In login form model

/**
 * LoginForm class.
 * LoginForm is the data structure for keeping
 * user login form data. It is used by the 'login' action of 'SiteController'.
 */
class LoginForm extends CFormModel
{
	public $password;
	public $rememberMe;
        public $email; // Email

	private $_identity;

	/**
	 * Declares the validation rules.
	 * The rules state that username and password are required,
	 * and password needs to be authenticated.
	 */
	public function rules()
	{
		return array(
			// username and password are required
			array('email, password', 'required'),
			// rememberMe needs to be a boolean
			array('rememberMe', 'boolean'),
                        array('email', 'email'), 
			// password needs to be authenticated
			array('password', 'authenticate'),
		);
	}

	/**
	 * Declares attribute labels.
	 */
	public function attributeLabels()
	{
		return array(
			'rememberMe'=>'Remember me next time',
		);
	}

	/**
	 * Authenticates the password.
	 * This is the 'authenticate' validator as declared in rules().
	 */
	public function authenticate($attribute,$params)
	{
		if(!$this->hasErrors())
		{
			$this->_identity=new UserIdentity($this->email,$this->password);
			if(!$this->_identity->authenticate())
				$this->addError('password','Incorrect username or password.');
		}
	}

	/**
	 * Logs in the user using the given username and password in the model.
	 * @return boolean whether login is successful
	 */
	public function login()
	{
		if($this->_identity===null)
		{
			$this->_identity=new UserIdentity($this->email,$this->password);
			$this->_identity->authenticate();
		}
		if($this->_identity->errorCode===UserIdentity::ERROR_NONE)
		{
			$duration=$this->rememberMe ? 3600*24*30 : 0; // 30 days
			Yii::app()->user->login($this->_identity,$duration);
			return true;
		}
		else
			return false;
	}
}

And then extends CUserIdentity

/**
 * UserIdentity represents the data needed to identity a user.
 * It contains the authentication method that checks if the provided
 * data can identity the user.
 */
class UserIdentity extends CUserIdentity
{
    /**
     * @var string email
     */
    public $email;
    const ERROR_EMAIL_INVALID=1;

    /**
     * @param string $email
     * @param string $password
     */
    public function __construct($email, $password)
    {
        parent::__construct($email, $password);
        $this->email=$email;
    }

    /**
	 * Authenticates a user.
	 * The example implementation makes sure if the username and password
	 * are both 'demo'.
	 * In practical applications, this should be changed to authenticate
	 * against some persistent user identity storage (e.g. database).
	 * @return boolean whether authentication succeeds.
	 */
	public function authenticate()
    {
		$users=array(
			// username => password
			'demo@demo.fr'=>'demo',
			'admin@admin.fr'=>'admin'
		);
		if(!isset($users[$this->email]))
			$this->errorCode=self::ERROR_EMAIL_INVALID;
		elseif($users[$this->email]!==$this->password)
			$this->errorCode=self::ERROR_PASSWORD_INVALID;
		else
			$this->errorCode=self::ERROR_NONE;
		return !$this->errorCode;
	}

    /**
     * @return mixed
     */
    public function getPassword()
    {
        return $this->password;
    }

    /**
     * @return mixed
     */
    public function getEmail()
    {
        return $this->email;
    }
}