## 1 Introduction  
With increasing smartphone usage, several studies have focused on user authentication based on behavior characteristics that can be acquired on a smartphone; these include keystroke dynamics [1], gaze tracking [2], and dynamic signature [3]. Among these studies, dynamic signature verification is an authentication method that employs both the uniqueness of the signature and behavioral characteristics corresponding to signing. Similar to other biometrics, a dynamic signature is safe from loss and theft. In addition, the user is less resistant to using signatures for authentication than other biometrics such as fingerprints and iris. Users can produce a signature on the smartphone screen by using a stylus or their finger. Early studies [4; 5; 6; 7; 8; 9; 10] primarily focused on verifying signatures drawn by a stylus. Finger-drawn signature verification [3; 11; 12; 13] is relatively not well researched yet; however, it is currently actively discussed because most smartphones do not have a stylus, and finger signing is more convenient. The verification of finger-drawn signatures involves new challenges because it results in less precise signals than signatures drawn using a stylus. Moreover, many effective features such as pen pressure, pen angle, and the number of times a pen is lifted, cannot be employed. To improve the accuracy of signature verification, some studies [8; 9; 10] utilize machine learning techniques, which are one of the most noteworthy technologies. [PERSON] et al. [3] used multilayerperceptron (MLP), a two-class classifier, for finger-drawn signature verification with dynamic features involving finger and phone movements. Their method exhibited a verification accuracy of 94.8% for classifying the subject and other objects. However, this technique does not represent the capability of distinguishing forged signatures. Two-class classifiers such as MLP are at greater risk of misclassifying a forged signature as the subject, because forged signatures closely resemble the subject [10; 14]. Although a signature marked on a smartphone screen disappears immediately after verification, it is easy for an adversary to imitate a signature through shoulder surfing and smudging, which involves tracing the smudge remaining on the screen [11]. Therefore, the verification for distinguishing forged signatures must be improved to provide secure services. Further, the difference in the time between registering a signature and verifying a new signature is also an important issue. Unlike biometrics, such as those involving the fingerprint and iris, behavioral patterns can change with time. Although [15] focused on the issue of this time difference, they worked towards verifying a PIN number, and not dynamic signatures, drawn using the finger. In this paper, we propose a novel dynamic verification approach for finger-drawn signatures, which provides improved accuracy against forged signatures and time-deferred signatures. The proposed method exploits two deep learning algorithms: Convolutional neural network (CNN) [16; 17] for feature extraction, and an autoencoder (AE) [18] as a classifier. CNNs are trained for distinguishing forged signatures from genuine signatures, and the trained CNN is used for feature extraction and not as a classifier. Specifically, the output of the CNN's intermediate layer, which we call _S-vector_, is used as the input to an AE for building the subject model. Because a CNN is known to be capable of extracting features for classification by itself [17], we assume that the CNN trained for a specific purpose could extract features effective for that purpose. For example, a CNN trained with forged signatures can extract features that are common in forging activities such as hesitation and delay before drawing the complicated part of a signature. The proposed method exploits AE as a classifier owing to its high accuracy in solving one-class distinction problems like user authentication. Our previous work [19] and [PERSON] et al.