class Binary extends Base (View source)

Curves over y^2 + xy = x^3 + ax^2 + b

Properties

protected object[] $doubles Doubles from  Base
protected BigInteger $order The Order
protected BinaryField $factory Binary Field Integer factory
protected object $a Cofficient for x^1
protected object $b Cofficient for x^0
protected object $p Base Point
protected object $one The number one over the specified finite field
protected BigInteger $modulo The modulo

Methods

object
randomInteger()

Returns a random integer

from  Base
object
convertInteger(BigInteger $x)

Converts a BigInteger to a FiniteField integer

from  Base
int
getLengthInBytes()

Returns the length, in bytes, of the modulo

from  Base
int
getLength()

Returns the length, in bits, of the modulo

from  Base
array
multiplyPoint(array $p, Integer $d)

Multiply a point on the curve by a scalar

from  Base
FiniteField
createRandomMultiplier()

Creates a random scalar multiplier

from  Base
setOrder(BigInteger $order)

Sets the Order

from  Base
getOrder()

Returns the Order

from  Base
object
setReduction(callable $func)

Use a custom defined modular reduction function

from  Base
object[]
convertToAffine(array $p)

Returns the affine point

object[]
convertToInternal(array $p)

Converts an affine point to a jacobian coordinate

object[]
negatePoint(array $p)

Negates a point

from  Base
int[]
multiplyAddPoints(array $points, array $scalars)

Multiply and Add Points

from  Base
setModulo(...$modulo)

Sets the modulo

setCoefficients(string $a, string $b)

Set coefficients a and b

setBasePoint(string|BinaryInteger $x, string|BinaryInteger $y)

Set x and y coordinates for the base point

array
getBasePoint()

Retrieve the base point as an array

FiniteField[]
addPoint(array $p, array $q)

Adds two points on the curve

FiniteField[]
doublePoint(array $p)

Doubles a point on a curve

array
derivePoint($m)

Returns the X coordinate and the derived Y coordinate

bool
verifyPoint(array $p)

Tests whether or not the x / y values satisfy the equation

getModulo()

Returns the modulo

getA()

Returns the a coefficient

getB()

Returns the a coefficient

Details

object randomInteger()

Returns a random integer

Return Value

object

object convertInteger(BigInteger $x)

Converts a BigInteger to a FiniteField integer

Parameters

BigInteger $x

Return Value

object

int getLengthInBytes()

Returns the length, in bytes, of the modulo

Return Value

int

int getLength()

Returns the length, in bits, of the modulo

Return Value

int

array multiplyPoint(array $p, Integer $d)

Multiply a point on the curve by a scalar

Uses the montgomery ladder technique as described here:

https://en.wikipedia.org/wiki/Elliptic_curve_point_multiplication#Montgomery_ladder https://github.com/phpecc/phpecc/issues/16#issuecomment-59176772

Parameters

array $p
Integer $d

Return Value

array

FiniteField createRandomMultiplier()

Creates a random scalar multiplier

Return Value

FiniteField

setOrder(BigInteger $order)

Sets the Order

Parameters

BigInteger $order

BigInteger getOrder()

Returns the Order

Return Value

BigInteger

object setReduction(callable $func)

Use a custom defined modular reduction function

Parameters

callable $func

Return Value

object

object[] convertToAffine(array $p)

Returns the affine point

A Jacobian Coordinate is of the form (x, y, z). To convert a Jacobian Coordinate to an Affine Point you do (x / z^2, y / z^3)

Parameters

array $p

Return Value

object[]

object[] convertToInternal(array $p)

Converts an affine point to a jacobian coordinate

Parameters

array $p

Return Value

object[]

object[] negatePoint(array $p)

Negates a point

Parameters

array $p

Return Value

object[]

int[] multiplyAddPoints(array $points, array $scalars)

Multiply and Add Points

Parameters

array $points
array $scalars

Return Value

int[]

setModulo(...$modulo)

Sets the modulo

Parameters

...$modulo

setCoefficients(string $a, string $b)

Set coefficients a and b

Parameters

string $a
string $b

setBasePoint(string|BinaryInteger $x, string|BinaryInteger $y)

Set x and y coordinates for the base point

Parameters

string|BinaryInteger $x
string|BinaryInteger $y

array getBasePoint()

Retrieve the base point as an array

Return Value

array

FiniteField[] addPoint(array $p, array $q)

Adds two points on the curve

Parameters

array $p
array $q

Return Value

FiniteField[]

FiniteField[] doublePoint(array $p)

Doubles a point on a curve

Parameters

array $p

Return Value

FiniteField[]

array derivePoint($m)

Returns the X coordinate and the derived Y coordinate

Not supported because it is covered by patents. Quoting https://www.openssl.org/docs/man1.1.0/apps/ecparam.html ,

"Due to patent issues the compressed option is disabled by default for binary curves and can be enabled by defining the preprocessor macro OPENSSL_EC_BIN_PT_COMP at compile time."

Parameters

$m

Return Value

array

bool verifyPoint(array $p)

Tests whether or not the x / y values satisfy the equation

Parameters

array $p

Return Value

bool

BigInteger getModulo()

Returns the modulo

Return Value

BigInteger

Integer getA()

Returns the a coefficient

Return Value

Integer

Integer getB()

Returns the a coefficient

Return Value

Integer