**1. Introduction**

The handwritten signature has been for a long time a usual mean to establish personal consent, with legal value for administrative and financial institutions. With the impressive proliferation of mobile devices having embedded sensors (smartphones, tablets), added to the development of online services, signing on digital platforms has become a reality in different sectors for identity security (banking, legal transactions, e-commerce among other). This reality has signified a turning point in the field of online signature biometrics.

In the last forty years, research studies were focused on online signatures captured on high quality sensors such as Wacom digitizing tablets, in controlled office-like scenarios, with a devoted ad-hoc pen stylus. Impedovo and Pirlo [1] published an article giving a detailed overview on the state-of-the-art techniques. Diaz et al. [2] presented a recent update on automatic signature verification (ASV). The research community made significant efforts for acquiring several online signature corpora [1–11] and conducting international evaluations of ASV systems [2,6,12–16].

Recent research studies have focused on signature verification in mobile conditions, using touch-screen sensors largely deployed nowadays. Nevertheless, the mobile scenario implies much more variability of acquisition conditions, like posture, writing tool (stylus or finger), screen size, sensor technology, interoperability, setting several new challenging issues that impact verification performance [2,17].

Usually, for improving verification performance, different strategies were exploited in the literature: (i) acquiring signatures in controlled conditions [1–16]; (ii) using a high quality sensor (such as a Wacom tablet) with high temporal and spatial resolution, and able to capture other time functions than pen coordinates, as pen pressure and pen inclination angles [18]; (iii) selecting reference signatures in order to control intra-personal variability [19–21]; (iv) extracting several features for signature description (as pressure, speed, and acceleration, etc.) [1–16] or by means of a deep neural network [2,22–25].

However, some of these strategies are no longer possible in the mobile scenario: as pointed out by [17], the sensors are not of the same quality, in terms of temporal resolution in particular, acquisition conditions are highly variable, and some sensors are limited to the capture of only pen coordinates. In the so-called "cloud scenario" [17], users acquire their signatures as they want, standing, sitting or moving, handling the device on the hand at different angles or orientations, or placing it on any support. A smartphone is usually handheld, while a tablet may be placed on the desktop or sustained by the left arm if the writer is right-handed. The consequence is that verification performance is strongly degraded in mobile conditions [2,15,16,26–39].

In the present paper, we study the online signature biometrics in the framework of uncontrolled mobile conditions. The challenging question then is how to improve verification performance in uncontrolled mobile conditions? To respond to this question, we propose a novel and original scheme for enhancing signature information content at the enrollment phase and reinforce its resistance to attacks, on a largely deployed touch-screen sensor technology. To this end, we propose different enrollment strategies for signature enrichment and assess them in terms of data quality and verification system performance.

The enrollment phase is critical for any biometric system since it determines the genuine signatures that will represent the user at the verification step. These signatures are called "Reference signatures". In our previous works on signature quality assessment, we have shown that a signature's resistance to attacks depends on its information content, quantified by an entropy-based measure, called personal entropy [28,40–43]. We identified automatically different risk levels in signatures related to three user categories, and in particular a "problematic" population, characterized by simple and highly variable signatures, very vulnerable to attacks.

Based on these findings, we propose in this paper, since the enrollment phase on a touch screen sensor, a novel strategy that turns any signature with a "high risk" into a "low risk" one. For signature enrichment, we use complementary personal handwritten information, as initials, name-surname, date and place of birth. We choose these information since a person is familiarized to append it for expressing her consent in administrative or legal frameworks. For this study, we consider different types of signatures (the usual signature, initials, name-surname, date and place of birth) and hybrid types as well (some combinations of the already mentioned types), and analyze the impact of each in terms of information content and resistance to attacks (skilled forgeries).

This paper is organized as follows: in Section 2, we present previous works of the literature related to online signature analysis on mobile devices. In Section 3, we describe the signature database and recall the personal entropy concept and the verification system used. In Section 4, we report the obtained results later summarized and discussed in Section 5. Finally, Section 6 presents the conclusions and future perspectives of our study.
