<?php
/**
* Curves over y^2 + x*y = x^3 + a*x^2 + b
*
* These are curves used in SEC 2 over prime fields: http://www.secg.org/SEC2-Ver-1.0.pdf
* The curve is a weierstrass curve with a[3] and a[2] set to 0.
*
* Uses Jacobian Coordinates for speed if able:
*
* https://en.wikipedia.org/wiki/Jacobian_curve
* https://en.wikibooks.org/wiki/Cryptography/Prime_Curve/Jacobian_Coordinates
*
* PHP version 5 and 7
*
* @author Jim Wigginton <terrafrost@php.net>
* @copyright 2017 Jim Wigginton
* @license http://www.opensource.org/licenses/mit-license.html MIT License
* @link http://pear.php.net/package/Math_BigInteger
*/
namespace phpseclib3\Crypt\EC\BaseCurves;
use phpseclib3\Math\BigInteger;
use phpseclib3\Math\BinaryField;
use phpseclib3\Math\BinaryField\Integer as BinaryInteger;
/**
* Curves over y^2 + x*y = x^3 + a*x^2 + b
*
* @author Jim Wigginton <terrafrost@php.net>
*/
class Binary extends Base
{
/**
* Binary Field Integer factory
*
* @var \phpseclib3\Math\BinaryField
*/
protected $factory;
/**
* Cofficient for x^1
*
* @var object
*/
protected $a;
/**
* Cofficient for x^0
*
* @var object
*/
protected $b;
/**
* Base Point
*
* @var object
*/
protected $p;
/**
* The number one over the specified finite field
*
* @var object
*/
protected $one;
/**
* The modulo
*
* @var BigInteger
*/
protected $modulo;
/**
* The Order
*
* @var BigInteger
*/
protected $order;
/**
* Sets the modulo
*/
public function setModulo(...$modulo)
{
$this->modulo = $modulo;
$this->factory = new BinaryField(...$modulo);
$this->one = $this->factory->newInteger("\1");
}
/**
* Set coefficients a and b
*
* @param string $a
* @param string $b
*/
public function setCoefficients($a, $b)
{
if (!isset($this->factory)) {
throw new \RuntimeException('setModulo needs to be called before this method');
}
$this->a = $this->factory->newInteger(pack('H*', $a));
$this->b = $this->factory->newInteger(pack('H*', $b));
}
/**
* Set x and y coordinates for the base point
*
* @param string|BinaryInteger $x
* @param string|BinaryInteger $y
*/
public function setBasePoint($x, $y)
{
switch (true) {
case !is_string($x) && !$x instanceof BinaryInteger:
throw new \UnexpectedValueException('Argument 1 passed to Binary::setBasePoint() must be a string or an instance of BinaryField\Integer');
case !is_string($y) && !$y instanceof BinaryInteger:
throw new \UnexpectedValueException('Argument 2 passed to Binary::setBasePoint() must be a string or an instance of BinaryField\Integer');
}
if (!isset($this->factory)) {
throw new \RuntimeException('setModulo needs to be called before this method');
}
$this->p = [
is_string($x) ? $this->factory->newInteger(pack('H*', $x)) : $x,
is_string($y) ? $this->factory->newInteger(pack('H*', $y)) : $y
];
}
/**
* Retrieve the base point as an array
*
* @return array
*/
public function getBasePoint()
{
if (!isset($this->factory)) {
throw new \RuntimeException('setModulo needs to be called before this method');
}
/*
if (!isset($this->p)) {
throw new \RuntimeException('setBasePoint needs to be called before this method');
}
*/
return $this->p;
}
/**
* Adds two points on the curve
*
* @return FiniteField[]
*/
public function addPoint(array $p, array $q)
{
if (!isset($this->factory)) {
throw new \RuntimeException('setModulo needs to be called before this method');
}
if (!count($p) || !count($q)) {
if (count($q)) {
return $q;
}
if (count($p)) {
return $p;
}
return [];
}
if (!isset($p[2]) || !isset($q[2])) {
throw new \RuntimeException('Affine coordinates need to be manually converted to "Jacobi" coordinates or vice versa');
}
if ($p[0]->equals($q[0])) {
return !$p[1]->equals($q[1]) ? [] : $this->doublePoint($p);
}
// formulas from http://hyperelliptic.org/EFD/g12o/auto-shortw-jacobian.html
list($x1, $y1, $z1) = $p;
list($x2, $y2, $z2) = $q;
$o1 = $z1->multiply($z1);
$b = $x2->multiply($o1);
if ($z2->equals($this->one)) {
$d = $y2->multiply($o1)->multiply($z1);
$e = $x1->add($b);
$f = $y1->add($d);
$z3 = $e->multiply($z1);
$h = $f->multiply($x2)->add($z3->multiply($y2));
$i = $f->add($z3);
$g = $z3->multiply($z3);
$p1 = $this->a->multiply($g);
$p2 = $f->multiply($i);
$p3 = $e->multiply($e)->multiply($e);
$x3 = $p1->add($p2)->add($p3);
$y3 = $i->multiply($x3)->add($g->multiply($h));
return [$x3, $y3, $z3];
}
$o2 = $z2->multiply($z2);
$a = $x1->multiply($o2);
$c = $y1->multiply($o2)->multiply($z2);
$d = $y2->multiply($o1)->multiply($z1);
$e = $a->add($b);
$f = $c->add($d);
$g = $e->multiply($z1);
$h = $f->multiply($x2)->add($g->multiply($y2));
$z3 = $g->multiply($z2);
$i = $f->add($z3);
$p1 = $this->a->multiply($z3->multiply($z3));
$p2 = $f->multiply($i);
$p3 = $e->multiply($e)->multiply($e);
$x3 = $p1->add($p2)->add($p3);
$y3 = $i->multiply($x3)->add($g->multiply($g)->multiply($h));
return [$x3, $y3, $z3];
}
/**
* Doubles a point on a curve
*
* @return FiniteField[]
*/
public function doublePoint(array $p)
{
if (!isset($this->factory)) {
throw new \RuntimeException('setModulo needs to be called before this method');
}
if (!count($p)) {
return [];
}
if (!isset($p[2])) {
throw new \RuntimeException('Affine coordinates need to be manually converted to "Jacobi" coordinates or vice versa');
}
// formulas from http://hyperelliptic.org/EFD/g12o/auto-shortw-jacobian.html
list($x1, $y1, $z1) = $p;
$a = $x1->multiply($x1);
$b = $a->multiply($a);
if ($z1->equals($this->one)) {
$x3 = $b->add($this->b);
$z3 = clone $x1;
$p1 = $a->add($y1)->add($z3)->multiply($this->b);
$p2 = $a->add($y1)->multiply($b);
$y3 = $p1->add($p2);
return [$x3, $y3, $z3];
}
$c = $z1->multiply($z1);
$d = $c->multiply($c);
$x3 = $b->add($this->b->multiply($d->multiply($d)));
$z3 = $x1->multiply($c);
$p1 = $b->multiply($z3);
$p2 = $a->add($y1->multiply($z1))->add($z3)->multiply($x3);
$y3 = $p1->add($p2);
return [$x3, $y3, $z3];
}
/**
* Returns the X coordinate and the derived Y coordinate
*
* Not supported because it is covered by patents.
* Quoting https://www.openssl.org/docs/man1.1.0/apps/ecparam.html ,
*
* "Due to patent issues the compressed option is disabled by default for binary curves
* and can be enabled by defining the preprocessor macro OPENSSL_EC_BIN_PT_COMP at
* compile time."
*
* @return array
*/
public function derivePoint($m)
{
throw new \RuntimeException('Point compression on binary finite field elliptic curves is not supported');
}
/**
* Tests whether or not the x / y values satisfy the equation
*
* @return boolean
*/
public function verifyPoint(array $p)
{
list($x, $y) = $p;
$lhs = $y->multiply($y);
$lhs = $lhs->add($x->multiply($y));
$x2 = $x->multiply($x);
$x3 = $x2->multiply($x);
$rhs = $x3->add($this->a->multiply($x2))->add($this->b);
return $lhs->equals($rhs);
}
/**
* Returns the modulo
*
* @return \phpseclib3\Math\BigInteger
*/
public function getModulo()
{
return $this->modulo;
}
/**
* Returns the a coefficient
*
* @return \phpseclib3\Math\PrimeField\Integer
*/
public function getA()
{
return $this->a;
}
/**
* Returns the a coefficient
*
* @return \phpseclib3\Math\PrimeField\Integer
*/
public function getB()
{
return $this->b;
}
/**
* 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)
*
* @return \phpseclib3\Math\PrimeField\Integer[]
*/
public function convertToAffine(array $p)
{
if (!isset($p[2])) {
return $p;
}
list($x, $y, $z) = $p;
$z = $this->one->divide($z);
$z2 = $z->multiply($z);
return [
$x->multiply($z2),
$y->multiply($z2)->multiply($z)
];
}
/**
* Converts an affine point to a jacobian coordinate
*
* @return \phpseclib3\Math\PrimeField\Integer[]
*/
public function convertToInternal(array $p)
{
if (isset($p[2])) {
return $p;
}
$p[2] = clone $this->one;
$p['fresh'] = true;
return $p;
}
}
NFC Pay was founded with a vision to transform the way people handle transactions. Our journey is defined by a commitment to innovation, security, and convenience. We strive to deliver seamless, user-friendly payment solutions that make everyday transactions effortless and secure. Our mission is to empower you to pay with ease and confidence, anytime, anywhere.
Simplifying Payments, One Tap at a Time.
Reinventing Your Wallet for Modern Convenience.
Smart Payments for a Effortless Lifestyle.
Experience the Ease of Tap and Pay.
Innovative Solutions for Your Daily Transactions.
FAQ Section
Frequently Asked Questions About NFC Pay
Here are answers to some common questions about NFC Pay. We aim to provide clear and concise information to help you understand how our platform works and how it can benefit you. If you have any further inquiries, please don’t hesitate to contact our support team.
How do I register for NFC Pay?
Download the app and sign up using your email or phone number, then complete the verification process.
Is my payment information secure?
Yes, we use advanced encryption and security protocols to protect your payment details.
Can I add multiple cards to my NFC Pay wallet?
Absolutely, you can link multiple debit or credit cards to your wallet.
How do I transfer money to another user?
Go to the transfer section, select the recipient, enter the amount, and authorize the transfer.
What should I do if I forget my PIN?
Use the “Forgot PIN” feature in the app to reset it following the provided instructions.
How can I activate my merchant account?
Sign up for a merchant account through the app and follow the setup instructions to start accepting payments.
Can I track my payment status?
Yes, you can view and track your payment status in the account dashboard
In the digital age, privacy concerns have become increasingly paramount, prompting the European Union to enact the General Data Protection Regulation (GDPR) in 2018. Among its many provisions, GDPR sets strict guidelines for the collection and processing of personal data, including the use of cookies on websites. Privacy Policy
