ed25519group

package
v0.0.0-...-d916299 Latest Latest
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 Go to latest Published: May 10, 2021 License: GPL-3.0, MIT Imports: 8 Imported by: 0

Documentation

Index

Constants

View Source 
const (
	// ScalarSize is size of the scalar in bits
	ScalarSize = 32
)

Variables

View Source 
var (
	// Q is the order of group which is 2^255 - 19
	Q = q()

	// L is the order of subgroup which is 2^252 + 27742317777372353535851937790883648493
	L = l()

	// D is a constant TODO: fix the documentation
	D = d()

	// By is y co-ordinate of base point
	By = by()

	// Bx is X co-ordinate of the base point
	Bx = bx()

	// I is constant TODO fix the documentation
	I = i()

	// B is curve base point (generator point) in Affine form
	B = b()

	// Base is curve base point (generator point) in extended form
	Base = base()

	// Zero is identity element in extended co-ordinate system
	Zero = extendedZero()
)

Functions

func IsEven 

func IsEven(x *big.Int) bool

IsEven returns true if x is even and false otherwise

Types

type AffinePoint 

type AffinePoint struct {
	X, Y *big.Int
}

AffinePoint is original representation of points on twisted edwards curve

func NewAffinePoint 

func NewAffinePoint(x, y string, base int) AffinePoint

NewAffinePoint creates new affine point with big integer's given in string format and of provided base.

func (*AffinePoint) Compress 

func (a *AffinePoint) Compress() []byte

Compress encodes the Affine Point into 32 byte little-endian b255 is the sign

func (*AffinePoint) Decompress 

func (a *AffinePoint) Decompress(s []byte) error

Decompress reconstructs the AffinePoint from given 32 byte which is considered as Y co-ordinate compressed using Compress function above

func (*AffinePoint) IsOnCurve 

func (a *AffinePoint) IsOnCurve() bool

IsOnCurve returns true if the given point is on curve

func (AffinePoint) String 

func (a AffinePoint) String() string

func (*AffinePoint) ToExtended 

func (a *AffinePoint) ToExtended() ExtendedPoint

ToExtended converts AffinePoint to ExtendedPoint representation

type Ed25519 

type Ed25519 struct{}

Ed25519 is a group over twisted Edwards curve

func (Ed25519) Add 

func (e Ed25519) Add(a, b group.Element) group.Element

Add adds other point to point e on curve and returns the result of addition

func (Ed25519) BasePointMult 

func (e Ed25519) BasePointMult(s *big.Int) group.Element

BasePointMult multiplies given scalar s to Base point of the curve and returns the result as big.Int

func (Ed25519) ConstM 

func (e Ed25519) ConstM() group.Element

ConstM returns the constant M used in SPAKE2 calculation Value returned by this function is calculated using following python code from python-spake2 module 

from spake2.parameters.ed25519 import ParamsEd25519
from spake2.ed25519_basic import bytes_to_scalar
bytes_to_scalar(ParamsEd25519.M.to_bytes())

func (Ed25519) ConstN 

func (e Ed25519) ConstN() group.Element

ConstN returns the constant N used in SPAKE2 calculation Value returned by this function is calculated using following python code from python-spake2 module 

from spake2.parameters.ed25519 import ParamsEd25519
from spake2.ed25519_basic import bytes_to_scalar
bytes_to_scalar(ParamsEd25519.N.to_bytes())

func (Ed25519) ConstS 

func (e Ed25519) ConstS() group.Element

ConstS returns the constant S used in SPAKE2 calculation in symmetric mode Value returned by this function is calculated using following python code from python-spake2 module 

from spake2.parameters.ed25519 import ParamsEd25519
from spake2.ed25519_basic import bytes_to_scalar
bytes_to_scalar(ParamsEd25519.S.to_bytes())

func (Ed25519) ElementFromBytes 

func (e Ed25519) ElementFromBytes(b []byte) (group.Element, error)

ElementFromBytes creates Ed25519 group element from given byte slice

func (Ed25519) ElementSize 

func (e Ed25519) ElementSize() int

ElementSize returns the size of group element in bytes

func (Ed25519) ElementToBytes 

func (e Ed25519) ElementToBytes(i group.Element) []byte

ElementToBytes convert Ed25519 point to array of bytes

func (Ed25519) Order 

func (e Ed25519) Order() *big.Int

Order returns the order of subgroup of twisted edward curve ed25519

func (Ed25519) PasswordToScalar 

func (e Ed25519) PasswordToScalar(pw []byte) *big.Int

PasswordToScalar expands given password bytes to ScalarSize + 16 and then reduces result to curve order.and returns big.Int resulting from the final bytes.

func (Ed25519) RandomScalar 

func (e Ed25519) RandomScalar() (*big.Int, error)

RandomScalar returns a random scalar which is on curve. For reducing bias to safe level function reads extra 256 bits and then reduces point to curve.

func (Ed25519) ScalarMult 

func (e Ed25519) ScalarMult(a group.Element, s *big.Int) group.Element

ScalarMult multiples given point with scalar and returns the result

type ExtendedPoint 

type ExtendedPoint struct {
	X, Y, Z, T *big.Int
}

ExtendedPoint represents co-ordinate on twisted edwards curve derived from Affine Points

func AddNonUnified 

func AddNonUnified(a, b *ExtendedPoint) ExtendedPoint

AddNonUnified adds 2 point on elliptic curve and returns the resulting extended co-ordinate. This is based on add-2008-hwcd-4 and only for a != b. This is 10% faster than Add and safe to use in ScalarMult if points of order 1/2/4/8 are not used

func AddUnified 

func AddUnified(a, b *ExtendedPoint) ExtendedPoint

AddUnified adds 2 extended co-ordinates and returns resulting extended co-ordinate. This is implemented using add-2008-hwcd-3. It is slightly slower than add-2008-hwcd-4 but is unified and is safe for general purpose addition

func NewExtendedPoint 

func NewExtendedPoint(x, y, z, t string, base int) ExtendedPoint

NewExtendedPoint creates ExtendedPoint with given x,y,z,t arguments as string and base of the integer

func (ExtendedPoint) Add 

func (e ExtendedPoint) Add(b group.Element) group.Element

Add implements the group.Element interface and adds 2 ExtendedPoint and returns the resulting point as type Element

func (*ExtendedPoint) Cmp 

func (e *ExtendedPoint) Cmp(other *ExtendedPoint) int

Cmp compares 2 points in CompressedEdwardsY (i.e. 32 byte format representing Y co-ordinate) form and returns integer. The result will be 0 if e == other, -1 if e < other and +1 if e > other

func (ExtendedPoint) Double 

func (e ExtendedPoint) Double() ExtendedPoint

Double doubles given extended point. Given point P this function returns 2P. This is dbl-2008-hwcd implementation from http://www.hyperelliptic.org/EFD/g1p/auto-twisted-extended-1.html

func (ExtendedPoint) Negate 

func (e ExtendedPoint) Negate() group.Element

Negate negates given point e and returns -e

func (ExtendedPoint) ScalarMult 

func (e ExtendedPoint) ScalarMult(s *big.Int) group.Element

ScalarMult multiplies given scalar to point on elliptic curve and returns the resutling point

func (*ExtendedPoint) ScalarMultFast 

func (e *ExtendedPoint) ScalarMultFast(s *big.Int) ExtendedPoint

ScalarMultFast multiplies a scalar (Integer) to the point on elliptic curve (Extended Co-ordinate) and reutns the resulting point. This form only works properly when given points that are member of the main 1*L subgroup. It will give incorrect answers when called with the points of order 1/2/4/6/8, including point Zero.

func (*ExtendedPoint) ScalarMultSlow 

func (e *ExtendedPoint) ScalarMultSlow(s *big.Int) ExtendedPoint

ScalarMultSlow multiplies a scalar (Integer) to the point on elliptic curve (Extended Co-ordinate) and reutns the resulting point. This form is slightly slower, but tolerates arbitrary points, including those which are not in the main 1*L subgroup. This includes points of order 1 (the neutral element Zero), 2, 4, 6, 8

func (ExtendedPoint) String 

func (e ExtendedPoint) String() string

func (*ExtendedPoint) ToAffine 

func (e *ExtendedPoint) ToAffine() AffinePoint

ToAffine converts ExtendedPoint back to AffinePoint representation

type NotOnCurve 

type NotOnCurve struct{}

NotOnCurve is error emmited when the point got is not on the curve

func (*NotOnCurve) Error 

func (n *NotOnCurve) Error() string

Source Files

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