Crypto.Lol.Types.ZqBasic

\( \def\Z{\mathbb{Z}} \) \( \def\C{\mathbb{C}} \) An implementation of the quotient ring \(\Z_q = \Z/(q\Z)\).

Documentation

data ZqBasic q z

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

Instances

Unbox z => Vector Vector (ZqBasic k q z)

Methods

basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) (ZqBasic k q z) -> m (Vector (ZqBasic k q z))

basicUnsafeThaw :: PrimMonad m => Vector (ZqBasic k q z) -> m (Mutable Vector (PrimState m) (ZqBasic k q z))

basicLength :: Vector (ZqBasic k q z) -> Int

basicUnsafeSlice :: Int -> Int -> Vector (ZqBasic k q z) -> Vector (ZqBasic k q z)

basicUnsafeIndexM :: Monad m => Vector (ZqBasic k q z) -> Int -> m (ZqBasic k q z)

basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) (ZqBasic k q z) -> Vector (ZqBasic k q z) -> m ()

elemseq :: Vector (ZqBasic k q z) -> ZqBasic k q z -> b -> b

Unbox z => MVector MVector (ZqBasic k q z)

Methods

basicLength :: MVector s (ZqBasic k q z) -> Int

basicUnsafeSlice :: Int -> Int -> MVector s (ZqBasic k q z) -> MVector s (ZqBasic k q z)

basicOverlaps :: MVector s (ZqBasic k q z) -> MVector s (ZqBasic k q z) -> Bool

basicUnsafeNew :: PrimMonad m => Int -> m (MVector (PrimState m) (ZqBasic k q z))

basicInitialize :: PrimMonad m => MVector (PrimState m) (ZqBasic k q z) -> m ()

basicUnsafeReplicate :: PrimMonad m => Int -> ZqBasic k q z -> m (MVector (PrimState m) (ZqBasic k q z))

basicUnsafeRead :: PrimMonad m => MVector (PrimState m) (ZqBasic k q z) -> Int -> m (ZqBasic k q z)

basicUnsafeWrite :: PrimMonad m => MVector (PrimState m) (ZqBasic k q z) -> Int -> ZqBasic k q z -> m ()

basicClear :: PrimMonad m => MVector (PrimState m) (ZqBasic k q z) -> m ()

basicSet :: PrimMonad m => MVector (PrimState m) (ZqBasic k q z) -> ZqBasic k q z -> m ()

basicUnsafeCopy :: PrimMonad m => MVector (PrimState m) (ZqBasic k q z) -> MVector (PrimState m) (ZqBasic k q z) -> m ()

basicUnsafeMove :: PrimMonad m => MVector (PrimState m) (ZqBasic k q z) -> MVector (PrimState m) (ZqBasic k q z) -> m ()

basicUnsafeGrow :: PrimMonad m => MVector (PrimState m) (ZqBasic k q z) -> Int -> m (MVector (PrimState m) (ZqBasic k q z))

(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 k m Int => TaggedT k * 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]

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

Associated Types

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

Methods

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

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

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

Associated Types

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

Methods

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

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

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

Methods

arbitrary :: Gen (ZqBasic k q z)

shrink :: ZqBasic k q z -> [ZqBasic k q z]

Storable z => Storable (ZqBasic k q z)

Methods

sizeOf :: ZqBasic k q z -> Int

alignment :: ZqBasic k q z -> Int

peekElemOff :: Ptr (ZqBasic k q z) -> Int -> IO (ZqBasic k q z)

pokeElemOff :: Ptr (ZqBasic k q z) -> Int -> ZqBasic k q z -> IO ()

peekByteOff :: Ptr b -> Int -> IO (ZqBasic k q z)

pokeByteOff :: Ptr b -> Int -> ZqBasic k q z -> IO ()

peek :: Ptr (ZqBasic k q z) -> IO (ZqBasic k q z)

poke :: Ptr (ZqBasic k q z) -> ZqBasic k q z -> IO ()

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)

(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

C z => C (ZqBasic k q z)

Methods

isZero :: ZqBasic k q z -> Bool

(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

Elt z => Elt (ZqBasic k q z)

Methods

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

zero :: ZqBasic k q z

one :: ZqBasic k q z

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

Methods

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

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

Methods

rescale :: ZqBasic k q z -> ZqBasic k1 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

data MVector s (ZqBasic k q z)

data MVector s (ZqBasic k q z) = MV_ZqBasic (MVector s z)

type CharOf k (ZqBasic k p z)

type CharOf k (ZqBasic k p z) = p

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

type ProtoType (CT m (ZqBasic k q Int64)) = Rq

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

type ProtoType (RT m (ZqBasic k q Int64)) = Rq

data Vector (ZqBasic k q z)

data Vector (ZqBasic k q z) = V_ZqBasic (Vector z)

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 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

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