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

Crypto.Lol.Gadget

Description

Interfaces for "gadgets," decomposition, and error correction.

Synopsis

class Ring u => Gadget gad u where
- gadget :: [u]
- encode :: u -> [u]
class (Gadget gad u, Reduce (DecompOf u) u) => Decompose gad u where
- type DecompOf u
- decompose :: u -> [DecompOf u]
class Gadget gad u => Correct gad u where
- correct :: [u] -> (u, [LiftOf u])
decomposeList :: forall gad u. Decompose gad u => [u] -> [DecompOf u]
decomposeMatrix :: forall gad u. Decompose gad u => Matrix u -> Matrix (DecompOf u)
data TrivGad
data BaseBGad b

Documentation

class Ring u => Gadget gad u where Source #

Gadget vectors, parameterized by an index type.

Minimal complete definition

gadget

Methods

gadget :: [u] Source #

The gadget vector over u.

encode :: u -> [u] Source #

Yield an error-tolerant encoding of an element with respect to the gadget. (Mathematically, this should just be the product of the input with the gadget, but it is a class method to allow for optimized implementations.)

Instances

(Gadget gad a, Gadget gad b) => Gadget (gad :: k) (a, b) Source #	Product ring: concatenate gadgets over component rings
Instance details Defined in Crypto.Lol.Gadget Methods gadget :: [(a, b)] Source # encode :: (a, b) -> [(a, b)] 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 #
(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, 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 #

class (Gadget gad u, Reduce (DecompOf u) u) => Decompose gad u where Source #

Decomposition relative to a gadget.

Associated Types

type DecompOf u Source #

The ring that u decomposes over.

Methods

decompose :: u -> [DecompOf u] Source #

Yield a short vector \( x \) such that \( \langle g, x\rangle = u \).

Instances

(Decompose gad a, Decompose gad b, DecompOf a ~ DecompOf b) => Decompose (gad :: k) (a, b) Source #	Product ring: concatenate decompositions for component rings
Instance details Defined in Crypto.Lol.Gadget Associated Types type DecompOf (a, b) :: Type Source # Methods decompose :: (a, b) -> [DecompOf (a, b)] 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 #
(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, 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 #

class Gadget gad u => Correct gad u where Source #

Error correction relative to a gadget.

Methods

correct :: [u] -> (u, [LiftOf u]) Source #

Error-correct a "noisy" encoding of an element (see encode), returning the encoded element and the error vector.

Instances

(Correct gad a, Correct gad b, Mod a, Mod b, Field a, Field b, Lift' a, Lift' b, ToInteger (LiftOf a), ToInteger (LiftOf b)) => Correct (gad :: k) (a, b) Source #	Product ring
Instance details Defined in Crypto.Lol.Gadget Methods correct :: [(a, b)] -> ((a, b), [LiftOf (a, b)]) Source #
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 #
(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, 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 #

decomposeList :: forall gad u. Decompose gad u => [u] -> [DecompOf u] Source #

Decompose a list entry-wise.

decomposeMatrix :: forall gad u. Decompose gad u => Matrix u -> Matrix (DecompOf u) Source #

Decompose a matrix entry-wise.

data TrivGad Source #

Dummy type representing the gadget \( [1] \).

Instances

(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 #
Show (ArgType TrivGad) Source #
Instance details Defined in Crypto.Lol.Utils.ShowType Methods showsPrec :: Int -> ArgType TrivGad -> ShowS # show :: ArgType TrivGad -> String # showList :: [ArgType TrivGad] -> ShowS #

data BaseBGad b Source #

Dummy type representing the gadget \( [1,b,b^2,\ldots] \).

Instances

(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 #
Reflects b Integer => Show (ArgType (BaseBGad b)) Source #
Instance details Defined in Crypto.Lol.Utils.ShowType Methods showsPrec :: Int -> ArgType (BaseBGad b) -> ShowS # show :: ArgType (BaseBGad b) -> String # showList :: [ArgType (BaseBGad b)] -> ShowS #