Copyright	(c) Eric Crockett 2011-2018 Chris Peikert 2011-2018
License	GPL-3
Maintainer	ecrockett0@gmail.com
Stability	experimental
Portability	POSIX \( \def\lcm{\text{lcm}} \)
Safe Haskell	None
Language	Haskell2010

Crypto.Lol.Cyclotomic.Linear

Description

Functions from one cyclotomic ring to another that are linear over a common subring.

Synopsis

data Linear c (e :: Factored) (r :: Factored) (s :: Factored) z
type ExtendLinCtx c e r s e' r' s' z = (e ~ FGCD r e', FLCM r e' `Divides` r', e' `Divides` s', s `Divides` s', ExtensionCyc c z, Additive (c s' z))
linearDec :: forall c e r s z. (e `Divides` r, e `Divides` s, Cyclotomic (c s z), ExtensionCyc c z) => [c s z] -> Linear c e r s z
evalLin :: forall c e r s z. (e `Divides` r, e `Divides` s, Ring (c s z), ExtensionCyc c z) => Linear c e r s z -> c r z -> c s z
liftLin :: (LiftCyc (c s zp), LiftOf (c s zp) ~ c s (LiftOf zp)) => Maybe Basis -> Linear c e r s zp -> Linear c e r s (LiftOf zp)
fmapLin :: (c s z -> c' s z) -> Linear c e r s z -> Linear c' e r s z
extendLin :: forall c e r s e' r' s' z. ExtendLinCtx c e r s e' r' s' z => Linear c e r s z -> Linear c e' r' s' z

Documentation

data Linear c (e :: Factored) (r :: Factored) (s :: Factored) z Source #

An \(E\)-linear function from \(R\) to \(S\).

Instances

Show (c s z) => Show (Linear c e r s z) Source #
Instance details Defined in Crypto.Lol.Cyclotomic.Linear Methods showsPrec :: Int -> Linear c e r s z -> ShowS # show :: Linear c e r s z -> String # showList :: [Linear c e r s z] -> ShowS #
NFData (c s z) => NFData (Linear c e r s z) Source #
Instance details Defined in Crypto.Lol.Cyclotomic.Linear Methods rnf :: Linear c e r s z -> () #
Additive (c s z) => C (Linear c e r s z) Source #
Instance details Defined in Crypto.Lol.Cyclotomic.Linear Methods zero :: Linear c e r s z # (+) :: Linear c e r s z -> Linear c e r s z -> Linear c e r s z # (-) :: Linear c e r s z -> Linear c e r s z -> Linear c e r s z # negate :: Linear c e r s z -> Linear c e r s z #
(Reflects e Word32, Reflects r Word32, Protoable (c s zq), ProtoType (c s zq) ~ RqProduct) => Protoable (Linear c e r s zq) Source #
Instance details Defined in Crypto.Lol.Cyclotomic.Linear Associated Types type ProtoType (Linear c e r s zq) :: Type Source # Methods toProto :: Linear c e r s zq -> ProtoType (Linear c e r s zq) Source # fromProto :: MonadError String m => ProtoType (Linear c e r s zq) -> m (Linear c e r s zq) Source #
Reduce (c s z) (c s zp) => Reduce (Linear c e r s z) (Linear c e r s zp) Source #
Instance details Defined in Crypto.Lol.Cyclotomic.Linear Methods reduce :: Linear c e r s z -> Linear c e r s zp Source #
type LiftOf (Linear c e r s zp) Source #
Instance details Defined in Crypto.Lol.Cyclotomic.Linear type LiftOf (Linear c e r s zp) = Linear c e r s (LiftOf zp)
type ProtoType (Linear c e r s zq) Source #
Instance details Defined in Crypto.Lol.Cyclotomic.Linear type ProtoType (Linear c e r s zq) = LinearRq

type ExtendLinCtx c e r s e' r' s' z = (e ~ FGCD r e', FLCM r e' `Divides` r', e' `Divides` s', s `Divides` s', ExtensionCyc c z, Additive (c s' z)) Source #

A convenient constraint synonym for extending a linear function to larger rings.

linearDec :: forall c e r s z. (e `Divides` r, e `Divides` s, Cyclotomic (c s z), ExtensionCyc c z) => [c s z] -> Linear c e r s z Source #

Construct an \(E\)-linear function given a list of its output values (in \(S\)) on the relative decoding basis of \(R/E\). The number of elements in the list must not exceed the size of the basis.

evalLin :: forall c e r s z. (e `Divides` r, e `Divides` s, Ring (c s z), ExtensionCyc c z) => Linear c e r s z -> c r z -> c s z Source #

Evaluates the given linear function on the input.

liftLin :: (LiftCyc (c s zp), LiftOf (c s zp) ~ c s (LiftOf zp)) => Maybe Basis -> Linear c e r s zp -> Linear c e r s (LiftOf zp) Source #

Lift the linear function in the specified basis (or any, if Nothing is given). The powerful basis is generally best, geometrically.

fmapLin :: (c s z -> c' s z) -> Linear c e r s z -> Linear c' e r s z Source #

Change the underlying cyclotomic representation.

extendLin :: forall c e r s e' r' s' z. ExtendLinCtx c e r s e' r' s' z => Linear c e r s z -> Linear c e' r' s' z Source #

Extend an \(E\)-linear function \(R\to S\) to an \(E'\)-linear function \(R'\to S'\).