DefaultModel.php

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<?php
namespace Magento\Captcha\Model;

use Magento\Captcha\Helper\Data;

class DefaultModel extends \Zend\Captcha\Image implements \Magento\Captcha\Model\CaptchaInterface
{
    const SESSION_WORD = 'word';

    const DEFAULT_WORD_LENGTH_FROM = 3;

    const DEFAULT_WORD_LENGTH_TO = 5;

    protected $captchaData;

    protected $expiration;

    protected $fsize = 22;

    protected $formId;

    protected $resLogFactory;

    protected $keepSession = true;

    protected $session;

    public function __construct(
        \Magento\Framework\Session\SessionManagerInterface $session,
        \Magento\Captcha\Helper\Data $captchaData,
        \Magento\Captcha\Model\ResourceModel\LogFactory $resLogFactory,
        $formId
    ) {
        parent::__construct();
        $this->session = $session;
        $this->captchaData = $captchaData;
        $this->resLogFactory = $resLogFactory;
        $this->formId = $formId;
    }

    private function getFormIdKey($key)
    {
        return $this->formId . '_' . $key;
    }

    public function getBlockName()
    {
        return \Magento\Captcha\Block\Captcha\DefaultCaptcha::class;
    }

    public function isRequired($login = null)
    {
        if (($this->isUserAuth()
                && !$this->isShownToLoggedInUser())
            || !$this->isEnabled()
            || !in_array(
                $this->formId,
                $this->getTargetForms()
            )
        ) {
            return false;
        }

        return $this->isShowAlways()
            || $this->isOverLimitAttempts($login)
            || $this->session->getData($this->getFormIdKey('show_captcha'));
    }

    public function isShownToLoggedInUser()
    {
        $forms = (array)$this->captchaData->getConfig('shown_to_logged_in_user');
        foreach ($forms as $formId => $isShownToLoggedIn) {
            if ($isShownToLoggedIn && $this->formId == $formId) {
                return true;
            }
        }
        return false;
    }

    private function isOverLimitAttempts($login)
    {
        return $this->isOverLimitIpAttempt() || $this->isOverLimitLoginAttempts($login);
    }

    private function getAllowedAttemptsForSameLogin()
    {
        return (int)$this->captchaData->getConfig('failed_attempts_login');
    }

    private function getAllowedAttemptsFromSameIp()
    {
        return (int)$this->captchaData->getConfig('failed_attempts_ip');
    }

    private function isOverLimitIpAttempt()
    {
        $countAttemptsByIp = $this->getResourceModel()->countAttemptsByRemoteAddress();
        return $countAttemptsByIp >= $this->getAllowedAttemptsFromSameIp();
    }

    private function isOverLimitLoginAttempts($login)
    {
        if ($login != false) {
            $countAttemptsByLogin = $this->getResourceModel()->countAttemptsByUserLogin($login);
            return $countAttemptsByLogin >= $this->getAllowedAttemptsForSameLogin();
        }
        return false;
    }

    private function isUserAuth()
    {
        return $this->session->isLoggedIn();
    }

    public function isCaseSensitive()
    {
        return (string)$this->captchaData->getConfig('case_sensitive');
    }

    public function getFont()
    {
        $font = (string)$this->captchaData->getConfig('font');
        $fonts = $this->captchaData->getFonts();

        if (isset($fonts[$font])) {
            $fontPath = $fonts[$font]['path'];
        } else {
            $fontData = array_shift($fonts);
            $fontPath = $fontData['path'];
        }

        return $fontPath;
    }

    public function getExpiration()
    {
        if (!$this->expiration) {
            $this->expiration = (int)$this->captchaData->getConfig('timeout') * 60;
        }
        return $this->expiration;
    }

    public function getTimeout()
    {
        return $this->getExpiration();
    }

    public function getImgDir()
    {
        return $this->captchaData->getImgDir();
    }

    public function getImgUrl()
    {
        return $this->captchaData->getImgUrl();
    }

    public function isCorrect($word)
    {
        $storedWord = $this->getWord();
        $this->clearWord();

        if (!$word || !$storedWord) {
            return false;
        }

        if (!$this->isCaseSensitive()) {
            $storedWord = strtolower($storedWord);
            $word = strtolower($word);
        }
        return $word === $storedWord;
    }

    public function getImgSrc()
    {
        return $this->getImgUrl() . $this->getId() . $this->getSuffix();
    }

    public function logAttempt($login)
    {
        if ($this->isEnabled() && in_array($this->formId, $this->getTargetForms())) {
            $this->getResourceModel()->logAttempt($login);
            if ($this->isOverLimitLoginAttempts($login)) {
                $this->setShowCaptchaInSession(true);
            }
        }
        return $this;
    }

    public function setShowCaptchaInSession($value = true)
    {
        if ($value !== true) {
            $value = false;
        }

        $this->session->setData($this->getFormIdKey('show_captcha'), $value);
    }

    protected function generateWord()
    {
        $word = '';
        $symbols = $this->getSymbols();
        $wordLen = $this->getWordLen();
        for ($i = 0; $i < $wordLen; $i++) {
            $word .= $symbols[array_rand($symbols)];
        }
        return $word;
    }

    private function getSymbols()
    {
        return str_split((string)$this->captchaData->getConfig('symbols'));
    }

    public function getWordLen()
    {
        $from = 0;
        $to = 0;
        $length = (string)$this->captchaData->getConfig('length');
        if (!is_numeric($length)) {
            if (preg_match('/(\d+)-(\d+)/', $length, $matches)) {
                $from = (int)$matches[1];
                $to = (int)$matches[2];
            }
        } else {
            $from = (int)$length;
            $to = (int)$length;
        }

        if ($to < $from || $from < 1 || $to < 1) {
            $from = self::DEFAULT_WORD_LENGTH_FROM;
            $to = self::DEFAULT_WORD_LENGTH_TO;
        }

        return \Magento\Framework\Math\Random::getRandomNumber($from, $to);
    }

    private function isShowAlways()
    {
        $captchaMode = (string)$this->captchaData->getConfig('mode');

        if ($captchaMode === Data::MODE_ALWAYS) {
            return true;
        }

        if ($captchaMode === Data::MODE_AFTER_FAIL
            && $this->getAllowedAttemptsForSameLogin() === 0
        ) {
            return true;
        }

        $alwaysFor = $this->captchaData->getConfig('always_for');
        foreach ($alwaysFor as $nodeFormId => $isAlwaysFor) {
            if ($isAlwaysFor && $this->formId == $nodeFormId) {
                return true;
            }
        }

        return false;
    }

    private function isEnabled()
    {
        return (string)$this->captchaData->getConfig('enable');
    }

    private function getTargetForms()
    {
        $formsString = (string)$this->captchaData->getConfig('forms');
        return explode(',', $formsString);
    }

    public function getWord()
    {
        $sessionData = $this->session->getData($this->getFormIdKey(self::SESSION_WORD));
        return time() < $sessionData['expires'] ? $sessionData['data'] : null;
    }

    protected function setWord($word)
    {
        $this->session->setData(
            $this->getFormIdKey(self::SESSION_WORD),
            ['data' => $word, 'expires' => time() + $this->getTimeout()]
        );
        $this->word = $word;
        return $this;
    }

    private function clearWord()
    {
        $this->session->unsetData($this->getFormIdKey(self::SESSION_WORD));
        $this->word = null;
        return $this;
    }

    protected function randomSize()
    {
        return \Magento\Framework\Math\Random::getRandomNumber(280, 300) / 100;
    }

    protected function gc()
    {
        //do nothing
    }

    private function getResourceModel()
    {
        return $this->resLogFactory->create();
    }
}