<?php

/**
 * Curves over y^2 = x^3 + a*x + 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[1], 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\Common\Functions\Strings;
use phpseclib3\Math\BigInteger;
use phpseclib3\Math\Common\FiniteField\Integer;
use phpseclib3\Math\PrimeField;
use phpseclib3\Math\PrimeField\Integer as PrimeInteger;

/**
 * Curves over y^2 = x^3 + a*x + b
 *
 * @author  Jim Wigginton <terrafrost@php.net>
 */
class Prime extends Base
{
    /**
     * Prime Field Integer factory
     *
     * @var \phpseclib3\Math\PrimeFields
     */
    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 number two over the specified finite field
     *
     * @var object
     */
    protected $two;

    /**
     * The number three over the specified finite field
     *
     * @var object
     */
    protected $three;

    /**
     * The number four over the specified finite field
     *
     * @var object
     */
    protected $four;

    /**
     * The number eight over the specified finite field
     *
     * @var object
     */
    protected $eight;

    /**
     * The modulo
     *
     * @var BigInteger
     */
    protected $modulo;

    /**
     * The Order
     *
     * @var BigInteger
     */
    protected $order;

    /**
     * Sets the modulo
     */
    public function setModulo(BigInteger $modulo)
    {
        $this->modulo = $modulo;
        $this->factory = new PrimeField($modulo);
        $this->two = $this->factory->newInteger(new BigInteger(2));
        $this->three = $this->factory->newInteger(new BigInteger(3));
        // used by jacobian coordinates
        $this->one = $this->factory->newInteger(new BigInteger(1));
        $this->four = $this->factory->newInteger(new BigInteger(4));
        $this->eight = $this->factory->newInteger(new BigInteger(8));
    }

    /**
     * Set coefficients a and b
     */
    public function setCoefficients(BigInteger $a, BigInteger $b)
    {
        if (!isset($this->factory)) {
            throw new \RuntimeException('setModulo needs to be called before this method');
        }
        $this->a = $this->factory->newInteger($a);
        $this->b = $this->factory->newInteger($b);
    }

    /**
     * Set x and y coordinates for the base point
     *
     * @param BigInteger|PrimeInteger $x
     * @param BigInteger|PrimeInteger $y
     * @return PrimeInteger[]
     */
    public function setBasePoint($x, $y)
    {
        switch (true) {
            case !$x instanceof BigInteger && !$x instanceof PrimeInteger:
                throw new \UnexpectedValueException('Argument 1 passed to Prime::setBasePoint() must be an instance of either BigInteger or PrimeField\Integer');
            case !$y instanceof BigInteger && !$y instanceof PrimeInteger:
                throw new \UnexpectedValueException('Argument 2 passed to Prime::setBasePoint() must be an instance of either BigInteger or PrimeField\Integer');
        }
        if (!isset($this->factory)) {
            throw new \RuntimeException('setModulo needs to be called before this method');
        }
        $this->p = [
            $x instanceof BigInteger ? $this->factory->newInteger($x) : $x,
            $y instanceof BigInteger ? $this->factory->newInteger($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 "fresh" jacobian form on the curve
     *
     * @return FiniteField[]
     */
    protected function jacobianAddPointMixedXY(array $p, array $q)
    {
        list($u1, $s1) = $p;
        list($u2, $s2) = $q;
        if ($u1->equals($u2)) {
            if (!$s1->equals($s2)) {
                return [];
            } else {
                return $this->doublePoint($p);
            }
        }
        $h = $u2->subtract($u1);
        $r = $s2->subtract($s1);
        $h2 = $h->multiply($h);
        $h3 = $h2->multiply($h);
        $v = $u1->multiply($h2);
        $x3 = $r->multiply($r)->subtract($h3)->subtract($v->multiply($this->two));
        $y3 = $r->multiply(
            $v->subtract($x3)
        )->subtract(
            $s1->multiply($h3)
        );
        return [$x3, $y3, $h];
    }

    /**
     * Adds one "fresh" jacobian form on the curve
     *
     * The second parameter should be the "fresh" one
     *
     * @return FiniteField[]
     */
    protected function jacobianAddPointMixedX(array $p, array $q)
    {
        list($u1, $s1, $z1) = $p;
        list($x2, $y2) = $q;

        $z12 = $z1->multiply($z1);

        $u2 = $x2->multiply($z12);
        $s2 = $y2->multiply($z12->multiply($z1));
        if ($u1->equals($u2)) {
            if (!$s1->equals($s2)) {
                return [];
            } else {
                return $this->doublePoint($p);
            }
        }
        $h = $u2->subtract($u1);
        $r = $s2->subtract($s1);
        $h2 = $h->multiply($h);
        $h3 = $h2->multiply($h);
        $v = $u1->multiply($h2);
        $x3 = $r->multiply($r)->subtract($h3)->subtract($v->multiply($this->two));
        $y3 = $r->multiply(
            $v->subtract($x3)
        )->subtract(
            $s1->multiply($h3)
        );
        $z3 = $h->multiply($z1);
        return [$x3, $y3, $z3];
    }

    /**
     * Adds two jacobian coordinates on the curve
     *
     * @return FiniteField[]
     */
    protected function jacobianAddPoint(array $p, array $q)
    {
        list($x1, $y1, $z1) = $p;
        list($x2, $y2, $z2) = $q;

        $z12 = $z1->multiply($z1);
        $z22 = $z2->multiply($z2);

        $u1 = $x1->multiply($z22);
        $u2 = $x2->multiply($z12);
        $s1 = $y1->multiply($z22->multiply($z2));
        $s2 = $y2->multiply($z12->multiply($z1));
        if ($u1->equals($u2)) {
            if (!$s1->equals($s2)) {
                return [];
            } else {
                return $this->doublePoint($p);
            }
        }
        $h = $u2->subtract($u1);
        $r = $s2->subtract($s1);
        $h2 = $h->multiply($h);
        $h3 = $h2->multiply($h);
        $v = $u1->multiply($h2);
        $x3 = $r->multiply($r)->subtract($h3)->subtract($v->multiply($this->two));
        $y3 = $r->multiply(
            $v->subtract($x3)
        )->subtract(
            $s1->multiply($h3)
        );
        $z3 = $h->multiply($z1)->multiply($z2);
        return [$x3, $y3, $z3];
    }

    /**
     * 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 [];
        }

        // use jacobian coordinates
        if (isset($p[2]) && isset($q[2])) {
            if (isset($p['fresh']) && isset($q['fresh'])) {
                return $this->jacobianAddPointMixedXY($p, $q);
            }
            if (isset($p['fresh'])) {
                return $this->jacobianAddPointMixedX($q, $p);
            }
            if (isset($q['fresh'])) {
                return $this->jacobianAddPointMixedX($p, $q);
            }
            return $this->jacobianAddPoint($p, $q);
        }

        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])) {
            if (!$p[1]->equals($q[1])) {
                return [];
            } else { // eg. doublePoint
                list($numerator, $denominator) = $this->doublePointHelper($p);
            }
        } else {
            $numerator = $q[1]->subtract($p[1]);
            $denominator = $q[0]->subtract($p[0]);
        }
        $slope = $numerator->divide($denominator);
        $x = $slope->multiply($slope)->subtract($p[0])->subtract($q[0]);
        $y = $slope->multiply($p[0]->subtract($x))->subtract($p[1]);

        return [$x, $y];
    }

    /**
     * Returns the numerator and denominator of the slope
     *
     * @return FiniteField[]
     */
    protected function doublePointHelper(array $p)
    {
        $numerator = $this->three->multiply($p[0])->multiply($p[0])->add($this->a);
        $denominator = $this->two->multiply($p[1]);
        return [$numerator, $denominator];
    }

    /**
     * Doubles a jacobian coordinate on the curve
     *
     * @return FiniteField[]
     */
    protected function jacobianDoublePoint(array $p)
    {
        list($x, $y, $z) = $p;
        $x2 = $x->multiply($x);
        $y2 = $y->multiply($y);
        $z2 = $z->multiply($z);
        $s = $this->four->multiply($x)->multiply($y2);
        $m1 = $this->three->multiply($x2);
        $m2 = $this->a->multiply($z2->multiply($z2));
        $m = $m1->add($m2);
        $x1 = $m->multiply($m)->subtract($this->two->multiply($s));
        $y1 = $m->multiply($s->subtract($x1))->subtract(
            $this->eight->multiply($y2->multiply($y2))
        );
        $z1 = $this->two->multiply($y)->multiply($z);
        return [$x1, $y1, $z1];
    }

    /**
     * Doubles a "fresh" jacobian coordinate on the curve
     *
     * @return FiniteField[]
     */
    protected function jacobianDoublePointMixed(array $p)
    {
        list($x, $y) = $p;
        $x2 = $x->multiply($x);
        $y2 = $y->multiply($y);
        $s = $this->four->multiply($x)->multiply($y2);
        $m1 = $this->three->multiply($x2);
        $m = $m1->add($this->a);
        $x1 = $m->multiply($m)->subtract($this->two->multiply($s));
        $y1 = $m->multiply($s->subtract($x1))->subtract(
            $this->eight->multiply($y2->multiply($y2))
        );
        $z1 = $this->two->multiply($y);
        return [$x1, $y1, $z1];
    }

    /**
     * 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 [];
        }

        // use jacobian coordinates
        if (isset($p[2])) {
            if (isset($p['fresh'])) {
                return $this->jacobianDoublePointMixed($p);
            }
            return $this->jacobianDoublePoint($p);
        }

        list($numerator, $denominator) = $this->doublePointHelper($p);

        $slope = $numerator->divide($denominator);

        $x = $slope->multiply($slope)->subtract($p[0])->subtract($p[0]);
        $y = $slope->multiply($p[0]->subtract($x))->subtract($p[1]);

        return [$x, $y];
    }

    /**
     * Returns the X coordinate and the derived Y coordinate
     *
     * @return array
     */
    public function derivePoint($m)
    {
        $y = ord(Strings::shift($m));
        $x = new BigInteger($m, 256);
        $xp = $this->convertInteger($x);
        switch ($y) {
            case 2:
                $ypn = false;
                break;
            case 3:
                $ypn = true;
                break;
            default:
                throw new \RuntimeException('Coordinate not in recognized format');
        }
        $temp = $xp->multiply($this->a);
        $temp = $xp->multiply($xp)->multiply($xp)->add($temp);
        $temp = $temp->add($this->b);
        $b = $temp->squareRoot();
        if (!$b) {
            throw new \RuntimeException('Unable to derive Y coordinate');
        }
        $bn = $b->isOdd();
        $yp = $ypn == $bn ? $b : $b->negate();
        return [$xp, $yp];
    }

    /**
     * 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);
        $temp = $x->multiply($this->a);
        $temp = $x->multiply($x)->multiply($x)->add($temp);
        $rhs = $temp->add($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;
    }

    /**
     * Multiply and Add Points
     *
     * Adapted from:
     * https://github.com/indutny/elliptic/blob/725bd91/lib/elliptic/curve/base.js#L125
     *
     * @return int[]
     */
    public function multiplyAddPoints(array $points, array $scalars)
    {
        $length = count($points);

        foreach ($points as &$point) {
            $point = $this->convertToInternal($point);
        }

        $wnd = [$this->getNAFPoints($points[0], 7)];
        $wndWidth = [isset($points[0]['nafwidth']) ? $points[0]['nafwidth'] : 7];
        for ($i = 1; $i < $length; $i++) {
            $wnd[] = $this->getNAFPoints($points[$i], 1);
            $wndWidth[] = isset($points[$i]['nafwidth']) ? $points[$i]['nafwidth'] : 1;
        }

        $naf = [];

        // comb all window NAFs

        $max = 0;
        for ($i = $length - 1; $i >= 1; $i -= 2) {
            $a = $i - 1;
            $b = $i;
            if ($wndWidth[$a] != 1 || $wndWidth[$b] != 1) {
                $naf[$a] = $scalars[$a]->getNAF($wndWidth[$a]);
                $naf[$b] = $scalars[$b]->getNAF($wndWidth[$b]);
                $max = max(count($naf[$a]), count($naf[$b]), $max);
                continue;
            }

            $comb = [
                $points[$a], // 1
                null,        // 3
                null,        // 5
                $points[$b]  // 7
            ];

            $comb[1] = $this->addPoint($points[$a], $points[$b]);
            $comb[2] = $this->addPoint($points[$a], $this->negatePoint($points[$b]));

            $index = [
                -3, /* -1 -1 */
                -1, /* -1  0 */
                -5, /* -1  1 */
                -7, /*  0 -1 */
                 0, /*  0 -1 */
                 7, /*  0  1 */
                 5, /*  1 -1 */
                 1, /*  1  0 */
                 3  /*  1  1 */
            ];

            $jsf = self::getJSFPoints($scalars[$a], $scalars[$b]);

            $max = max(count($jsf[0]), $max);
            if ($max > 0) {
                $naf[$a] = array_fill(0, $max, 0);
                $naf[$b] = array_fill(0, $max, 0);
            } else {
                $naf[$a] = [];
                $naf[$b] = [];
            }

            for ($j = 0; $j < $max; $j++) {
                $ja = isset($jsf[0][$j]) ? $jsf[0][$j] : 0;
                $jb = isset($jsf[1][$j]) ? $jsf[1][$j] : 0;

                $naf[$a][$j] = $index[3 * ($ja + 1) + $jb + 1];
                $naf[$b][$j] = 0;
                $wnd[$a] = $comb;
            }
        }

        $acc = [];
        $temp = [0, 0, 0, 0];
        for ($i = $max; $i >= 0; $i--) {
            $k = 0;
            while ($i >= 0) {
                $zero = true;
                for ($j = 0; $j < $length; $j++) {
                    $temp[$j] = isset($naf[$j][$i]) ? $naf[$j][$i] : 0;
                    if ($temp[$j] != 0) {
                        $zero = false;
                    }
                }
                if (!$zero) {
                    break;
                }
                $k++;
                $i--;
            }

            if ($i >= 0) {
                $k++;
            }
            while ($k--) {
                $acc = $this->doublePoint($acc);
            }

            if ($i < 0) {
                break;
            }

            for ($j = 0; $j < $length; $j++) {
                $z = $temp[$j];
                $p = null;
                if ($z == 0) {
                    continue;
                }
                $p = $z > 0 ?
                    $wnd[$j][($z - 1) >> 1] :
                    $this->negatePoint($wnd[$j][(-$z - 1) >> 1]);
                $acc = $this->addPoint($acc, $p);
            }
        }

        return $this->convertToAffine($acc);
    }

    /**
     * Precomputes NAF points
     *
     * Adapted from:
     * https://github.com/indutny/elliptic/blob/725bd91/lib/elliptic/curve/base.js#L351
     *
     * @return int[]
     */
    private function getNAFPoints(array $point, $wnd)
    {
        if (isset($point['naf'])) {
            return $point['naf'];
        }

        $res = [$point];
        $max = (1 << $wnd) - 1;
        $dbl = $max == 1 ? null : $this->doublePoint($point);
        for ($i = 1; $i < $max; $i++) {
            $res[] = $this->addPoint($res[$i - 1], $dbl);
        }

        $point['naf'] = $res;

        /*
        $str = '';
        foreach ($res as $re) {
            $re[0] = bin2hex($re[0]->toBytes());
            $re[1] = bin2hex($re[1]->toBytes());
            $str.= "            ['$re[0]', '$re[1]'],\r\n";
        }
        file_put_contents('temp.txt', $str);
        exit;
        */

        return $res;
    }

    /**
     * Precomputes points in Joint Sparse Form
     *
     * Adapted from:
     * https://github.com/indutny/elliptic/blob/725bd91/lib/elliptic/utils.js#L96
     *
     * @return int[]
     */
    private static function getJSFPoints(Integer $k1, Integer $k2)
    {
        static $three;
        if (!isset($three)) {
            $three = new BigInteger(3);
        }

        $jsf = [[], []];
        $k1 = $k1->toBigInteger();
        $k2 = $k2->toBigInteger();
        $d1 = 0;
        $d2 = 0;

        while ($k1->compare(new BigInteger(-$d1)) > 0 || $k2->compare(new BigInteger(-$d2)) > 0) {
            // first phase
            $m14 = $k1->testBit(0) + 2 * $k1->testBit(1);
            $m14 += $d1;
            $m14 &= 3;

            $m24 = $k2->testBit(0) + 2 * $k2->testBit(1);
            $m24 += $d2;
            $m24 &= 3;

            if ($m14 == 3) {
                $m14 = -1;
            }
            if ($m24 == 3) {
                $m24 = -1;
            }

            $u1 = 0;
            if ($m14 & 1) { // if $m14 is odd
                $m8 = $k1->testBit(0) + 2 * $k1->testBit(1) + 4 * $k1->testBit(2);
                $m8 += $d1;
                $m8 &= 7;
                $u1 = ($m8 == 3 || $m8 == 5) && $m24 == 2 ? -$m14 : $m14;
            }
            $jsf[0][] = $u1;

            $u2 = 0;
            if ($m24 & 1) { // if $m24 is odd
                $m8 = $k2->testBit(0) + 2 * $k2->testBit(1) + 4 * $k2->testBit(2);
                $m8 += $d2;
                $m8 &= 7;
                $u2 = ($m8 == 3 || $m8 == 5) && $m14 == 2 ? -$m24 : $m24;
            }
            $jsf[1][] = $u2;

            // second phase
            if (2 * $d1 == $u1 + 1) {
                $d1 = 1 - $d1;
            }
            if (2 * $d2 == $u2 + 1) {
                $d2 = 1 - $d2;
            }
            $k1 = $k1->bitwise_rightShift(1);
            $k2 = $k2->bitwise_rightShift(1);
        }

        return $jsf;
    }

    /**
     * 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;
    }
}

• [F] Base.php
  Delete
• [F] Binary.php
  Delete
• [F] KoblitzPrime.php
  Delete
• [F] Montgomery.php
  Delete
• [F] Prime.php
  Delete
• [F] TwistedEdwards.php
  Delete

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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