field

Documentation

Overview

Package field provides Golang code generation for efficient field arithmetic operations.

Index

• func BigIntMatchUint64Slice(aInt *big.Int, a []uint64) error
• func CoordNameForExtensionDegree(degree uint8) string
• func NewElement(s []string) []big.Int
• type Element
• type Extension
  • func NewTower(base *FieldConfig, degree uint8, rootOf int64) Extension
  • func (f *Extension) Add(x Element, y Element) Element
  • func (f *Extension) Div(u, v Element) Element
  • func (f *Extension) Equal(x Element, y Element) bool
  • func (f *Extension) Exp(x Element, exp *big.Int) Element
  • func (f *Extension) FromInt64(i ...int64) Element
  • func (f *Extension) Halve(z Element)
  • func (f *Extension) Inverse(x Element) Element
  • func (f *Extension) IsZero(u Element) bool
  • func (f *Extension) Mul(x Element, y Element) Element
  • func (f *Extension) MulScalar(c *big.Int, x Element) Element
  • func (f *Extension) Neg(x Element) Element
  • func (f *Extension) Sqrt(x Element) Element
  • func (f *Extension) ToMont(x Element) Element
• type FieldConfig
  • func NewFieldConfig(packageName, elementName, modulus string, useAddChain bool) (*FieldConfig, error)
  • func (f *FieldConfig) Add(z *big.Int, x *big.Int, y *big.Int) *FieldConfig
  • func (f *FieldConfig) Exp(res *big.Int, x *big.Int, pow *big.Int) *FieldConfig
  • func (f *FieldConfig) FromMont(nonMont *big.Int, mont *big.Int) *FieldConfig
  • func (f *FieldConfig) Mul(z *big.Int, x *big.Int, y *big.Int) *FieldConfig
  • func (f *FieldConfig) StringToMont(str string) big.Int
  • func (f *FieldConfig) ToMont(nonMont big.Int) big.Int
  • func (f *FieldConfig) ToMontSlice(x []big.Int) []big.Int
  • func (f *FieldConfig) WriteElement(element Element) string

Functions

func BigIntMatchUint64Slice

func BigIntMatchUint64Slice(aInt *big.Int, a []uint64) error

func CoordNameForExtensionDegree

func CoordNameForExtensionDegree(degree uint8) string

TODO: Spaghetti Alert: Okay to have codegen functions here?

func NewElement

func NewElement(s []string) []big.Int

Types

type Element

type Element []big.Int

type Extension

type Extension struct {
	Base   *FieldConfig //Fp
	Size   big.Int      //q
	Degree int          //n such that q = pⁿ TODO: Make uint8 so forced to be positive and small
	RootOf int64        //α
}

Extension is a simple radical extension, obtained by adjoining ⁿ√α to Fp

func NewTower

func NewTower(base *FieldConfig, degree uint8, rootOf int64) Extension

func (*Extension) Add

func (f *Extension) Add(x Element, y Element) Element

func (*Extension) Div

func (f *Extension) Div(u, v Element) Element

Div returns u/v

func (*Extension) Equal

func (f *Extension) Equal(x Element, y Element) bool

func (*Extension) Exp

func (f *Extension) Exp(x Element, exp *big.Int) Element

func (*Extension) FromInt64

func (f *Extension) FromInt64(i ...int64) Element

func (*Extension) Halve

func (f *Extension) Halve(z Element)

func (*Extension) Inverse

func (f *Extension) Inverse(x Element) Element

func (*Extension) IsZero

func (f *Extension) IsZero(u Element) bool

func (*Extension) Mul

func (f *Extension) Mul(x Element, y Element) Element

func (*Extension) MulScalar

func (f *Extension) MulScalar(c *big.Int, x Element) Element

func (*Extension) Neg

func (f *Extension) Neg(x Element) Element

func (*Extension) Sqrt

func (f *Extension) Sqrt(x Element) Element

Sqrt returning √ x, or nil if x is not qr.

func (*Extension) ToMont

func (f *Extension) ToMont(x Element) Element

type FieldConfig

type FieldConfig struct {
	PackageName               string
	ElementName               string
	ModulusBig                *big.Int
	Modulus                   string
	ModulusHex                string
	NbWords                   int
	NbBits                    int
	NbWordsLastIndex          int
	NbWordsIndexesNoZero      []int
	NbWordsIndexesFull        []int
	P20InversionCorrectiveFac []uint64
	P20InversionNbIterations  int
	UsingP20Inverse           bool
	IsMSWSaturated            bool // indicates if the most significant word is 0xFFFFF...FFFF
	Q                         []uint64
	QInverse                  []uint64
	QMinusOneHalvedP          []uint64 // ((q-1) / 2 ) + 1
	ASM                       bool
	RSquare                   []uint64
	One, Thirteen             []uint64
	LegendreExponent          string // big.Int to base16 string
	NoCarry                   bool
	NoCarrySquare             bool // used if NoCarry is set, but some op may overflow in square optimization
	SqrtQ3Mod4                bool
	SqrtAtkin                 bool
	SqrtTonelliShanks         bool
	SqrtE                     uint64
	SqrtS                     []uint64
	SqrtAtkinExponent         string   // big.Int to base16 string
	SqrtSMinusOneOver2        string   // big.Int to base16 string
	SqrtQ3Mod4Exponent        string   // big.Int to base16 string
	SqrtG                     []uint64 // NonResidue ^  SqrtR (montgomery form)
	NonResidue                big.Int  // (montgomery form)
	LegendreExponentData      *addchain.AddChainData
	SqrtAtkinExponentData     *addchain.AddChainData
	SqrtSMinusOneOver2Data    *addchain.AddChainData
	SqrtQ3Mod4ExponentData    *addchain.AddChainData
	UseAddChain               bool
}

FieldConfig precomputed values used in template for code generation of field element APIs

func NewFieldConfig

func NewFieldConfig(packageName, elementName, modulus string, useAddChain bool) (*FieldConfig, error)

NewFieldConfig returns a data structure with needed information to generate apis for field element

See field/generator package

func (*FieldConfig) Add

func (f *FieldConfig) Add(z *big.Int, x *big.Int, y *big.Int) *FieldConfig

func (*FieldConfig) Exp

func (f *FieldConfig) Exp(res *big.Int, x *big.Int, pow *big.Int) *FieldConfig

func (*FieldConfig) FromMont

func (f *FieldConfig) FromMont(nonMont *big.Int, mont *big.Int) *FieldConfig

func (*FieldConfig) Mul

func (f *FieldConfig) Mul(z *big.Int, x *big.Int, y *big.Int) *FieldConfig

func (*FieldConfig) StringToMont

func (f *FieldConfig) StringToMont(str string) big.Int

StringToMont takes an element written in string form, and returns it in Montgomery form Useful for hard-coding in implementation field elements from standards documents

func (*FieldConfig) ToMont

func (f *FieldConfig) ToMont(nonMont big.Int) big.Int

func (*FieldConfig) ToMontSlice

func (f *FieldConfig) ToMontSlice(x []big.Int) []big.Int

func (*FieldConfig) WriteElement

func (f *FieldConfig) WriteElement(element Element) string