namespace Elementor; use Elementor\Core\Admin\Menu\Admin_Menu_Manager; use Elementor\Core\Wp_Api; use Elementor\Core\Admin\Admin; use Elementor\Core\Breakpoints\Manager as Breakpoints_Manager; use Elementor\Core\Common\App as CommonApp; use Elementor\Core\Debug\Inspector; use Elementor\Core\Documents_Manager; use Elementor\Core\Experiments\Manager as Experiments_Manager; use Elementor\Core\Kits\Manager as Kits_Manager; use Elementor\Core\Editor\Editor; use Elementor\Core\Files\Manager as Files_Manager; use Elementor\Core\Files\Assets\Manager as Assets_Manager; use Elementor\Core\Modules_Manager; use Elementor\Core\Schemes\Manager as Schemes_Manager; use Elementor\Core\Settings\Manager as Settings_Manager; use Elementor\Core\Settings\Page\Manager as Page_Settings_Manager; use Elementor\Core\Upgrade\Elementor_3_Re_Migrate_Globals; use Elementor\Modules\History\Revisions_Manager; use Elementor\Core\DynamicTags\Manager as Dynamic_Tags_Manager; use Elementor\Core\Logger\Manager as Log_Manager; use Elementor\Core\Page_Assets\Loader as Assets_Loader; use Elementor\Modules\System_Info\Module as System_Info_Module; use Elementor\Data\Manager as Data_Manager; use Elementor\Data\V2\Manager as Data_Manager_V2; use Elementor\Core\Common\Modules\DevTools\Module as Dev_Tools; use Elementor\Core\Files\Uploads_Manager as Uploads_Manager; if ( ! defined( 'ABSPATH' ) ) { exit; } /** * Elementor plugin. * * The main plugin handler class is responsible for initializing Elementor. The * class registers and all the components required to run the plugin. * * @since 1.0.0 */ class Plugin { const ELEMENTOR_DEFAULT_POST_TYPES = [ 'page', 'post' ]; /** * Instance. * * Holds the plugin instance. * * @since 1.0.0 * @access public * @static * * @var Plugin */ public static $instance = null; /** * Database. * * Holds the plugin database handler which is responsible for communicating * with the database. * * @since 1.0.0 * @access public * * @var DB */ public $db; /** * Controls manager. * * Holds the plugin controls manager handler is responsible for registering * and initializing controls. * * @since 1.0.0 * @access public * * @var Controls_Manager */ public $controls_manager; /** * Documents manager. * * Holds the documents manager. * * @since 2.0.0 * @access public * * @var Documents_Manager */ public $documents; /** * Schemes manager. * * Holds the plugin schemes manager. * * @since 1.0.0 * @access public * * @var Schemes_Manager */ public $schemes_manager; /** * Elements manager. * * Holds the plugin elements manager. * * @since 1.0.0 * @access public * * @var Elements_Manager */ public $elements_manager; /** * Widgets manager. * * Holds the plugin widgets manager which is responsible for registering and * initializing widgets. * * @since 1.0.0 * @access public * * @var Widgets_Manager */ public $widgets_manager; /** * Revisions manager. * * Holds the plugin revisions manager which handles history and revisions * functionality. * * @since 1.0.0 * @access public * * @var Revisions_Manager */ public $revisions_manager; /** * Images manager. * * Holds the plugin images manager which is responsible for retrieving image * details. * * @since 2.9.0 * @access public * * @var Images_Manager */ public $images_manager; /** * Maintenance mode. * * Holds the maintenance mode manager responsible for the "Maintenance Mode" * and the "Coming Soon" features. * * @since 1.0.0 * @access public * * @var Maintenance_Mode */ public $maintenance_mode; /** * Page settings manager. * * Holds the page settings manager. * * @since 1.0.0 * @access public * * @var Page_Settings_Manager */ public $page_settings_manager; /** * Dynamic tags manager. * * Holds the dynamic tags manager. * * @since 1.0.0 * @access public * * @var Dynamic_Tags_Manager */ public $dynamic_tags; /** * Settings. * * Holds the plugin settings. * * @since 1.0.0 * @access public * * @var Settings */ public $settings; /** * Role Manager. * * Holds the plugin role manager. * * @since 2.0.0 * @access public * * @var Core\RoleManager\Role_Manager */ public $role_manager; /** * Admin. * * Holds the plugin admin. * * @since 1.0.0 * @access public * * @var Admin */ public $admin; /** * Tools. * * Holds the plugin tools. * * @since 1.0.0 * @access public * * @var Tools */ public $tools; /** * Preview. * * Holds the plugin preview. * * @since 1.0.0 * @access public * * @var Preview */ public $preview; /** * Editor. * * Holds the plugin editor. * * @since 1.0.0 * @access public * * @var Editor */ public $editor; /** * Frontend. * * Holds the plugin frontend. * * @since 1.0.0 * @access public * * @var Frontend */ public $frontend; /** * Heartbeat. * * Holds the plugin heartbeat. * * @since 1.0.0 * @access public * * @var Heartbeat */ public $heartbeat; /** * System info. * * Holds the system info data. * * @since 1.0.0 * @access public * * @var System_Info_Module */ public $system_info; /** * Template library manager. * * Holds the template library manager. * * @since 1.0.0 * @access public * * @var TemplateLibrary\Manager */ public $templates_manager; /** * Skins manager. * * Holds the skins manager. * * @since 1.0.0 * @access public * * @var Skins_Manager */ public $skins_manager; /** * Files manager. * * Holds the plugin files manager. * * @since 2.1.0 * @access public * * @var Files_Manager */ public $files_manager; /** * Assets manager. * * Holds the plugin assets manager. * * @since 2.6.0 * @access public * * @var Assets_Manager */ public $assets_manager; /** * Icons Manager. * * Holds the plugin icons manager. * * @access public * * @var Icons_Manager */ public $icons_manager; /** * WordPress widgets manager. * * Holds the WordPress widgets manager. * * @since 1.0.0 * @access public * * @var WordPress_Widgets_Manager */ public $wordpress_widgets_manager; /** * Modules manager. * * Holds the plugin modules manager. * * @since 1.0.0 * @access public * * @var Modules_Manager */ public $modules_manager; /** * Beta testers. * * Holds the plugin beta testers. * * @since 1.0.0 * @access public * * @var Beta_Testers */ public $beta_testers; /** * Inspector. * * Holds the plugin inspector data. * * @since 2.1.2 * @access public * * @var Inspector */ public $inspector; /** * @var Admin_Menu_Manager */ public $admin_menu_manager; /** * Common functionality. * * Holds the plugin common functionality. * * @since 2.3.0 * @access public * * @var CommonApp */ public $common; /** * Log manager. * * Holds the plugin log manager. * * @access public * * @var Log_Manager */ public $logger; /** * Dev tools. * * Holds the plugin dev tools. * * @access private * * @var Dev_Tools */ private $dev_tools; /** * Upgrade manager. * * Holds the plugin upgrade manager. * * @access public * * @var Core\Upgrade\Manager */ public $upgrade; /** * Tasks manager. * * Holds the plugin tasks manager. * * @var Core\Upgrade\Custom_Tasks_Manager */ public $custom_tasks; /** * Kits manager. * * Holds the plugin kits manager. * * @access public * * @var Core\Kits\Manager */ public $kits_manager; /** * @var \Elementor\Data\V2\Manager */ public $data_manager_v2; /** * Legacy mode. * * Holds the plugin legacy mode data. * * @access public * * @var array */ public $legacy_mode; /** * App. * * Holds the plugin app data. * * @since 3.0.0 * @access public * * @var App\App */ public $app; /** * WordPress API. * * Holds the methods that interact with WordPress Core API. * * @since 3.0.0 * @access public * * @var Wp_Api */ public $wp; /** * Experiments manager. * * Holds the plugin experiments manager. * * @since 3.1.0 * @access public * * @var Experiments_Manager */ public $experiments; /** * Uploads manager. * * Holds the plugin uploads manager responsible for handling file uploads * that are not done with WordPress Media. * * @since 3.3.0 * @access public * * @var Uploads_Manager */ public $uploads_manager; /** * Breakpoints manager. * * Holds the plugin breakpoints manager. * * @since 3.2.0 * @access public * * @var Breakpoints_Manager */ public $breakpoints; /** * Assets loader. * * Holds the plugin assets loader responsible for conditionally enqueuing * styles and script assets that were pre-enabled. * * @since 3.3.0 * @access public * * @var Assets_Loader */ public $assets_loader; /** * Clone. * * Disable class cloning and throw an error on object clone. * * The whole idea of the singleton design pattern is that there is a single * object. Therefore, we don't want the object to be cloned. * * @access public * @since 1.0.0 */ public function __clone() { _doing_it_wrong( __FUNCTION__, sprintf( 'Cloning instances of the singleton "%s" class is forbidden.', get_class( $this ) ), // phpcs:ignore WordPress.Security.EscapeOutput.OutputNotEscaped '1.0.0' ); } /** * Wakeup. * * Disable unserializing of the class. * * @access public * @since 1.0.0 */ public function __wakeup() { _doing_it_wrong( __FUNCTION__, sprintf( 'Unserializing instances of the singleton "%s" class is forbidden.', get_class( $this ) ), // phpcs:ignore WordPress.Security.EscapeOutput.OutputNotEscaped '1.0.0' ); } /** * Instance. * * Ensures only one instance of the plugin class is loaded or can be loaded. * * @since 1.0.0 * @access public * @static * * @return Plugin An instance of the class. */ public static function instance() { if ( is_null( self::$instance ) ) { self::$instance = new self(); /** * Elementor loaded. * * Fires when Elementor was fully loaded and instantiated. * * @since 1.0.0 */ do_action( 'elementor/loaded' ); } return self::$instance; } /** * Init. * * Initialize Elementor Plugin. Register Elementor support for all the * supported post types and initialize Elementor components. * * @since 1.0.0 * @access public */ public function init() { $this->add_cpt_support(); $this->init_components(); /** * Elementor init. * * Fires when Elementor components are initialized. * * After Elementor finished loading but before any headers are sent. * * @since 1.0.0 */ do_action( 'elementor/init' ); } /** * Get install time. * * Retrieve the time when Elementor was installed. * * @since 2.6.0 * @access public * @static * * @return int Unix timestamp when Elementor was installed. */ public function get_install_time() { $installed_time = get_option( '_elementor_installed_time' ); if ( ! $installed_time ) { $installed_time = time(); update_option( '_elementor_installed_time', $installed_time ); } return $installed_time; } /** * @since 2.3.0 * @access public */ public function on_rest_api_init() { // On admin/frontend sometimes the rest API is initialized after the common is initialized. if ( ! $this->common ) { $this->init_common(); } } /** * Init components. * * Initialize Elementor components. Register actions, run setting manager, * initialize all the components that run elementor, and if in admin page * initialize admin components. * * @since 1.0.0 * @access private */ private function init_components() { $this->experiments = new Experiments_Manager(); $this->breakpoints = new Breakpoints_Manager(); $this->inspector = new Inspector(); Settings_Manager::run(); $this->db = new DB(); $this->controls_manager = new Controls_Manager(); $this->documents = new Documents_Manager(); $this->kits_manager = new Kits_Manager(); $this->schemes_manager = new Schemes_Manager(); $this->elements_manager = new Elements_Manager(); $this->widgets_manager = new Widgets_Manager(); $this->skins_manager = new Skins_Manager(); $this->files_manager = new Files_Manager(); $this->assets_manager = new Assets_Manager(); $this->icons_manager = new Icons_Manager(); $this->settings = new Settings(); $this->tools = new Tools(); $this->editor = new Editor(); $this->preview = new Preview(); $this->frontend = new Frontend(); $this->maintenance_mode = new Maintenance_Mode(); $this->dynamic_tags = new Dynamic_Tags_Manager(); $this->modules_manager = new Modules_Manager(); $this->templates_manager = new TemplateLibrary\Manager(); $this->role_manager = new Core\RoleManager\Role_Manager(); $this->system_info = new System_Info_Module(); $this->revisions_manager = new Revisions_Manager(); $this->images_manager = new Images_Manager(); $this->wp = new Wp_Api(); $this->assets_loader = new Assets_Loader(); $this->uploads_manager = new Uploads_Manager(); $this->admin_menu_manager = new Admin_Menu_Manager(); $this->admin_menu_manager->register_actions(); User::init(); Api::init(); Tracker::init(); $this->upgrade = new Core\Upgrade\Manager(); $this->custom_tasks = new Core\Upgrade\Custom_Tasks_Manager(); $this->app = new App\App(); if ( is_admin() ) { $this->heartbeat = new Heartbeat(); $this->wordpress_widgets_manager = new WordPress_Widgets_Manager(); $this->admin = new Admin(); $this->beta_testers = new Beta_Testers(); new Elementor_3_Re_Migrate_Globals(); } } /** * @since 2.3.0 * @access public */ public function init_common() { $this->common = new CommonApp(); $this->common->init_components(); } /** * Get Legacy Mode * * @since 3.0.0 * @deprecated 3.1.0 Use `Plugin::$instance->experiments->is_feature_active()` instead * * @param string $mode_name Optional. Default is null * * @return bool|bool[] */ public function get_legacy_mode( $mode_name = null ) { self::$instance->modules_manager->get_modules( 'dev-tools' )->deprecation ->deprecated_function( __METHOD__, '3.1.0', 'Plugin::$instance->experiments->is_feature_active()' ); $legacy_mode = [ 'elementWrappers' => ! self::$instance->experiments->is_feature_active( 'e_dom_optimization' ), ]; if ( ! $mode_name ) { return $legacy_mode; } if ( isset( $legacy_mode[ $mode_name ] ) ) { return $legacy_mode[ $mode_name ]; } // If there is no legacy mode with the given mode name; return false; } /** * Add custom post type support. * * Register Elementor support for all the supported post types defined by * the user in the admin screen and saved as `elementor_cpt_support` option * in WordPress `$wpdb->options` table. * * If no custom post type selected, usually in new installs, this method * will return the two default post types: `page` and `post`. * * @since 1.0.0 * @access private */ private function add_cpt_support() { $cpt_support = get_option( 'elementor_cpt_support', self::ELEMENTOR_DEFAULT_POST_TYPES ); foreach ( $cpt_support as $cpt_slug ) { add_post_type_support( $cpt_slug, 'elementor' ); } } /** * Register autoloader. * * Elementor autoloader loads all the classes needed to run the plugin. * * @since 1.6.0 * @access private */ private function register_autoloader() { require_once ELEMENTOR_PATH . '/includes/autoloader.php'; Autoloader::run(); } /** * Plugin Magic Getter * * @since 3.1.0 * @access public * * @param $property * @return mixed * @throws \Exception */ public function __get( $property ) { if ( 'posts_css_manager' === $property ) { self::$instance->modules_manager->get_modules( 'dev-tools' )->deprecation->deprecated_argument( 'Plugin::$instance->posts_css_manager', '2.7.0', 'Plugin::$instance->files_manager' ); return $this->files_manager; } if ( 'data_manager' === $property ) { return Data_Manager::instance(); } if ( property_exists( $this, $property ) ) { throw new \Exception( 'Cannot access private property.' ); } return null; } /** * Plugin constructor. * * Initializing Elementor plugin. * * @since 1.0.0 * @access private */ private function __construct() { $this->register_autoloader(); $this->logger = Log_Manager::instance(); $this->data_manager_v2 = Data_Manager_V2::instance(); Maintenance::init(); Compatibility::register_actions(); add_action( 'init', [ $this, 'init' ], 0 ); add_action( 'rest_api_init', [ $this, 'on_rest_api_init' ], 9 ); } final public static function get_title() { return esc_html__( 'Elementor', 'elementor' ); } } if ( ! defined( 'ELEMENTOR_TESTS' ) ) { // In tests we run the instance manually. Plugin::instance(); } {"id":26146,"date":"2025-07-06T07:04:41","date_gmt":"2025-07-06T01:34:41","guid":{"rendered":"https:\/\/urbanedge.co.in\/vrsi\/?p=26146"},"modified":"2026-03-29T16:11:18","modified_gmt":"2026-03-29T10:41:18","slug":"securite-des-paiements-plongee-mathematique-dans-le-double-facteur-et-son-influence-sur-les-bonus-des-casinos-en-ligne","status":"publish","type":"post","link":"https:\/\/urbanedge.co.in\/vrsi\/securite-des-paiements-plongee-mathematique-dans-le-double-facteur-et-son-influence-sur-les-bonus-des-casinos-en-ligne\/","title":{"rendered":"S\u00e9curit\u00e9 des paiements : plong\u00e9e math\u00e9matique dans le double facteur et son influence sur les bonus des casinos en ligne"},"content":{"rendered":"

S\u00e9curit\u00e9 des paiements : plong\u00e9e math\u00e9matique dans le double facteur et son influence sur les bonus des casinos en ligne<\/h1>\n

La protection des transactions est aujourd\u2019hui au c\u0153ur des pr\u00e9occupations des joueurs de jeux d\u2019argent sur internet. Chaque d\u00e9p\u00f4t ou retrait expose \u00e0 un risque de fraude qui peut rapidement transformer une session lucrative en cauchemar financier. Les joueurs cherchent donc \u00e0 conjuguer deux exigences : s\u00e9curiser leurs mouvements d\u2019argent tout en profitant au maximum des promotions telles que le welcome\u2011bonus, le cash\u2011back ou les free spins offerts par les sites fran\u00e7ais les plus attractifs. <\/p>\n

Dans ce contexte, la plupart des plateformes ont adopt\u00e9 le Two\u2011Factor Authentication (2FA) comme bouclier suppl\u00e9mentaire contre le phishing et le vol d\u2019identit\u00e9. Le guide d\u2019Associationlasource.Fr, site de revue ind\u00e9pendant sp\u00e9cialis\u00e9 dans le classement des meilleurs casino\u202fen\u202fligne<\/a>, montre que les op\u00e9rateurs qui int\u00e8grent un deuxi\u00e8me facteur voient leurs taux de fraude chuter de fa\u00e7on spectaculaire tout en conservant une offre promotionnelle comp\u00e9titive. <\/p>\n

Nous allons d\u00e9cortiquer les algorithmes sous\u2011jacents au\u202f2FA, comparer diff\u00e9rentes impl\u00e9mentations utilis\u00e9es par les leaders du march\u00e9, quantifier leur robustesse via des mod\u00e8les probabilistes et finalement \u00e9valuer comment cette s\u00e9curit\u00e9 accrue modifie la dynamique des programmes de bonus (welcome\u2011bonus, cash\u2011back, free spins\u2026). <\/p>\n

Les bases math\u00e9matiques du Two\u2011Factor Authentication<\/h2>\n

Un \u00ab\u202ffacteur\u202f\u00bb se d\u00e9finit cryptographiquement comme une preuve ind\u00e9pendante appartenant \u00e0 l\u2019une des trois cat\u00e9gories suivantes\u202f: connaissance (mot\u2011de\u2011passe), possession (token ou code re\u00e7u) ou inherence (biom\u00e9trie). En combinant deux cat\u00e9gories on obtient un syst\u00e8me o\u00f9 l\u2019acc\u00e8s ne peut \u00eatre valid\u00e9 que si les deux preuves sont pr\u00e9sent\u00e9es simultan\u00e9ment. <\/p>\n

Dans un mod\u00e8le probabiliste simple on note A l\u2019\u00e9v\u00e9nement \u00ab\u202fattaque r\u00e9ussie\u202f\u00bb. Si p\u2081 repr\u00e9sente la probabilit\u00e9 qu\u2019un attaquant devine ou vole le mot\u2011de\u2011passe et p\u2082 la probabilit\u00e9 d\u2019intercepter ou de reproduire le second facteur, alors la probabilit\u00e9 totale d\u2019intrusion s\u2019\u00e9crit :<\/p>\n

P(intrusion)=p\u2081\u00b7p\u2082 <\/p>\n

L\u2019effet multiplicatif montre que m\u00eame une petite am\u00e9lioration du deuxi\u00e8me facteur diminue drastiquement le risque global. Prenons deux sc\u00e9narios chiffr\u00e9s\u202f: pour un mot\u2011de\u2011passe fort on estime p\u2081\u224810\u207b\u2076 tandis qu\u2019un mot\u2011de\u2011pas faible donne p\u2081\u224810\u207b\u00b3. Le second facteur d\u00e9pend du support\u202f: un TOTP g\u00e9n\u00e9r\u00e9 par une application peut offrir p\u2082\u224810\u207b\u2074 ; un SMS intercept\u00e9 dans certaines conditions grimpe \u00e0 p\u2082\u224810\u207b\u00b2 voire plus selon la vuln\u00e9rabilit\u00e9 du r\u00e9seau SS7. <\/p>\n

En combinant ces valeurs on obtient par exemple pour un compte prot\u00e9g\u00e9 par TOTP et mot\u2011de\u2011passe fort\u202f: P(intrusion)=10\u207b\u2076\u00b710\u207b\u2074=10\u207b\u00b9\u2070, soit une chance sur dix milliards d\u2019\u00eatre compromis lors d\u2019une tentative unique. Ce calcul illustre pourquoi Associationlasource.Fr recommande aux joueurs fran\u00e7ais de privil\u00e9gier les casinos qui imposent un facteur suppl\u00e9mentaire robuste avant tout mouvement mon\u00e9taire. <\/p>\n

Algorithmes TOTP vs OTP SMS : comparaison quantitative<\/h2>\n

Le standard RFC\u202f6238 d\u00e9crit le Time\u2011Based One\u2011Time Password (TOTP). Un secret partag\u00e9 de longueur L bits est combin\u00e9 \u00e0 l\u2019horloge Unix pour produire un code \u00e0 six chiffres chaque tranche \u0394t de trente secondes. L\u2019espace cl\u00e9 possible vaut donc 10\u2076 \u2248\u202f20 bits d\u2019entropie par intervalle ; la fen\u00eatre temporelle autoris\u00e9e \u00e9largit l\u00e9g\u00e8rement cet espace lorsqu\u2019on accepte les codes g\u00e9n\u00e9r\u00e9s \u00b11 intervalle autour du temps exact, portant l\u2019entropie effective \u00e0 environ 19 bits pour la plupart des impl\u00e9mentations courantes sur mobile. <\/p>\n

En revanche, l\u2019OTP envoy\u00e9 par SMS repose sur l\u2019infrastructure t\u00e9l\u00e9phonique SS7 dont plusieurs \u00e9tudes ont mesur\u00e9 une probabilit\u00e9 d\u2019interception p_sms\u224810\u207b\u2074 \u00e0 cause de vuln\u00e9rabilit\u00e9s exploit\u00e9es par des op\u00e9rateurs malveillants ou des logiciels espionnants install\u00e9s sur le t\u00e9l\u00e9phone cible. Cette probabilit\u00e9 s\u2019ajoute aux risques li\u00e9s aux num\u00e9ros port\u00e9s ou aux forfaits pr\u00e9pay\u00e9s non s\u00e9curis\u00e9s souvent utilis\u00e9s par les joueurs de casino en ligne France l\u00e9gal qui souhaitent rester anonymes via paysafecard ou autres solutions similaires. <\/p>\n\n\n\n\n\n\n
M\u00e9thode<\/th>\nEntropie moyenne<\/th>\nLatence moyenne<\/th>\nCo\u00fbt op\u00e9rationnel<\/th>\n<\/tr>\n<\/thead>\n
TOTP<\/td>\n\u224819 bits<\/td>\n\u22641 s<\/td>\nAucun frais serveur<\/td>\n<\/tr>\n
SMS OTP<\/td>\n\u224816 bits<\/td>\n3\u20135 s<\/td>\nFrais SMS + infrastructure SS7<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Le tableau ci\u2011dessus r\u00e9sume que TOTP apporte plus d\u2019entropie avec une latence quasi nulle et sans co\u00fbt additionnel pour le casino \u2013 crit\u00e8re crucial pour un casino fiable en ligne o\u00f9 chaque seconde compte pendant la phase de validation du d\u00e9p\u00f4t avant que le joueur ne d\u00e9clenche son bonus de bienvenue ou ses free spins sur Starburst<\/em> ou Gonzo\u2019s Quest<\/em>. <\/p>\n

Du point de vue de l\u2019utilisateur final, la perception de s\u00e9curit\u00e9 augmente lorsqu\u2019il voit appara\u00eetre une petite fen\u00eatre demandant son code TOTP plut\u00f4t qu\u2019un texte \u00ab\u00a0SMS re\u00e7u\u00a0\u00bb. Cette impression psychologique renforce la confiance et encourage davantage de d\u00e9p\u00f4ts \u2013 un effet indirect mais mesurable sur le ROI global du programme promotionnel du casino online \u00e9tudi\u00e9 par Associationlasource.Fr. <\/p>\n

Impact du Double Facteur sur les processus de paiement<\/h2>\n

Un d\u00e9p\u00f4t typique dans un casino fran\u00e7ais passe par deux \u00e9tapes distinctes\u00a0: A) authentification initiale (login + mot\u2011de\u2011passe) puis B) validation du paiement via un code \u00e0 usage unique envoy\u00e9 par TOTP ou SMS. On peut mod\u00e9liser ce flux avec une cha\u00eene de Markov comportant trois \u00e9tats \u2013 \u00ab\u202fattente\u00bb, \u00ab\u202fvalidation\u00bb, \u00ab\u202f\u00e9chec\u00bb. La probabilit\u00e9 de transition entre \u00ab\u202fattente\u00bb et \u00ab\u202fvalidation\u00bb d\u00e9pend directement du temps moyen requis pour saisir le deuxi\u00e8me facteur (t\u2082). <\/p>\n

Pour TOTP t\u2082 se situe g\u00e9n\u00e9ralement entre 1 et 3 secondes ; pour SMS il varie entre 4 et 7 secondes selon la qualit\u00e9 du r\u00e9seau mobile et les \u00e9ventuels retards li\u00e9s aux op\u00e9rateurs t\u00e9l\u00e9coms fran\u00e7ais. Si \u03bb repr\u00e9sente le nombre moyen quotidien de d\u00e9p\u00f4ts trait\u00e9s par un casino online (~150\u2009000 transactions), alors l\u2019impact mon\u00e9taire additionnel se calcule ainsi\u00a0:<\/p>\n

Co\u00fbt_friction = \u03bb \u00d7 t\u2082 \u00d7 Valeur_horaire<\/p>\n

En prenant une valeur horaire moyenne estim\u00e9e \u00e0 \u20ac15\/h pour le joueur amateur qui consid\u00e8re son temps comme capital lorsqu\u2019il joue aux machines \u00e0 sous vid\u00e9o (Book of Dead<\/em>, RTP\u00a096,21 %), on obtient :<\/p>\n