp z), PrimeField (ZpOf zq), Ring zq) => ZPP (ZqBasic PrimePower pp z)

Associated Types

type ZpOf (ZqBasic PrimePower pp z) :: *

Methods

modulusZPP :: Tagged * (ZqBasic PrimePower pp z) PP

liftZp :: ZpOf (ZqBasic PrimePower pp z) -> ZqBasic PrimePower pp z

(Reflects k1 p z, Reflects k q z, ToInteger z, Field (ZqBasic k q z), Field (ZqBasic k1 p z)) => Encode (ZqBasic k1 p z) (ZqBasic k q z)

Methods

lsdToMSD :: (ZqBasic k1 p z, ZqBasic k q z)

(Reflects k1 q z, ToInteger z, Reflects k q' z, Ring z) => Rescale (ZqBasic k1 q z) (ZqBasic k q' z)

Methods

rescale :: ZqBasic k1 q z -> ZqBasic k q' z

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

Methods

fromSubgroup :: ZqBasic k q i -> RRq k q r

type CharOf k (ZqBasic k p z)

type CharOf k (ZqBasic k p z) = p

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

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

type ProtoType (IZipVector m (ZqBasic k q Int64))

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

type LiftOf (ZqBasic k q z)

type LiftOf (ZqBasic k q z) = z

type ModRep (ZqBasic k q z)

type ModRep (ZqBasic k q z) = z

type DecompOf (ZqBasic k q z)

type DecompOf (ZqBasic k q z) = z

type DecompOf (ZqBasic k q z)

type DecompOf (ZqBasic k q z) = z

type CRTExt (ZqBasic k q z)

type CRTExt (ZqBasic k q z) = Complex Double

type ZpOf (ZqBasic PrimePower pp z)

type ZpOf (ZqBasic PrimePower pp z) = ZqBasic PrimeBin (PrimePP pp) z

goodQs :: (IntegralDomain a, ToInteger a) => a -> a -> [a]