Crypto.Lol.Gadget

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

Documentation

class Ring u => Gadget gad u where

Gadget vectors, parameterized by an index type.

Minimal complete definition

gadget

Methods

gadget :: Tagged gad [u]

The gadget vector over u.

encode :: u -> Tagged gad [u]

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 k gad a, Gadget k gad b) => Gadget k gad (a, b)

(ReflectsTI k q z, Additive z) => Gadget * TrivGad (ZqBasic k q z)

(Gadget k gad zq, Fact m, CElt t zq) => Gadget k gad (UCyc t m zq)

Gadget k gad (UCyc t m a) => Gadget k gad (Cyc t m a)

(ReflectsTI k1 q z, Additive z, Reflects k b z) => Gadget * (BaseBGad k b) (ZqBasic k q z)

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

Decomposition relative to a gadget.

Associated Types

type DecompOf u

The ring that u decomposes over.

Methods

decompose :: u -> Tagged gad [DecompOf u]

Yield a short vector x such that <g, x> = u.

Instances

(Decompose k gad a, Decompose k gad b, (~) * (DecompOf a) (DecompOf b)) => Decompose k gad (a, b)

(ReflectsTI k q z, Ring z) => Decompose * TrivGad (ZqBasic k q z)

(Decompose k gad zq, Fact m, CElt t zq, Reduce (UCyc t m (DecompOf zq)) (UCyc t m zq)) => Decompose k gad (UCyc t m zq)

(Decompose k gad (UCyc t m zq), Reduce (Cyc t m (DecompOf zq)) (Cyc t m zq)) => Decompose k gad (Cyc t m zq)

(ReflectsTI k1 q z, Ring z, Reflects k b z) => Decompose * (BaseBGad k b) (ZqBasic k q z)

class Gadget gad u => Correct gad u where

Error correction relative to a gadget.

Methods

correct :: Tagged gad [u] -> u

Correct a "noisy" encoding of an element (see encode).

Instances

(ReflectsTI k q z, Ring z) => Correct * TrivGad (ZqBasic k q z)

(Correct k gad zq, Fact m, CElt t zq) => Correct k gad (UCyc t m zq)

Correct k gad (UCyc t m a) => Correct k gad (Cyc t m a)

data TrivGad

Dummy type representing the gadget [1].

Instances

(ReflectsTI k q z, Ring z) => Correct * TrivGad (ZqBasic k q z)

(ReflectsTI k q z, Ring z) => Decompose * TrivGad (ZqBasic k q z)

(ReflectsTI k q z, Additive z) => Gadget * TrivGad (ZqBasic k q z)

data BaseBGad b

Dummy type representing the gadget [1,b,b^2,...].

Instances

(ReflectsTI k1 q z, Ring z, Reflects k b z) => Decompose * (BaseBGad k b) (ZqBasic k q z)

(ReflectsTI k1 q z, Additive z, Reflects k b z) => Gadget * (BaseBGad k b) (ZqBasic k q z)