## 1 Introduction  
In the hyper-connected world of today, everything is equipped with connectivity. Since 2010, the smartphone has become a key device for networking, and its rapid evolution has provided us with improved quality of life. The smartphone's personal assistant feature can help users with almost everything in their daily lives. However, smartphones have access to a considerable amount of private information of its owner/user; therefore, data privacy and mobile security mechanisms have seen a manifold increase in order to protect the data and privacy of the owner/user against various security attacks attempted by unauthorized users [1]. To provide a safe and reliable mobile experience to users, numerous companies have invested a large amount of capital in both hardware and software development to enhance the security mechanisms for mobile devices. Among the different layers of a mobile security system, user authentication is the first and most important because a successful unauthorized access to the device would be the worst possible compromise to the user's data and privacy. Consequently, various studies have been conducted on user authentication for mobile devices [2]. Three well-known user authentication methods for mobile devices with touchscreens are personal identification number (PIN), password, and pattern lock [3]. These methods are known to be vulnerable to certain threat scenarios, such as shoulder surfing attack (SSA) and smudge attack (SA). For example, in SSA, the intruder snoops over the authorized user's shoulder while the user enters their PIN, and later unlocks the device with the same PIN [4]. To overcome the vulnerability of these static information-based user authentication methods, physical biometric-based, e.g., face-, fingerprint-, iris-, blood-vessel-, and voice-based user authentication has been studied [5]. Although physical biometric-based authentication methods reported excellent authentication performance in previous studies, they have limited expandability because they require expensive additional hardware to be installed to recognize the physical biometrics [6]. Moreover, it is well known that physical biometrics can be spoofed; previous studies reported that techniques, such as printed face forgery, copied fingerprint, and copied iris, were successful in gaining unauthorized access to an authorized user's device [7]. To address this problem, human behavioral biometric-based user authentication for mobile devices has been studied. These studies employed various features of the built-in smartphone sensors, such as pressure, velocity, acceleration, and keystroke [8]. However, they have several limitations as follows. First, the authentication performance in them relies considerably on handcrafted features. In other words, theirs is not an end-to-end authentication model that is optimized for raw sequential data. Therefore, information loss of human behavioral characteristics can occur [9]. Second, there are few studies for human behavioral biometric-based user authentication with deep learning methods, such as temporal convolution neural network (TCN) [10] and recurrent neural network (RNN) [11] that have demonstrated outstanding performance for sequential data analytics. Third, these studies demonstrated that the authentication performance decreased rapidly in the case of intrusion attacks, such as SSA and SA. To overcome the aforementioned limitations, in this study, we propose a draw-a-deep-pattern (DDP) that is a deep learning-based end-to-end smartphone user authentication method using sequential data obtained from drawing a character or freestyle pattern on a smartphone touchscreen. Characteristics of the proposed DDP method are outlined below. First, we used drawing patterns, which can significantly increase the number of input attempts than the authentication types of PIN, \(3\times 3\) grid pattern lock [12], and drawing PIN number [13]. Second, we designed an end-to-end model that works with raw sequential data instead of handcrafted features.