Safe Haskell	None
Language	Haskell2010

Crypto.Lol.Types.FiniteField

Description

Basic (unoptimized) finite field arithmetic.

Synopsis

Documentation

data GF fp d Source

A finite field of given degree over F_p.

Instances

(Eq fp, C fp) => Eq (GF k fp d) Source
Show fp => Show (GF k fp d) Source
NFData fp => NFData (GF k fp d) Source
GFCtx k fp d => C (GF k fp d) Source
GFCtx k fp d => C (GF k fp d) Source
C fp => C (GF k fp d) Source
C fp => C (GF k fp d) Source
GFCtx k fp d => Enumerable (GF k fp d) Source
GFCtx k fp d => CRTrans (GF k fp d) Source
(Additive fp, Ring (GF k fp d), Reflects k d Int) => C (GF k fp d) (TensorCoeffs fp) Source
(GFCtx k fp d, Fact m, Additive (CT m fp)) => C (GF k fp d) (CT m fp)
(GFCtx k fp d, Fact m, Additive (RT m fp)) => C (GF k fp d) (RT m fp)
(GFCtx k fp d, Fact m, CElt t fp) => C (GF k fp d) (Cyc t m fp)
(GFCtx k fp d, Fact m, UCElt t fp) => C (GF k fp d) (UCyc Factored t m P fp)

type PrimeField fp = (Enumerable fp, Field fp, Eq fp, ZeroTestable fp, Prim (CharOf fp), IrreduciblePoly fp) Source

type GFCtx fp d = (PrimeField fp, Reflects d Int) Source

size :: GFCtx fp d => Tagged (GF fp d) Int Source

The order of the field: size (GF fp d) = p^d

trace :: forall fp d. GFCtx fp d => GF fp d -> fp Source

Trace into the prime subfield.

toList :: forall fp d. (Reflects d Int, Additive fp) => GF fp d -> [fp] Source

Yield a list of length exactly d (i.e., including trailing zeros) of the fp-coefficients with respect to the power basis

fromList :: forall fp d. Reflects d Int => [fp] -> GF fp d Source

Yield a field element given up to d coefficients with respect to the power basis.

class Field fp => IrreduciblePoly fp where Source

Represents fields over which we can get irreducible polynomials of desired degrees. (An instance of this class is defined in IrreducibleChar2 and exported from Lol.)

Methods

irreduciblePoly :: Reflects d Int => Tagged d (Polynomial fp) Source

data X Source

Convenience data type for writing IrreduciblePoly instances.

Constructors

X

(^^) :: Ring a => X -> Int -> Polynomial a Source

Convenience function for writing IrreduciblePoly instances.

newtype TensorCoeffs a Source

Constructors

Coeffs
Fields unCoeffs :: [a]

Instances

C a => C (TensorCoeffs a) Source
(Additive fp, Ring (GF k fp d), Reflects k d Int) => C (GF k fp d) (TensorCoeffs fp) Source