Copyright	(c) Eric Crockett 2011-2018 Chris Peikert 2011-2018
License	GPL-3
Maintainer	ecrockett0@gmail.com
Stability	experimental
Portability	POSIX \( \def\Z{\mathbb{Z}} \) \( \def\F{\mathbb{F}} \) \( \def\Q{\mathbb{Q}} \) \( \def\Tw{\text{Tw}} \) \( \def\Tr{\text{Tr}} \) \( \def\O{\mathcal{O}} \)
Safe Haskell	None
Language	Haskell2010

Crypto.Lol.Cyclotomic.Cyc

Contents

Data type
Constructors/deconstructors

Description

An implementation of cyclotomic rings that hides the internal representations of ring elements (e.g., the choice of basis), and also offers more efficient storage and operations on subring elements (including elements from the base ring itself).

For an implementation that allows (and requires) the programmer to control the underlying representation, see Crypto.Lol.Cyclotomic.CycRep.

WARNING: as with all fixed-point arithmetic, the functions associated with Cyc may result in overflow (and thereby incorrect answers and potential security flaws) if the input arguments are too close to the bounds imposed by the base type. The acceptable range of inputs for each function is determined by the internal linear transforms and other operations it performs.

Synopsis

data family Cyc (t :: Factored -> * -> *) (m :: Factored) r
class UnCyc t r where
- cycPow :: Fact m => CycRep t P m r -> Cyc t m r
- cycDec :: Fact m => CycRep t D m r -> Cyc t m r
- unCycPow :: Fact m => Cyc t m r -> CycRep t P m r
- unCycDec :: Fact m => Cyc t m r -> CycRep t D m r

Data type

data family Cyc (t :: Factored -> * -> *) (m :: Factored) r Source #

A cyclotomic ring such as \( \Z[\zeta_m] \), \( \Z_q[\zeta_m] \), or \( \Q[\zeta_m] \): t is the Tensor type for storing coefficient tensors; m is the cyclotomic index; r is the base ring of the coefficients (e.g., \(\ \Q \), \( \Z \), \( \Z_q \)).

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 (Cyc t m a), Decompose gad (Cyc t m b), DecompOf (Cyc t m a) ~ DecompOf (Cyc t m b), Reduce (DecompOf (Cyc t m a)) (Cyc t m (a, b))) => Decompose (gad :: k) (Cyc t m (a, b)) Source #
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc Associated Types type DecompOf (Cyc t m (a, b)) :: Type Source # Methods decompose :: Cyc t m (a, b) -> [DecompOf (Cyc t m (a, b))] 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 (Cyc t m a), Gadget gad (Cyc t m b)) => Gadget (gad :: k) (Cyc t m (a, b)) Source #
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc Methods gadget :: [Cyc t m (a, b)] Source # encode :: Cyc t m (a, b) -> [Cyc t m (a, b)] 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 #
Module Double (CycG t m Double) => C Double (Cyc t m Double) Source #
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc Methods (*>) :: Double -> Cyc t m Double -> Cyc t m Double #
Module Int64 (CycG t m Int64) => C Int64 (Cyc t m Int64) Source #
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc Methods (*>) :: Int64 -> Cyc t m Int64 -> Cyc t m Int64 #
CRTElt t Int64 => ExtensionCyc (Cyc t) Int64 Source #
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc Methods embed :: Divides m m' => Cyc t m Int64 -> Cyc t m' Int64 Source # twace :: Divides m m' => Cyc t m' Int64 -> Cyc t m Int64 Source # powBasis :: Divides m m' => Tagged m [Cyc t m' Int64] Source # coeffsCyc :: Divides m m' => Basis -> Cyc t m' Int64 -> [Cyc t m Int64] Source #
CRTElt t Double => ExtensionCyc (Cyc t) Double Source #
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc Methods embed :: Divides m m' => Cyc t m Double -> Cyc t m' Double Source # twace :: Divides m m' => Cyc t m' Double -> Cyc t m Double Source # powBasis :: Divides m m' => Tagged m [Cyc t m' Double] Source # coeffsCyc :: Divides m m' => Basis -> Cyc t m' Double -> [Cyc t m Double] Source #
(ExtensionCyc (Cyc t) a, ExtensionCyc (Cyc t) b) => ExtensionCyc (Cyc t) (a, b) Source #
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc Methods embed :: Divides m m' => Cyc t m (a, b) -> Cyc t m' (a, b) Source # twace :: Divides m m' => Cyc t m' (a, b) -> Cyc t m (a, b) Source # powBasis :: Divides m m' => Tagged m [Cyc t m' (a, b)] Source # coeffsCyc :: Divides m m' => Basis -> Cyc t m' (a, b) -> [Cyc t m (a, b)] 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 #
TensorPowDec t (RRq q r) => ExtensionCyc (Cyc t) (RRq q r) Source #
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc Methods embed :: Divides m m' => Cyc t m (RRq q r) -> Cyc t m' (RRq q r) Source # twace :: Divides m m' => Cyc t m' (RRq q r) -> Cyc t m (RRq q r) Source # powBasis :: Divides m m' => Tagged m [Cyc t m' (RRq q r)] Source # coeffsCyc :: Divides m m' => Basis -> Cyc t m' (RRq q r) -> [Cyc t m (RRq q r)] 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 #
Foldable (t m) => FoldableCyc (Cyc t m) Integer Source #
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc Methods foldrCyc :: Maybe Basis -> (Integer -> b -> b) -> b -> Cyc t m Integer -> b Source #
FoldableCyc (CycG t m) Int64 => FoldableCyc (Cyc t m) Int64 Source #
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc Methods foldrCyc :: Maybe Basis -> (Int64 -> b -> b) -> b -> Cyc t m Int64 -> b Source #
FoldableCyc (CycG t m) Double => FoldableCyc (Cyc t m) Double Source #
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc Methods foldrCyc :: Maybe Basis -> (Double -> b -> b) -> b -> Cyc t m Double -> b Source #
(Fact m, TensorGSqNorm t Int64, CRTElt t Int64) => GSqNormCyc (Cyc t m) Int64 Source #
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc Methods gSqNorm :: Cyc t m Int64 -> Int64 Source #
(Fact m, TensorGSqNorm t Double, CRTElt t Double) => GSqNormCyc (Cyc t m) Double Source #
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc Methods gSqNorm :: Cyc t m Double -> Double Source #
Functor (t m) => FunctorCyc (Cyc t m) Integer Integer Source #
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc Methods fmapCyc :: Maybe Basis -> (Integer -> Integer) -> Cyc t m Integer -> Cyc t m Integer Source #
(Fact m, UnCyc t Int64, UnCyc t Int64, IFunctor t, IFElt t Int64, IFElt t Int64) => FunctorCyc (Cyc t m) Int64 Int64 Source #
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc Methods fmapCyc :: Maybe Basis -> (Int64 -> Int64) -> Cyc t m Int64 -> Cyc t m Int64 Source #
(Fact m, UnCyc t Int64, UnCyc t Double, IFunctor t, IFElt t Int64, IFElt t Double) => FunctorCyc (Cyc t m) Int64 Double Source #
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc Methods fmapCyc :: Maybe Basis -> (Int64 -> Double) -> Cyc t m Int64 -> Cyc t m Double Source #
(Fact m, UnCyc t Double, UnCyc t Int64, IFunctor t, IFElt t Double, IFElt t Int64) => FunctorCyc (Cyc t m) Double Int64 Source #
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc Methods fmapCyc :: Maybe Basis -> (Double -> Int64) -> Cyc t m Double -> Cyc t m Int64 Source #
(Fact m, UnCyc t Double, UnCyc t Double, IFunctor t, IFElt t Double, IFElt t Double) => FunctorCyc (Cyc t m) Double Double Source #
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc Methods fmapCyc :: Maybe Basis -> (Double -> Double) -> Cyc t m Double -> Cyc t m Double Source #
(Fact m, Functor (t m), UnCyc t Int64) => FunctorCyc (Cyc t m) Int64 Integer Source #
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc Methods fmapCyc :: Maybe Basis -> (Int64 -> Integer) -> Cyc t m Int64 -> Cyc t m Integer Source #
(Fact m, Functor (t m), UnCyc t Double) => FunctorCyc (Cyc t m) Double Integer Source #
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc Methods fmapCyc :: Maybe Basis -> (Double -> Integer) -> Cyc t m Double -> Cyc t m Integer 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 (a, b), IFunctor t, IFElt t Int64, IFElt t (a, b)) => FunctorCyc (Cyc t m) Int64 (a, b) Source #
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc Methods fmapCyc :: Maybe Basis -> (Int64 -> (a, b)) -> Cyc t m Int64 -> Cyc t m (a, b) Source #
(Fact m, UnCyc t Double, UnCyc t (a, b), IFunctor t, IFElt t Double, IFElt t (a, b)) => FunctorCyc (Cyc t m) Double (a, b) Source #
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc Methods fmapCyc :: Maybe Basis -> (Double -> (a, b)) -> Cyc t m Double -> Cyc t m (a, 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 Int64, UnCyc t (RRq q r), IFunctor t, IFElt t Int64, IFElt t (RRq q r)) => FunctorCyc (Cyc t m) Int64 (RRq q r) Source #
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc Methods fmapCyc :: Maybe Basis -> (Int64 -> RRq q r) -> Cyc t m Int64 -> Cyc t m (RRq q r) 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 #
(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) Source #
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc Methods fmapCyc :: Maybe Basis -> (Double -> RRq q r) -> Cyc t m Double -> Cyc t m (RRq q r) Source #
(RescaleCyc (Cyc t m) (b, (c, (d, e))) e, RescaleCyc (Cyc t m) (a, (b, (c, (d, e)))) (b, (c, (d, e)))) => RescaleCyc (Cyc t m) (a, (b, (c, (d, e)))) e Source #	convenient rescale-down by multiple components at once
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc Methods rescaleCyc :: Basis -> Cyc t m (a, (b, (c, (d, e)))) -> Cyc t m e Source #
(RescaleCyc (Cyc t m) (b, (c, d)) d, RescaleCyc (Cyc t m) (a, (b, (c, d))) (b, (c, d))) => RescaleCyc (Cyc t m) (a, (b, (c, d))) d Source #	convenient rescale-down by multiple components at once
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc Methods rescaleCyc :: Basis -> Cyc t m (a, (b, (c, d))) -> Cyc t m d Source #
(RescaleCyc (Cyc t m) (b, c) c, RescaleCyc (Cyc t m) (a, (b, c)) (b, c)) => RescaleCyc (Cyc t m) (a, (b, c)) c Source #	convenient rescale-down by multiple components at once
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc Methods rescaleCyc :: Basis -> Cyc t m (a, (b, c)) -> Cyc t m c 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 Int64, IFunctor t, IFElt t (a, b), IFElt t Int64) => FunctorCyc (Cyc t m) (a, b) Int64 Source #
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc Methods fmapCyc :: Maybe Basis -> ((a, b) -> Int64) -> Cyc t m (a, b) -> Cyc t m Int64 Source #
(Fact m, UnCyc t (a, b), UnCyc t Double, IFunctor t, IFElt t (a, b), IFElt t Double) => FunctorCyc (Cyc t m) (a, b) Double Source #
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc Methods fmapCyc :: Maybe Basis -> ((a, b) -> Double) -> Cyc t m (a, b) -> Cyc t m Double Source #
(Fact m, Functor (t m), UnCyc t (a, b)) => FunctorCyc (Cyc t m) (a, b) Integer Source #
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc Methods fmapCyc :: Maybe Basis -> ((a, b) -> Integer) -> Cyc t m (a, b) -> Cyc t m Integer Source #
RescaleCyc (Cyc t m) (a, b) (a, b) Source #	no-op rescale for Cyc over pairs
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc Methods rescaleCyc :: Basis -> Cyc t m (a, b) -> Cyc t m (a, b) Source #
(Fact m, UnCyc t (a, b), UnCyc t (a, b), IFunctor t, IFElt t (a, b), IFElt t (a, b)) => FunctorCyc (Cyc t m) (a, b) (a, b) Source #
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc Methods fmapCyc :: Maybe Basis -> ((a, b) -> (a, b)) -> Cyc t m (a, b) -> Cyc t m (a, 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 #
(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) Source #
Instance details 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) Source #
(Module a (Cyc t m a), Module b (Cyc t m b)) => C (a, b) (Cyc t m (a, b)) Source #
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc Methods (*>) :: (a, b) -> Cyc t m (a, b) -> Cyc t m (a, b) #
(Fact m, TensorPowDec t (RRq q r), Foldable (t m)) => FoldableCyc (Cyc t m) (RRq q r) Source #
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc Methods foldrCyc :: Maybe Basis -> (RRq q r -> b -> b) -> b -> Cyc t m (RRq q r) -> b 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, 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 Source #
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc Methods fmapCyc :: Maybe Basis -> (RRq q r -> Int64) -> Cyc t m (RRq q r) -> Cyc t m Int64 Source #
(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 Source #
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc Methods fmapCyc :: Maybe Basis -> (RRq q r -> Double) -> Cyc t m (RRq q r) -> 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, Functor (t m), UnCyc t (RRq q r)) => FunctorCyc (Cyc t m) (RRq q r) Integer Source #
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc Methods fmapCyc :: Maybe Basis -> (RRq q r -> Integer) -> Cyc t m (RRq q r) -> 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 #
(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) Source #
Instance details 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) Source #
(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) Source #	rescale from one modulus to another
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc Methods rescaleCyc :: Basis -> Cyc t m (RRq q r) -> Cyc t m (RRq p r) 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 #
(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) Source #
Instance details 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) Source #
(Eq (Cyc t m a), Eq (Cyc t m b)) => Eq (Cyc t m (a, b)) Source #
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc Methods (==) :: Cyc t m (a, b) -> Cyc t m (a, b) -> Bool # (/=) :: Cyc t m (a, b) -> Cyc t m (a, b) -> 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 #
Eq (CycG t m Int64) => Eq (Cyc t m Int64) Source #
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc Methods (==) :: Cyc t m Int64 -> Cyc t m Int64 -> Bool # (/=) :: Cyc t m Int64 -> Cyc t m Int64 -> Bool #
Show (t m (RRq q r)) => Show (Cyc t m (RRq q r)) Source #
Instance details 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 #
Show (t m Integer) => Show (Cyc t m Integer) Source #
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc Methods showsPrec :: Int -> Cyc t m Integer -> ShowS # show :: Cyc t m Integer -> String # showList :: [Cyc t m Integer] -> ShowS #
(Show (Cyc t m a), Show (Cyc t m b)) => Show (Cyc t m (a, b)) Source #
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc Methods showsPrec :: Int -> Cyc t m (a, b) -> ShowS # show :: Cyc t m (a, b) -> String # showList :: [Cyc t m (a, b)] -> 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 #
Show (CycG t m Int64) => Show (Cyc t m Int64) Source #
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc Methods showsPrec :: Int -> Cyc t m Int64 -> ShowS # show :: Cyc t m Int64 -> String # showList :: [Cyc t m Int64] -> ShowS #
Show (CycG t m Double) => Show (Cyc t m Double) Source #
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc Methods showsPrec :: Int -> Cyc t m Double -> ShowS # show :: Cyc t m Double -> String # showList :: [Cyc t m Double] -> ShowS #
Random (t m (RRq q r)) => Random (Cyc t m (RRq q r)) Source #
Instance details 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)) #
(Random (t m Integer), Fact m) => Random (Cyc t m Integer) Source #
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc Methods randomR :: RandomGen g => (Cyc t m Integer, Cyc t m Integer) -> g -> (Cyc t m Integer, g) # random :: RandomGen g => g -> (Cyc t m Integer, g) # randomRs :: RandomGen g => (Cyc t m Integer, Cyc t m Integer) -> g -> [Cyc t m Integer] # randoms :: RandomGen g => g -> [Cyc t m Integer] # randomRIO :: (Cyc t m Integer, Cyc t m Integer) -> IO (Cyc t m Integer) # randomIO :: IO (Cyc t m Integer) #
(Random (Cyc t m a), Random (Cyc t m b)) => Random (Cyc t m (a, b)) Source #
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc Methods randomR :: RandomGen g => (Cyc t m (a, b), Cyc t m (a, b)) -> g -> (Cyc t m (a, b), g) # random :: RandomGen g => g -> (Cyc t m (a, b), g) # randomRs :: RandomGen g => (Cyc t m (a, b), Cyc t m (a, b)) -> g -> [Cyc t m (a, b)] # randoms :: RandomGen g => g -> [Cyc t m (a, b)] # randomRIO :: (Cyc t m (a, b), Cyc t m (a, b)) -> IO (Cyc t m (a, b)) # randomIO :: IO (Cyc t m (a, b)) #
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)) #
Random (CycG t m Int64) => Random (Cyc t m Int64) Source #
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc Methods randomR :: RandomGen g => (Cyc t m Int64, Cyc t m Int64) -> g -> (Cyc t m Int64, g) # random :: RandomGen g => g -> (Cyc t m Int64, g) # randomRs :: RandomGen g => (Cyc t m Int64, Cyc t m Int64) -> g -> [Cyc t m Int64] # randoms :: RandomGen g => g -> [Cyc t m Int64] # randomRIO :: (Cyc t m Int64, Cyc t m Int64) -> IO (Cyc t m Int64) # randomIO :: IO (Cyc t m Int64) #
Random (CycG t m Double) => Random (Cyc t m Double) Source #
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc Methods randomR :: RandomGen g => (Cyc t m Double, Cyc t m Double) -> g -> (Cyc t m Double, g) # random :: RandomGen g => g -> (Cyc t m Double, g) # randomRs :: RandomGen g => (Cyc t m Double, Cyc t m Double) -> g -> [Cyc t m Double] # randoms :: RandomGen g => g -> [Cyc t m Double] # randomRIO :: (Cyc t m Double, Cyc t m Double) -> IO (Cyc t m Double) # randomIO :: IO (Cyc t m Double) #
(Fact m, forall (m' :: Factored). Fact m' => NFData (t m' (RRq q r))) => NFData (Cyc t m (RRq q r)) Source #
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc Methods rnf :: Cyc t m (RRq q r) -> () #
(Fact m, forall (m' :: Factored). Fact m' => NFData (t m' Integer)) => NFData (Cyc t m Integer) Source #
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc Methods rnf :: Cyc t m Integer -> () #
(NFData (Cyc t m a), NFData (Cyc t m b)) => NFData (Cyc t m (a, b)) Source #
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc Methods rnf :: Cyc t m (a, b) -> () #
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) -> () #
NFData (CycG t m Int64) => NFData (Cyc t m Int64) Source #
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc Methods rnf :: Cyc t m Int64 -> () #
NFData (CycG t m Double) => NFData (Cyc t m Double) Source #
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc Methods rnf :: Cyc t m Double -> () #
(Ring (Cyc t m a), Ring (Cyc t m b)) => C (Cyc t m (a, b)) Source #
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc Methods (*) :: Cyc t m (a, b) -> Cyc t m (a, b) -> Cyc t m (a, b) # one :: Cyc t m (a, b) # fromInteger :: Integer -> Cyc t m (a, b) # (^) :: Cyc t m (a, b) -> Integer -> Cyc t m (a, b) #
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) #
Ring (CycG t m Int64) => C (Cyc t m Int64) Source #
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc Methods (*) :: Cyc t m Int64 -> Cyc t m Int64 -> Cyc t m Int64 # one :: Cyc t m Int64 # fromInteger :: Integer -> Cyc t m Int64 # (^) :: Cyc t m Int64 -> Integer -> Cyc t m Int64 #
Ring (CycG t m Double) => C (Cyc t m Double) Source #
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc Methods (*) :: Cyc t m Double -> Cyc t m Double -> Cyc t m Double # one :: Cyc t m Double # fromInteger :: Integer -> Cyc t m Double # (^) :: Cyc t m Double -> Integer -> Cyc t m Double #
ZeroTestable (t m (RRq q r)) => C (Cyc t m (RRq q r)) Source #
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc Methods isZero :: Cyc t m (RRq q r) -> Bool #
ZeroTestable (t m Integer) => C (Cyc t m Integer) Source #
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc Methods isZero :: Cyc t m Integer -> Bool #
(ZeroTestable (Cyc t m a), ZeroTestable (Cyc t m b)) => C (Cyc t m (a, b)) Source #
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc Methods isZero :: Cyc t m (a, b) -> 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 #
ZeroTestable (CycG t m Int64) => C (Cyc t m Int64) Source #
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc Methods isZero :: Cyc t m Int64 -> Bool #
ZeroTestable (CycG t m Double) => C (Cyc t m Double) Source #
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc Methods isZero :: Cyc t m Double -> Bool #
(Additive (RRq q r), TensorPowDec t (RRq q r), IFunctor t, Fact m) => C (Cyc t m (RRq q r)) Source #
Instance details 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) #
(Additive (Cyc t m a), Additive (Cyc t m b)) => C (Cyc t m (a, b)) Source #
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc Methods zero :: Cyc t m (a, b) # (+) :: Cyc t m (a, b) -> Cyc t m (a, b) -> Cyc t m (a, b) # (-) :: Cyc t m (a, b) -> Cyc t m (a, b) -> Cyc t m (a, b) # negate :: Cyc t m (a, b) -> Cyc t m (a, b) #
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) #
Additive (CycG t m Int64) => C (Cyc t m Int64) Source #
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc Methods zero :: Cyc t m Int64 # (+) :: Cyc t m Int64 -> Cyc t m Int64 -> Cyc t m Int64 # (-) :: Cyc t m Int64 -> Cyc t m Int64 -> Cyc t m Int64 # negate :: Cyc t m Int64 -> Cyc t m Int64 #
Additive (CycG t m Double) => C (Cyc t m Double) Source #
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc Methods zero :: Cyc t m Double # (+) :: Cyc t m Double -> Cyc t m Double -> Cyc t m Double # (-) :: Cyc t m Double -> Cyc t m Double -> Cyc t m Double # negate :: Cyc t m Double -> Cyc t m Double #
(Lift' r, FunctorCyc (Cyc t m) r (LiftOf r)) => LiftCyc (Cyc t m r) Source #
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc Methods liftCyc :: Maybe Basis -> Cyc t m r -> LiftOf (Cyc t m r) 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 #
(Fact m, TensorGaussian t Double, FunctorCyc (Cyc t m) Double Int64) => RoundedGaussianCyc (Cyc t m Int64) Source #	uses `Double` for the intermediate Gaussian sample
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc Methods roundedGaussian :: (ToRational v, MonadRandom rnd) => v -> rnd (Cyc t m Int64) Source #
(Fact m, TensorGaussian t Double) => GaussianCyc (Cyc t m Double) Source #
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc Methods tweakedGaussian :: (ToRational v, MonadRandom rnd) => v -> rnd (Cyc t m Double) Source #
(Cyclotomic (Cyc t m a), Cyclotomic (Cyc t m b)) => Cyclotomic (Cyc t m (a, b)) Source #
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc Methods mulG :: Cyc t m (a, b) -> Cyc t m (a, b) Source # divG :: Cyc t m (a, b) -> Maybe (Cyc t m (a, b)) Source # advisePow :: Cyc t m (a, b) -> Cyc t m (a, b) Source # adviseDec :: Cyc t m (a, b) -> Cyc t m (a, b) Source # adviseCRT :: Cyc t m (a, b) -> Cyc t m (a, b) 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 #
Cyclotomic (CycG t m Int64) => Cyclotomic (Cyc t m Int64) Source #
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc Methods mulG :: Cyc t m Int64 -> Cyc t m Int64 Source # divG :: Cyc t m Int64 -> Maybe (Cyc t m Int64) Source # advisePow :: Cyc t m Int64 -> Cyc t m Int64 Source # adviseDec :: Cyc t m Int64 -> Cyc t m Int64 Source # adviseCRT :: Cyc t m Int64 -> Cyc t m Int64 Source #
Cyclotomic (CycG t m Double) => Cyclotomic (Cyc t m Double) Source #
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc Methods mulG :: Cyc t m Double -> Cyc t m Double Source # divG :: Cyc t m Double -> Maybe (Cyc t m Double) Source # advisePow :: Cyc t m Double -> Cyc t m Double Source # adviseDec :: Cyc t m Double -> Cyc t m Double Source # adviseCRT :: Cyc t m Double -> Cyc t m Double Source #
(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)) Source #
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc Associated Types type ProtoType (Cyc t m (RRq q Double)) :: Type Source # Methods toProto :: Cyc t m (RRq q Double) -> ProtoType (Cyc t m (RRq q Double)) Source # fromProto :: MonadError String m0 => ProtoType (Cyc t m (RRq q Double)) -> m0 (Cyc t m (RRq q Double)) 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 #
(Fact m, CRTElt t Int64, Protoable (CycG t m Int64)) => Protoable (Cyc t m Int64) Source #
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc Associated Types type ProtoType (Cyc t m Int64) :: Type Source # Methods toProto :: Cyc t m Int64 -> ProtoType (Cyc t m Int64) Source # fromProto :: MonadError String m0 => ProtoType (Cyc t m Int64) -> m0 (Cyc t m Int64) Source #
(Fact m, CRTElt t Double, Protoable (CycG t m Double)) => Protoable (Cyc t m Double) Source #
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc Associated Types type ProtoType (Cyc t m Double) :: Type Source # Methods toProto :: Cyc t m Double -> ProtoType (Cyc t m Double) Source # fromProto :: MonadError String m0 => ProtoType (Cyc t m Double) -> m0 (Cyc t m Double) 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) #
(RescaleCyc (Cyc t m) a b, Fact m, Additive (Cyc t m a), Additive (Cyc t m b)) => Rescale (Cyc t m a) (Cyc t m b) Source #	Rescales relative to the powerful basis. This instance is provided for convenience, but usage of `RescaleCyc` is preferred to explicitly specify which basis by which to rescale.
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc Methods rescale :: Cyc t m a -> Cyc t m b Source #
(Reduce (Cyc t m z) (Cyc t m a), Reduce (Cyc t m z) (Cyc t m b)) => Reduce (Cyc t m z) (Cyc t m (a, b)) Source #
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc Methods reduce :: Cyc t m z -> Cyc t m (a, b) Source #
(Reflects q Double, FunctorCyc (Cyc t m) Double (RRq q Double)) => Reduce (Cyc t m Double) (Cyc t m (RRq q Double)) Source #
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc Methods reduce :: Cyc t m Double -> Cyc t m (RRq q Double) 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 #
data Cyc t m Integer Source #	cyclotomic ring of integers with unbounded precision, limited to powerful- or decoding-basis representation.
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc data Cyc t m Integer = PowIgr !(CycRep t P m Integer) \| DecIgr !(CycRep t D m Integer)
newtype Cyc t m Int64 Source #
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc newtype Cyc t m Int64 = CycI64 { unCycI64 :: CycG t m Int64 }
newtype Cyc t m Double Source #
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc newtype Cyc t m Double = CycDbl { unCycDbl :: CycG t m Double }
data Cyc t m (a, b) Source #	cyclotomic over a product base ring, represented as a product of cyclotomics over the individual rings
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc data Cyc t m (a, b) = CycPair !(Cyc t m a) !(Cyc t m b)
data Cyc t m (RRq q r) Source #	additive group \( K/qR \), limited to powerful- or decoding-basis representation
Instance details 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))
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 LiftOf (Cyc t m r) Source #
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc type LiftOf (Cyc t m r) = Cyc t m (LiftOf r)
type DecompOf (Cyc t m (a, b)) Source #
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc type DecompOf (Cyc t m (a, b)) = DecompOf (Cyc t m a)
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 ProtoType (Cyc t m (RRq q Double)) Source #
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc type ProtoType (Cyc t m (RRq q 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))
type ProtoType (Cyc t m Int64) Source #
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc type ProtoType (Cyc t m Int64)
type ProtoType (Cyc t m Double) Source #
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc type ProtoType (Cyc t m Double)

Constructors/deconstructors

class UnCyc t r where Source #

Go between Cyc and CycRep, in a desired representation.

Methods

cycPow :: Fact m => CycRep t P m r -> Cyc t m r Source #

cycDec :: Fact m => CycRep t D m r -> Cyc t m r Source #

unCycPow :: Fact m => Cyc t m r -> CycRep t P m r Source #

unCycDec :: Fact m => Cyc t m r -> CycRep t D m r Source #

Instances

CRTElt t Int64 => UnCyc t Int64 Source #
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc Methods cycPow :: Fact m => CycRep t P m Int64 -> Cyc t m Int64 Source # cycDec :: Fact m => CycRep t D m Int64 -> Cyc t m Int64 Source # unCycPow :: Fact m => Cyc t m Int64 -> CycRep t P m Int64 Source # unCycDec :: Fact m => Cyc t m Int64 -> CycRep t D m Int64 Source #
CRTElt t Double => UnCyc t Double Source #
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc Methods cycPow :: Fact m => CycRep t P m Double -> Cyc t m Double Source # cycDec :: Fact m => CycRep t D m Double -> Cyc t m Double Source # unCycPow :: Fact m => Cyc t m Double -> CycRep t P m Double Source # unCycDec :: Fact m => Cyc t m Double -> CycRep t D m Double Source #
(UnCyc t a, UnCyc t b, IFunctor t, IFElt t a, IFElt t b, IFElt t (a, b)) => UnCyc t (a, b) Source #
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc Methods cycPow :: Fact m => CycRep t P m (a, b) -> Cyc t m (a, b) Source # cycDec :: Fact m => CycRep t D m (a, b) -> Cyc t m (a, b) Source # unCycPow :: Fact m => Cyc t m (a, b) -> CycRep t P m (a, b) Source # unCycDec :: Fact m => Cyc t m (a, b) -> CycRep t D m (a, b) Source #
TensorPowDec t (RRq q r) => UnCyc t (RRq q r) Source #
Instance details Defined in Crypto.Lol.Cyclotomic.Cyc Methods cycPow :: Fact m => CycRep t P m (RRq q r) -> Cyc t m (RRq q r) Source # cycDec :: Fact m => CycRep t D m (RRq q r) -> Cyc t m (RRq q r) Source # unCycPow :: Fact m => Cyc t m (RRq q r) -> CycRep t P m (RRq q r) Source # unCycDec :: Fact m => Cyc t m (RRq q r) -> CycRep t D m (RRq q r) 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 #