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In file /app/config/parameters.php, add the parameters for your ldap connection.

For BackOffice part

In /controllers/admin/AdminLogController.php, add "use Symfony\Component\Ldap\Ldap;" before the class.

In function __construct, I've 

if (!headers_sent()) {
$this->testLdap();
//header('Login: true');
}

And the 2 function I created:

public function testLdap()
{
  //l'HTTP_USER_AGENT est de la forme "FedPol-Portal/2.0 44123456F"
  $sso = $_SERVER['HTTP_USER_AGENT'];
  $ssoPart = array_pop(explode(' ', $sso));
  $langue=substr($ssoPart,9,1);
  $uid = substr($ssoPart, 0, 9);
  $container = $this->buildContainer();
  $host = $container->getParameter('ldap_host');
  $port = intval($container->getParameter('ldap_port'));
  $base = $container->getParameter('ldap_base');
  $classeObject = $container->getParameter('ldap_classe');
  $ldap = Ldap::create('ext_ldap', [
  'host' => $host,
  'port' => $port
  ]);
  $ldap->bind();
  $query = $ldap->query($base, '(&(uid='.$uid.')(objectclass='.$classeObject.'))');
  $results = $query->execute()->toArray();
  $mail = $results[0]->getAttribute("mail")[0];
  $password = $results[0]->getAttribute("userPassword")[0];
  $admin = $results[0]->getAttribute("bePolbruAuthEditShopFin")[0];
  $this->processLoginTest($mail,$password);
}

//it's a copy of processLogin function
public function processLoginTest($email,$passwd)
    {
        /* Check fields validity */
        /*$passwd = trim(Tools::getValue('passwd'));
        $email = trim(Tools::getValue('email'));*/
		
        if (empty($email)) {
            $this->errors[] = $this->trans('Email is empty.', array(), 'Admin.Notifications.Error');
        } elseif (!Validate::isEmail($email)) {
            $this->errors[] = $this->trans('Invalid email address.', array(), 'Admin.Notifications.Error');
        }
		
        if (empty($passwd)) {
            $this->errors[] = $this->trans('The password field is blank.', array(), 'Admin.Notifications.Error');
        } elseif (!Validate::isPasswd($passwd)) {
            $this->errors[] = $this->trans('Invalid password.', array(), 'Admin.Notifications.Error');
        }
        if (!count($this->errors)) {
            // Find employee
            $this->context->employee = new Employee();
            $is_employee_loaded = $this->context->employee->getByEmail($email);
            $employee_associated_shop = $this->context->employee->getAssociatedShops();
            if (!$is_employee_loaded) {
                $this->errors[] = $this->trans('The employee does not exist, or the password provided is incorrect.', array(), 'Admin.Login.Notification');
                $this->context->employee->logout();
            } elseif (empty($employee_associated_shop) && !$this->context->employee->isSuperAdmin()) {
                $this->errors[] = $this->trans('This employee does not manage the shop anymore (either the shop has been deleted or permissions have been revoked).', array(), 'Admin.Login.Notification');
                $this->context->employee->logout();
            } else {
                PrestaShopLogger::addLog($this->trans('Back office connection from %ip%', array('%ip%' => Tools::getRemoteAddr()), 'Admin.Advparameters.Feature'), 1, null, '', 0, true, (int) $this->context->employee->id);

                $this->context->employee->remote_addr = (int) ip2long(Tools::getRemoteAddr());
                // Update cookie
                $cookie = Context::getContext()->cookie;
                $cookie->id_employee = $this->context->employee->id;
                $cookie->email = $this->context->employee->email;
                $cookie->profile = $this->context->employee->id_profile;
                $cookie->passwd = $this->context->employee->passwd;
                $cookie->remote_addr = $this->context->employee->remote_addr;

                if (!Tools::getValue('stay_logged_in')) {
                    $cookie->last_activity = time();
                }

                $cookie->write();

                // If there is a valid controller name submitted, redirect to it
                if (isset($_POST['redirect']) && Validate::isControllerName($_POST['redirect'])) {
                    $url = $this->context->link->getAdminLink($_POST['redirect']);
                } else {
                    $tab = new Tab((int) $this->context->employee->default_tab);
                    $url = $this->context->link->getAdminLink($tab->class_name);
                }

                if (Tools::isSubmit('ajax')) {
                    die(json_encode(array('hasErrors' => false, 'redirect' => $url)));
                } else {
                    $this->redirect_after = $url;
                }
            }
        }
        if (Tools::isSubmit('ajax')) {
            die(json_encode(array('hasErrors' => true, 'errors' => $this->errors)));
        }
    }

In /classes/Employee.php, set the required option for passwd at false.

For front part

Solution in this topic (with removed link to Sign out)