fp

Documentation

Overview

Package fp (generated by goff) contains field arithmetics operations

Index

• Constants
• type Element
  • func FromInterface(i1 interface{}) Element
  • func One() Element
  • func (z *Element) Add(x, y *Element) *Element
  • func (z *Element) AddAssign(x *Element) *Element
  • func (z *Element) Div(x, y *Element) *Element
  • func (z *Element) Double(x *Element) *Element
  • func (z *Element) Equal(x *Element) bool
  • func (z *Element) Exp(x Element, exponent ...uint64) *Element
  • func (z *Element) FromMont() *Element
  • func (z *Element) Inverse(x *Element) *Element
  • func (z *Element) IsZero() bool
  • func (z *Element) Legendre() int
  • func (z *Element) Mul(x, y *Element) *Element
  • func (z *Element) MulAssign(x *Element) *Element
  • func (z *Element) Neg(x *Element) *Element
  • func (z *Element) Set(x *Element) *Element
  • func (z *Element) SetBigInt(v *big.Int) *Element
  • func (z *Element) SetOne() *Element
  • func (z *Element) SetRandom() *Element
  • func (z *Element) SetString(s string) *Element
  • func (z *Element) SetUint64(v uint64) *Element
  • func (z *Element) SetZero() *Element
  • func (z *Element) Sqrt(x *Element) *Element
  • func (z *Element) Square(x *Element) *Element
  • func (z *Element) String() string
  • func (z *Element) Sub(x, y *Element) *Element
  • func (z *Element) SubAssign(x *Element) *Element
  • func (z *Element) ToBigInt(res *big.Int) *big.Int
  • func (z Element) ToBigIntRegular(res *big.Int) *big.Int
  • func (z *Element) ToMont() *Element
  • func (z Element) ToRegular() Element

Constants

const ElementBits = 377

ElementBits number bits needed to represent Element

const ElementLimbs = 6

ElementLimbs number of 64 bits words needed to represent Element

Types

type Element

type Element [6]uint64

Element represents a field element stored on 6 words (uint64) Element are assumed to be in Montgomery form in all methods

func FromInterface

func FromInterface(i1 interface{}) Element

func One

func One() Element

func (*Element) Add

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

Add z = x + y mod q

func (*Element) AddAssign

func (z *Element) AddAssign(x *Element) *Element

AddAssign z = z + x mod q

func (*Element) Div

func (z *Element) Div(x, y *Element) *Element

Div z = x*y^-1 mod q

func (*Element) Double

func (z *Element) Double(x *Element) *Element

Double z = x + x mod q, aka Lsh 1

func (*Element) Equal

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

Equal returns z == x

func (*Element) Exp

func (z *Element) Exp(x Element, exponent ...uint64) *Element

Exp z = x^exponent mod q (not optimized) exponent (non-montgomery form) is ordered from least significant word to most significant word

func (*Element) FromMont

func (z *Element) FromMont() *Element

FromMont converts z in place (i.e. mutates) from Montgomery to regular representation sets and returns z = z * 1

func (*Element) Inverse

func (z *Element) Inverse(x *Element) *Element

Inverse z = x^-1 mod q Algorithm 16 in "Efficient Software-Implementation of Finite Fields with Applications to Cryptography" if x == 0, sets and returns z = x

func (*Element) IsZero

func (z *Element) IsZero() bool

IsZero returns z == 0

func (*Element) Legendre

func (z *Element) Legendre() int

Legendre returns the Legendre symbol of z (either +1, -1, or 0.)

func (*Element) Mul

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

Mul z = x * y mod q see https://hackmd.io/@zkteam/modular_multiplication

func (*Element) MulAssign

func (z *Element) MulAssign(x *Element) *Element

MulAssign z = z * x mod q see https://hackmd.io/@zkteam/modular_multiplication

func (*Element) Neg

func (z *Element) Neg(x *Element) *Element

Neg z = q - x

func (*Element) Set

func (z *Element) Set(x *Element) *Element

Set z = x

func (*Element) SetBigInt

func (z *Element) SetBigInt(v *big.Int) *Element

SetBigInt sets z to v (regular form) and returns z in Montgomery form

func (*Element) SetOne

func (z *Element) SetOne() *Element

SetOne z = 1 (in Montgomery form)

func (*Element) SetRandom

func (z *Element) SetRandom() *Element

SetRandom sets z to a random element < q

func (*Element) SetString

func (z *Element) SetString(s string) *Element

SetString creates a big.Int with s (in base 10) and calls SetBigInt on z

func (*Element) SetUint64

func (z *Element) SetUint64(v uint64) *Element

SetUint64 z = v, sets z LSB to v (non-Montgomery form) and convert z to Montgomery form

func (*Element) SetZero

func (z *Element) SetZero() *Element

SetZero z = 0

func (*Element) Sqrt

func (z *Element) Sqrt(x *Element) *Element

Sqrt z = √x mod q if the square root doesn't exist (x is not a square mod q) Sqrt leaves z unchanged and returns nil

func (*Element) Square

func (z *Element) Square(x *Element) *Element

Square z = x * x mod q see https://hackmd.io/@zkteam/modular_multiplication

func (*Element) String

func (z *Element) String() string

String returns the string form of an Element in Montgomery form

func (*Element) Sub

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

Sub z = x - y mod q

func (*Element) SubAssign

func (z *Element) SubAssign(x *Element) *Element

SubAssign z = z - x mod q

func (*Element) ToBigInt

func (z *Element) ToBigInt(res *big.Int) *big.Int

ToBigInt returns z as a big.Int in Montgomery form

func (Element) ToBigIntRegular

func (z Element) ToBigIntRegular(res *big.Int) *big.Int

ToBigIntRegular returns z as a big.Int in regular form

func (*Element) ToMont

func (z *Element) ToMont() *Element

ToMont converts z to Montgomery form sets and returns z = z * r^2

func (Element) ToRegular

func (z Element) ToRegular() Element

ToRegular returns z in regular form (doesn't mutate z)