class secp160r2 extends Prime (View source)

Properties

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

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

from  Prime
object[]
convertToInternal(array $p)

Converts an affine point to a jacobian coordinate

from  Prime
object[]
negatePoint(array $p)

Negates a point

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

Multiply and Add Points

from  Prime
setModulo(BigInteger $modulo)

Sets the modulo

from  Prime
setCoefficients(BigInteger $a, BigInteger $b)

Set coefficients a and b

from  Prime
PrimeInteger[]
setBasePoint(BigInteger|PrimeInteger $x, BigInteger|PrimeInteger $y)

Set x and y coordinates for the base point

from  Prime
array
getBasePoint()

Retrieve the base point as an array

from  Prime
FiniteField[]
jacobianAddPointMixedXY(array $p, array $q)

Adds two "fresh" jacobian form on the curve

from  Prime
FiniteField[]
jacobianAddPointMixedX(array $p, array $q)

Adds one "fresh" jacobian form on the curve

from  Prime
FiniteField[]
jacobianAddPoint(array $p, array $q)

Adds two jacobian coordinates on the curve

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

Adds two points on the curve

from  Prime
FiniteField[]
doublePointHelper(array $p)

Returns the numerator and denominator of the slope

from  Prime
FiniteField[]
jacobianDoublePoint(array $p)

Doubles a jacobian coordinate on the curve

from  Prime
FiniteField[]
jacobianDoublePointMixed(array $p)

Doubles a "fresh" jacobian coordinate on the curve

from  Prime
FiniteField[]
doublePoint(array $p)

Doubles a point on a curve

from  Prime
array
derivePoint($m)

Returns the X coordinate and the derived Y coordinate

from  Prime
bool
verifyPoint(array $p)

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

from  Prime
getModulo()

Returns the modulo

from  Prime
getA()

Returns the a coefficient

from  Prime
getB()

Returns the a coefficient

from  Prime
__construct()

No description

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

Adapted from https://git.io/vxPUH

Parameters

array $points
array $scalars

Return Value

int[]

setModulo(BigInteger $modulo)

Sets the modulo

Parameters

BigInteger $modulo

setCoefficients(BigInteger $a, BigInteger $b)

Set coefficients a and b

Parameters

BigInteger $a
BigInteger $b

PrimeInteger[] setBasePoint(BigInteger|PrimeInteger $x, BigInteger|PrimeInteger $y)

Set x and y coordinates for the base point

Parameters

BigInteger|PrimeInteger $x
BigInteger|PrimeInteger $y

Return Value

PrimeInteger[]

array getBasePoint()

Retrieve the base point as an array

Return Value

array

protected FiniteField[] jacobianAddPointMixedXY(array $p, array $q)

Adds two "fresh" jacobian form on the curve

Parameters

array $p
array $q

Return Value

FiniteField[]

protected FiniteField[] jacobianAddPointMixedX(array $p, array $q)

Adds one "fresh" jacobian form on the curve

The second parameter should be the "fresh" one

Parameters

array $p
array $q

Return Value

FiniteField[]

protected FiniteField[] jacobianAddPoint(array $p, array $q)

Adds two jacobian coordinates on the curve

Parameters

array $p
array $q

Return Value

FiniteField[]

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

Adds two points on the curve

Parameters

array $p
array $q

Return Value

FiniteField[]

protected FiniteField[] doublePointHelper(array $p)

Returns the numerator and denominator of the slope

Parameters

array $p

Return Value

FiniteField[]

protected FiniteField[] jacobianDoublePoint(array $p)

Doubles a jacobian coordinate on the curve

Parameters

array $p

Return Value

FiniteField[]

protected FiniteField[] jacobianDoublePointMixed(array $p)

Doubles a "fresh" jacobian coordinate on the curve

Parameters

array $p

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

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

__construct()