Documentation

sect163k1 extends Binary
in package

Curves over y^2 + x*y = x^3 + a*x^2 + b

Table of Contents

Properties

$a  : object
Cofficient for x^1
$b  : object
Cofficient for x^0
$doubles  : array<string|int, object>
Doubles
$factory  : BinaryField
Binary Field Integer factory
$modulo  : BigInteger
The modulo
$one  : object
The number one over the specified finite field
$order  : BigInteger
The Order
$p  : object
Base Point
$naf  : array<string|int, int>
NAF Points

Methods

__construct()  : mixed
addPoint()  : array<string|int, FiniteField>
Adds two points on the curve
convertInteger()  : object
Converts a BigInteger to a FiniteField integer
convertToAffine()  : array<string|int, Integer>
Returns the affine point
convertToInternal()  : array<string|int, Integer>
Converts an affine point to a jacobian coordinate
createRandomMultiplier()  : FiniteField
Creates a random scalar multiplier
derivePoint()  : array<string|int, mixed>
Returns the X coordinate and the derived Y coordinate
doublePoint()  : array<string|int, FiniteField>
Doubles a point on a curve
getA()  : Integer
Returns the a coefficient
getB()  : Integer
Returns the a coefficient
getBasePoint()  : array<string|int, mixed>
Retrieve the base point as an array
getLength()  : int
Returns the length, in bits, of the modulo
getLengthInBytes()  : int
Returns the length, in bytes, of the modulo
getModulo()  : BigInteger
Returns the modulo
getOrder()  : BigInteger
Returns the Order
multiplyAddPoints()  : array<string|int, int>
Multiply and Add Points
multiplyPoint()  : array<string|int, mixed>
Multiply a point on the curve by a scalar
negatePoint()  : array<string|int, object>
Negates a point
randomInteger()  : object
Returns a random integer
setBasePoint()  : mixed
Set x and y coordinates for the base point
setCoefficients()  : mixed
Set coefficients a and b
setModulo()  : mixed
Sets the modulo
setOrder()  : mixed
Sets the Order
setReduction()  : object
Use a custom defined modular reduction function
verifyPoint()  : bool
Tests whether or not the x / y values satisfy the equation

Properties

$a

Cofficient for x^1

protected object $a

$b

Cofficient for x^0

protected object $b

$doubles

Doubles

protected array<string|int, object> $doubles

$one

The number one over the specified finite field

protected object $one

$p

Base Point

protected object $p

$naf

NAF Points

private array<string|int, int> $naf

Methods

addPoint()

Adds two points on the curve

public addPoint(array<string|int, mixed> $p, array<string|int, mixed> $q) : array<string|int, FiniteField>
Parameters
$p : array<string|int, mixed>
$q : array<string|int, mixed>
Return values
array<string|int, FiniteField>

convertInteger()

Converts a BigInteger to a FiniteField integer

public convertInteger(BigInteger $x) : object
Parameters
$x : BigInteger
Return values
object

convertToAffine()

Returns the affine point

public convertToAffine(array<string|int, mixed> $p) : array<string|int, Integer>

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
$p : array<string|int, mixed>
Return values
array<string|int, Integer>

convertToInternal()

Converts an affine point to a jacobian coordinate

public convertToInternal(array<string|int, mixed> $p) : array<string|int, Integer>
Parameters
$p : array<string|int, mixed>
Return values
array<string|int, Integer>

derivePoint()

Returns the X coordinate and the derived Y coordinate

public derivePoint(mixed $m) : array<string|int, mixed>

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 : mixed
Return values
array<string|int, mixed>

doublePoint()

Doubles a point on a curve

public doublePoint(array<string|int, mixed> $p) : array<string|int, FiniteField>
Parameters
$p : array<string|int, mixed>
Return values
array<string|int, FiniteField>

getBasePoint()

Retrieve the base point as an array

public getBasePoint() : array<string|int, mixed>
Return values
array<string|int, mixed>

getLength()

Returns the length, in bits, of the modulo

public getLength() : int
Return values
int

getLengthInBytes()

Returns the length, in bytes, of the modulo

public getLengthInBytes() : int
Return values
int

multiplyAddPoints()

Multiply and Add Points

public multiplyAddPoints(array<string|int, mixed> $points, array<string|int, mixed> $scalars) : array<string|int, int>
Parameters
$points : array<string|int, mixed>
$scalars : array<string|int, mixed>
Return values
array<string|int, int>

multiplyPoint()

Multiply a point on the curve by a scalar

public multiplyPoint(array<string|int, mixed> $p, Integer $d) : array<string|int, mixed>

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
$p : array<string|int, mixed>
$d : Integer
Return values
array<string|int, mixed>

negatePoint()

Negates a point

public negatePoint(array<string|int, mixed> $p) : array<string|int, object>
Parameters
$p : array<string|int, mixed>
Return values
array<string|int, object>

randomInteger()

Returns a random integer

public randomInteger() : object
Return values
object

setBasePoint()

Set x and y coordinates for the base point

public setBasePoint(string|Integer $x, string|Integer $y) : mixed
Parameters
$x : string|Integer
$y : string|Integer

setCoefficients()

Set coefficients a and b

public setCoefficients(string $a, string $b) : mixed
Parameters
$a : string
$b : string

setModulo()

Sets the modulo

public setModulo(mixed ...$modulo) : mixed
Parameters
$modulo : mixed

setReduction()

Use a custom defined modular reduction function

public setReduction(callable $func) : object
Parameters
$func : callable
Return values
object

verifyPoint()

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

public verifyPoint(array<string|int, mixed> $p) : bool
Parameters
$p : array<string|int, mixed>
Return values
bool 

        

        
    




    

    

                                

                

                                
    

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