Copyright	(c) Eric Crockett 2011-2017 Chris Peikert 2011-2017
License	GPL-3
Maintainer	ecrockett0@email.com
Stability	experimental
Portability	POSIX \( \def\Z{\mathbb{Z}} \) \( \def\C{\mathbb{C}} \)
Safe Haskell	None
Language	Haskell2010

Crypto.Lol.Types.Unsafe.ZqBasic

Description

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.

Synopsis

newtype ZqBasic q z = ZqB {
- unZqB :: z
}
goodQs :: ToInteger a => a -> a -> [a]

Documentation

newtype ZqBasic q z Source #

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

Constructors

ZqB
Fields unZqB :: z

Instances

Correct gad (CycG t m (ZqBasic q Int64)) => Correct (gad :: k2) (Cyc t m (ZqBasic q Int64)) Source #
Instance details 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))]) Source #
(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)) Source #
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc Associated Types type DecompOf (Cyc t m (ZqBasic q Int64)) :: Type Source # Methods decompose :: Cyc t m (ZqBasic q Int64) -> [DecompOf (Cyc t m (ZqBasic q Int64))] Source #
Gadget gad (CycG t m (ZqBasic q z)) => Gadget (gad :: k2) (Cyc t m (ZqBasic q z)) Source #
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc Methods gadget :: [Cyc t m (ZqBasic q z)] Source # encode :: Cyc t m (ZqBasic q z) -> [Cyc t m (ZqBasic q z)] Source #
(Reflects q z, ToInteger z) => Reduce Integer (ZqBasic q z) Source #
Instance details Defined in Crypto.Lol.Types.Unsafe.ZqBasic Methods reduce :: Integer -> ZqBasic q z Source #
(Reflects q z, IntegralDomain z) => Reduce z (ZqBasic q z) Source #
Instance details Defined in Crypto.Lol.Types.Unsafe.ZqBasic Methods reduce :: z -> ZqBasic q z Source #
(Reflects q z, ToInteger z, PID z, Enum z, NFData z) => CRTrans Maybe (ZqBasic q z) Source #
Instance details Defined in Crypto.Lol.Types.Unsafe.ZqBasic Methods crtInfo :: Reflects m Int => TaggedT m Maybe (CRTInfo (ZqBasic q z)) Source #
CRTElt t (ZqBasic q z) => UnCyc t (ZqBasic q z) Source #
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc Methods cycPow :: Fact m => CycRep t P m (ZqBasic q z) -> Cyc t m (ZqBasic q z) Source # cycDec :: Fact m => CycRep t D m (ZqBasic q z) -> Cyc t m (ZqBasic q z) Source # unCycPow :: Fact m => Cyc t m (ZqBasic q z) -> CycRep t P m (ZqBasic q z) Source # unCycDec :: Fact m => Cyc t m (ZqBasic q z) -> CycRep t D m (ZqBasic q z) Source #
(Reflects q z, ToInteger z, Ring z) => Correct TrivGad (ZqBasic q z) Source #
Instance details Defined in Crypto.Lol.Types.Unsafe.ZqBasic Methods correct :: [ZqBasic q z] -> (ZqBasic q z, [LiftOf (ZqBasic q z)]) Source #
(Reflects q z, ToInteger z) => Decompose TrivGad (ZqBasic q z) Source #
Instance details Defined in Crypto.Lol.Types.Unsafe.ZqBasic Associated Types type DecompOf (ZqBasic q z) :: Type Source # Methods decompose :: ZqBasic q z -> [DecompOf (ZqBasic q z)] Source #
(Reflects q z, ToInteger z) => Gadget TrivGad (ZqBasic q z) Source #
Instance details Defined in Crypto.Lol.Types.Unsafe.ZqBasic Methods gadget :: [ZqBasic q z] Source # encode :: ZqBasic q z -> [ZqBasic q z] Source #
(Reflects q z, ToInteger z, Reflects b z) => Correct (BaseBGad b :: Type) (ZqBasic q z) Source #
Instance details Defined in Crypto.Lol.Types.Unsafe.ZqBasic Methods correct :: [ZqBasic q z] -> (ZqBasic q z, [LiftOf (ZqBasic q z)]) Source #
(Reflects q z, ToInteger z, Reflects b z) => Decompose (BaseBGad b :: Type) (ZqBasic q z) Source #
Instance details Defined in Crypto.Lol.Types.Unsafe.ZqBasic Associated Types type DecompOf (ZqBasic q z) :: Type Source # Methods decompose :: ZqBasic q z -> [DecompOf (ZqBasic q z)] Source #
(Reflects q z, ToInteger z, RealIntegral z, Reflects b z) => Gadget (BaseBGad b :: Type) (ZqBasic q z) Source #
Instance details Defined in Crypto.Lol.Types.Unsafe.ZqBasic Methods gadget :: [ZqBasic q z] Source # encode :: ZqBasic q z -> [ZqBasic q z] Source #
CRTSetCyc (CycG t) (ZqBasic q z) => CRTSetCyc (Cyc t) (ZqBasic q z) Source #
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc Methods crtSet :: Divides m m' => Tagged m [Cyc t m' (ZqBasic q z)] Source #
ExtensionCyc (CycG t) (ZqBasic q z) => ExtensionCyc (Cyc t) (ZqBasic q z) Source #
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc Methods embed :: Divides m m' => Cyc t m (ZqBasic q z) -> Cyc t m' (ZqBasic q z) Source # twace :: Divides m m' => Cyc t m' (ZqBasic q z) -> Cyc t m (ZqBasic q z) Source # powBasis :: Divides m m' => Tagged m [Cyc t m' (ZqBasic q z)] Source # coeffsCyc :: Divides m m' => Basis -> Cyc t m' (ZqBasic q z) -> [Cyc t m (ZqBasic q z)] Source #
(Mod (ZqBasic q z), Show z) => Show (ArgType (ZqBasic q z)) Source #
Instance details 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)) Source #
Instance details Defined in Crypto.Lol.Types.IZipVector Associated Types type ProtoType (IZipVector m (ZqBasic q Int64, b)) :: Type Source # Methods toProto :: IZipVector m (ZqBasic q Int64, b) -> ProtoType (IZipVector m (ZqBasic q Int64, b)) Source # fromProto :: MonadError String m0 => ProtoType (IZipVector m (ZqBasic q Int64, b)) -> m0 (IZipVector m (ZqBasic q Int64, b)) Source #
(Fact m, Reflects q Int64) => Protoable (IZipVector m (ZqBasic q Int64)) Source #
Instance details Defined in Crypto.Lol.Types.IZipVector Associated Types type ProtoType (IZipVector m (ZqBasic q Int64)) :: Type Source # Methods toProto :: IZipVector m (ZqBasic q Int64) -> ProtoType (IZipVector m (ZqBasic q Int64)) Source # fromProto :: MonadError String m0 => ProtoType (IZipVector m (ZqBasic q Int64)) -> m0 (IZipVector m (ZqBasic q Int64)) Source #
(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) Source #	rescale up by one additional modulus
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc Methods rescaleCyc :: Basis -> Cyc t m b -> Cyc t m (ZqBasic q z, b) Source #
(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) Source #
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc Methods fmapCyc :: Maybe Basis -> (Int64 -> ZqBasic q z) -> Cyc t m Int64 -> Cyc t m (ZqBasic q z) Source #
(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) Source #
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc Methods fmapCyc :: Maybe Basis -> (Double -> ZqBasic q z) -> Cyc t m Double -> Cyc t m (ZqBasic q z) Source #
(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 Source #	specialized (faster) rescale-down by a single \(\Z_q\)
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc Methods rescaleCyc :: Basis -> Cyc t m (ZqBasic q z, b) -> Cyc t m b Source #
(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) Source #
Instance details 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) Source #
FoldableCyc (CycG t m) (ZqBasic q z) => FoldableCyc (Cyc t m) (ZqBasic q z) Source #
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc Methods foldrCyc :: Maybe Basis -> (ZqBasic q z -> b -> b) -> b -> Cyc t m (ZqBasic q z) -> b Source #
(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 Source #
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc Methods fmapCyc :: Maybe Basis -> (ZqBasic q z -> Int64) -> Cyc t m (ZqBasic q z) -> Cyc t m Int64 Source #
(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 Source #
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc Methods fmapCyc :: Maybe Basis -> (ZqBasic q z -> Double) -> Cyc t m (ZqBasic q z) -> Cyc t m Double Source #
(Fact m, Functor (t m), UnCyc t (ZqBasic q z)) => FunctorCyc (Cyc t m) (ZqBasic q z) Integer Source #
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc Methods fmapCyc :: Maybe Basis -> (ZqBasic q z -> Integer) -> Cyc t m (ZqBasic q z) -> Cyc t m Integer Source #
(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) Source #
Instance details 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) Source #
RescaleCyc (CycG t m) (ZqBasic q z) (ZqBasic p z) => RescaleCyc (Cyc t m) (ZqBasic q z) (ZqBasic p z) Source #	rescale from one modulus to another
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc Methods rescaleCyc :: Basis -> Cyc t m (ZqBasic q z) -> Cyc t m (ZqBasic p z) Source #
(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) Source #
Instance details 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) Source #
(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) Source #
Instance details 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) Source #
(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) Source #
Instance details 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) Source #
Eq z => Eq (ZqBasic q z) Source #
Instance details 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)) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details 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)) Source #
Instance details 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) Source #
Instance details 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)) Source #
Instance details 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) Source #
Instance details 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)) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details 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)) Source #
Instance details 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) Source #
Instance details 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)) Source #
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc Methods isZero :: Cyc t m (ZqBasic q z) -> Bool #
(Reflects q z, IntegralDomain z) => C (ZqBasic q z) Source #
Instance details 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)) Source #
Instance details 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) Source #
Instance details Defined in Crypto.Lol.Types.Unsafe.ZqBasic Methods lift :: ZqBasic q z -> LiftOf (ZqBasic q z) Source #
(Reflects q z, ToInteger z) => Mod (ZqBasic q z) Source #
Instance details Defined in Crypto.Lol.Types.Unsafe.ZqBasic Associated Types type ModRep (ZqBasic q z) :: Type Source # Methods modulus :: ModRep (ZqBasic q z) Source #
(Reflects q z, Ring z, Enum z) => Enumerable (ZqBasic q z) Source #
Instance details Defined in Crypto.Lol.Types.Unsafe.ZqBasic Methods values :: [ZqBasic q z] Source #
CosetGaussianCyc (CycG t m (ZqBasic q Int64)) => CosetGaussianCyc (Cyc t m (ZqBasic q Int64)) Source #	uses `Double` for the intermediate Gaussian samples
Instance details 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))) Source #
Cyclotomic (CycG t m (ZqBasic q z)) => Cyclotomic (Cyc t m (ZqBasic q z)) Source #
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc Methods mulG :: Cyc t m (ZqBasic q z) -> Cyc t m (ZqBasic q z) Source # divG :: Cyc t m (ZqBasic q z) -> Maybe (Cyc t m (ZqBasic q z)) Source # advisePow :: Cyc t m (ZqBasic q z) -> Cyc t m (ZqBasic q z) Source # adviseDec :: Cyc t m (ZqBasic q z) -> Cyc t m (ZqBasic q z) Source # adviseCRT :: Cyc t m (ZqBasic q z) -> Cyc t m (ZqBasic q z) Source #
(Reflects q z, ToInteger z, Ring (ZqBasic q z)) => CRTEmbed (ZqBasic q z) Source #	Embeds into the complex numbers \( \C \).
Instance details Defined in Crypto.Lol.Types.Unsafe.ZqBasic Associated Types type CRTExt (ZqBasic q z) :: Type Source # Methods toExt :: ZqBasic q z -> CRTExt (ZqBasic q z) Source # fromExt :: CRTExt (ZqBasic q z) -> ZqBasic q z Source #
Eq r => ApproxEqual (ZqBasic q r) Source #
Instance details Defined in Crypto.Lol.Utils.Tests Methods (=~=) :: ZqBasic q r -> ZqBasic q r -> Bool Source #
(Fact m, CRTElt t Double, Protoable (CycG t m (ZqBasic q z))) => Protoable (Cyc t m (ZqBasic q z)) Source #
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc Associated Types type ProtoType (Cyc t m (ZqBasic q z)) :: Type Source # Methods toProto :: Cyc t m (ZqBasic q z) -> ProtoType (Cyc t m (ZqBasic q z)) Source # fromProto :: MonadError String m0 => ProtoType (Cyc t m (ZqBasic q z)) -> m0 (Cyc t m (ZqBasic q z)) Source #
(Module (ZqBasic q z) (CycG t m (ZqBasic q z)), Ring (ZqBasic q z)) => C (ZqBasic q z) (Cyc t m (ZqBasic q z)) Source #
Instance details 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)) Source #
Instance details 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) Source #
Instance details Defined in Crypto.Lol.Types.Unsafe.ZqBasic Methods lsdToMSD :: (ZqBasic p z, ZqBasic q z) Source #
(Reflects q z, ToInteger z, Reflects q' z, Ring z) => Rescale (ZqBasic q z) (ZqBasic q' z) Source #
Instance details Defined in Crypto.Lol.Types.Unsafe.ZqBasic Methods rescale :: ZqBasic q z -> ZqBasic q' z Source #
(Reflects q Int64, Functor (t m)) => Reduce (Cyc t m Integer) (Cyc t m (ZqBasic q Int64)) Source #
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc Methods reduce :: Cyc t m Integer -> Cyc t m (ZqBasic q Int64) Source #
Reduce (CycG t m Int64) (CycG t m (ZqBasic q Int64)) => Reduce (Cyc t m Int64) (Cyc t m (ZqBasic q Int64)) Source #
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc Methods reduce :: Cyc t m Int64 -> Cyc t m (ZqBasic q Int64) Source #
(ToInteger z, RealField r, Reflects q z, Reflects q r) => Subgroup (ZqBasic q z) (RRq q r) Source #
Instance details Defined in Crypto.Lol.Types.Unsafe.RRq Methods fromSubgroup :: ZqBasic q z -> RRq q r Source #
newtype Cyc t m (ZqBasic q z) Source #
Instance details 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) Source #
Instance details Defined in Crypto.Lol.Types.Unsafe.ZqBasic type CharOf (ZqBasic p z) = p
type ProtoType (IZipVector m (ZqBasic q Int64, b)) Source #
Instance details Defined in Crypto.Lol.Types.IZipVector type ProtoType (IZipVector m (ZqBasic q Int64, b)) = RqProduct
type ProtoType (IZipVector m (ZqBasic q Int64)) Source #
Instance details Defined in Crypto.Lol.Types.IZipVector type ProtoType (IZipVector m (ZqBasic q Int64)) = RqProduct
type LiftOf (ZqBasic q z) Source #
Instance details Defined in Crypto.Lol.Types.Unsafe.ZqBasic type LiftOf (ZqBasic q z) = z
type ModRep (ZqBasic q z) Source #
Instance details Defined in Crypto.Lol.Types.Unsafe.ZqBasic type ModRep (ZqBasic q z) = z
type DecompOf (ZqBasic q z) Source #
Instance details Defined in Crypto.Lol.Types.Unsafe.ZqBasic type DecompOf (ZqBasic q z) = z
type DecompOf (ZqBasic q z) Source #
Instance details Defined in Crypto.Lol.Types.Unsafe.ZqBasic type DecompOf (ZqBasic q z) = z
type DecompOf (Cyc t m (ZqBasic q Int64)) Source #
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc type DecompOf (Cyc t m (ZqBasic q Int64)) = Cyc t m Int64
type CRTExt (ZqBasic q z) Source #
Instance details Defined in Crypto.Lol.Types.Unsafe.ZqBasic type CRTExt (ZqBasic q z) = Complex Double
type ProtoType (Cyc t m (ZqBasic q z)) Source #
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc type ProtoType (Cyc t m (ZqBasic q z))

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

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