field

Documentation

Overview

Package field provides modular operations over very high integers.

Index

• func String2Int(s string) big.Int
• type Field
  • func NewField(prime *big.Int) Field
  • func (f Field) Add(res, x, y *big.Int)
  • func (f Field) AreEqual(f1, f2 *big.Int) bool
  • func (f Field) BitLen() int
  • func (f Field) CondMov(res, x, y *big.Int, b bool)
  • func (f Field) CondNeg(res, x *big.Int, cond int)
  • func (f Field) Exponent(res, x, n *big.Int) *big.Int
  • func (f Field) Inv(res, x *big.Int)
  • func (f Field) IsEqual(f2 *Field) bool
  • func (f Field) IsSquare(e *big.Int) bool
  • func (f Field) IsZero(e *big.Int) bool
  • func (f Field) LegendreSymbol(a *big.Int) *big.Int
  • func (f Field) Lsh(res, x *big.Int, n uint)
  • func (f Field) Mod(x *big.Int) *big.Int
  • func (f Field) Mul(res, x, y *big.Int)
  • func (f Field) Neg(res, x *big.Int) *big.Int
  • func (f Field) One() *big.Int
  • func (f Field) Order() *big.Int
  • func (f Field) Random(res *big.Int) *big.Int
  • func (f Field) Sgn0(x *big.Int) int
  • func (f Field) SqrtRatio(res, zMapConstant, e, v *big.Int) bool
  • func (f Field) Square(res, x *big.Int)
  • func (f Field) SquareRoot(res, e *big.Int) *big.Int
  • func (f Field) Sub(res, x, y *big.Int) *big.Int
  • func (f Field) Zero() *big.Int

Functions

func String2Int

func String2Int(s string) big.Int

String2Int returns a big.Int representation of the integer s.

Types

type Field

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

Field represents a Gaulois Field.

func NewField

func NewField(prime *big.Int) Field

NewField returns a newly instantiated field for the given prime order.

func (Field) Add

func (f Field) Add(res, x, y *big.Int)

Add sets res to x + y modulo the field order.

func (Field) AreEqual

func (f Field) AreEqual(f1, f2 *big.Int) bool

AreEqual returns whether both elements are equal.

func (Field) BitLen

func (f Field) BitLen() int

BitLen of the order.

func (Field) CondMov

func (f Field) CondMov(res, x, y *big.Int, b bool)

CondMov sets res to y if b true, and to x otherwise.

func (Field) CondNeg

func (f Field) CondNeg(res, x *big.Int, cond int)

CondNeg sets res to -x if cond == 1.

func (Field) Exponent

func (f Field) Exponent(res, x, n *big.Int) *big.Int

Exponent returns x^n mod field order.

func (Field) Inv

func (f Field) Inv(res, x *big.Int)

Inv sets res to the modular inverse of x mod field order.

func (Field) IsEqual

func (f Field) IsEqual(f2 *Field) bool

IsEqual returns whether the two fields have the same order.

func (Field) IsSquare

func (f Field) IsSquare(e *big.Int) bool

IsSquare returns whether e is a quadratic square.

func (Field) IsZero

func (f Field) IsZero(e *big.Int) bool

IsZero returns whether the big.Int is equivalent to zero.

func (Field) LegendreSymbol

func (f Field) LegendreSymbol(a *big.Int) *big.Int

LegendreSymbol applies the Legendre symbole on (a/p) and returns either {-1, 0, 1} mod field order.

func (Field) Lsh

func (f Field) Lsh(res, x *big.Int, n uint)

Lsh sets res to the left shift of n bits on x modulo the field order.

func (Field) Mod

func (f Field) Mod(x *big.Int) *big.Int

Mod reduces x modulo the field order.

func (Field) Mul

func (f Field) Mul(res, x, y *big.Int)

Mul sets res to the multiplication of x and y modulo the field order.

func (Field) Neg

func (f Field) Neg(res, x *big.Int) *big.Int

Neg sets res to the -x modulo the field order.

func (Field) One

func (f Field) One() *big.Int

One returns one big.Int of the finite Field.

func (Field) Order

func (f Field) Order() *big.Int

Order returns the size of the Field.

func (Field) Random

func (f Field) Random(res *big.Int) *big.Int

Random sets res to a random big.Int in the Field.

func (Field) Sgn0

func (f Field) Sgn0(x *big.Int) int

Sgn0 returns the first bit in the big-endian representation.

func (Field) SqrtRatio

func (f Field) SqrtRatio(res, zMapConstant, e, v *big.Int) bool

SqrtRatio res result to the square root of (e/v), and indicates whether (e/v) is a square.

func (Field) Square

func (f Field) Square(res, x *big.Int)

Square sets res to the square of x modulo the field order.

func (Field) SquareRoot

func (f Field) SquareRoot(res, e *big.Int) *big.Int

SquareRoot sets res to a square root of e mod the field's order, if such a square root exists.

func (Field) Sub

func (f Field) Sub(res, x, y *big.Int) *big.Int

Sub sets res to x - y modulo the field order.

func (Field) Zero

func (f Field) Zero() *big.Int

Zero returns the zero big.Int of the finite Field.