Crypto.Lol.Types.FiniteField

Basic (unoptimized) finite field arithmetic.

Documentation

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

Constraint synonym for prime-order fields.

type family CharOf fp :: Nat

The characteristic of a field, represented as a type.

Instances

type CharOf * (ZqBasic Nat p z) = p

data GF fp deg

A finite field of given degree over F_p.

Instances

(Eq fp, C fp) => Eq (GF k fp deg)

Show fp => Show (GF k fp deg)

NFData fp => NFData (GF k fp deg)

GFCtx k fp deg => C (GF k fp deg)

GFCtx k fp deg => C (GF k fp deg)

C fp => C (GF k fp deg)

C fp => C (GF k fp deg)

GFCtx k fp deg => Enumerable (GF k fp deg)

GFCtx k fp deg => CRTrans (GF k fp deg)

trace :: forall fp deg. GFCtx fp deg => GF fp deg -> fp

Trace into the prime subfield.

size :: GFCtx fp deg => Tagged (GF fp deg) Int

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