gf2n

README

Binary Extension Field

Introduction

This is an experimental implementation of binary extension field operations.

To construct a binary extension finite field GF(2^n), an irreducible polynomial f(x) over GF(2) of degree n is used. In current implementation, it requires that the degree must be strictly less than 64.

Documentation

Index

• type GF2nElement
  • func (z *GF2nElement) Add(x, y *GF2nElement) *GF2nElement
  • func (z *GF2nElement) Equal(x *GF2nElement) bool
  • func (z *GF2nElement) Field() *GF2nField
  • func (z *GF2nElement) Mul(x, y *GF2nElement) *GF2nElement
  • func (z *GF2nElement) Pow(n uint64) *GF2nElement
  • func (z *GF2nElement) SetFromElement(x *GF2nElement) *GF2nElement
  • func (z *GF2nElement) SetFromValues(v uint64, field *GF2nField) *GF2nElement
  • func (z *GF2nElement) Sub(x, y *GF2nElement) *GF2nElement
  • func (z *GF2nElement) Value() uint64
• type GF2nField
  • func NewGF2nField(n uint8, irre uint64) (*GF2nField, error)
  • func (f *GF2nField) Equal(e *GF2nField) bool
  • func (f *GF2nField) ExtDegree() uint8
  • func (f *GF2nField) IrrePolyWithoutHighest() uint64
  • func (f *GF2nField) NewGF2nElement(v uint64) *GF2nElement
  • func (f *GF2nField) NewGF2nPoly(coeff []*GF2nElement) *GF2nPoly
• type GF2nPoly
  • func (f *GF2nPoly) Eval(x *GF2nElement) *GF2nElement

Types

type GF2nElement

type GF2nElement struct {
	// contains filtered or unexported fields
}

func (*GF2nElement) Add

func (z *GF2nElement) Add(x, y *GF2nElement) *GF2nElement

Add will add two field elements and return their sum

func (*GF2nElement) Equal

func (z *GF2nElement) Equal(x *GF2nElement) bool

return whether two elements are equal

func (*GF2nElement) Field

func (z *GF2nElement) Field() *GF2nField

func (*GF2nElement) Mul

func (z *GF2nElement) Mul(x, y *GF2nElement) *GF2nElement

Multiply two field elements and return their product

func (*GF2nElement) Pow

func (z *GF2nElement) Pow(n uint64) *GF2nElement

Return the power of a field element to a power

func (*GF2nElement) SetFromElement

func (z *GF2nElement) SetFromElement(x *GF2nElement) *GF2nElement

func (*GF2nElement) SetFromValues

func (z *GF2nElement) SetFromValues(v uint64, field *GF2nField) *GF2nElement

func (*GF2nElement) Sub

func (z *GF2nElement) Sub(x, y *GF2nElement) *GF2nElement

Substract a field element from another element and return their difference

func (*GF2nElement) Value

func (z *GF2nElement) Value() uint64

type GF2nField

type GF2nField struct {
	// contains filtered or unexported fields
}

arithmetic over GF(2^n) n must be less than 64 x^n + irre must be a irreducible polynomial over GF(2^n) where irre is a polynomial over GF(2) of degree less than n

func NewGF2nField

func NewGF2nField(n uint8, irre uint64) (*GF2nField, error)

generate a binary extension field we do not check whether x^n + irre is irreducible

func (*GF2nField) Equal

func (f *GF2nField) Equal(e *GF2nField) bool

func (*GF2nField) ExtDegree

func (f *GF2nField) ExtDegree() uint8

return the degree of extension

func (*GF2nField) IrrePolyWithoutHighest

func (f *GF2nField) IrrePolyWithoutHighest() uint64

return irreducible polynomial wo/ the highest order term

func (*GF2nField) NewGF2nElement

func (f *GF2nField) NewGF2nElement(v uint64) *GF2nElement

func (*GF2nField) NewGF2nPoly

func (f *GF2nField) NewGF2nPoly(coeff []*GF2nElement) *GF2nPoly

type GF2nPoly

type GF2nPoly struct {
	Coeff []*GF2nElement
	Field *GF2nField
}

func (*GF2nPoly) Eval

func (f *GF2nPoly) Eval(x *GF2nElement) *GF2nElement