**6. Conclusions and Future Work**

The important outcome of our study is the possibility of extending the concept of handwritten identity to other personal information than the usual signature. Actually, by combining the usual signature with alphanumeric (date) and handwritten (place) personal information, personal identity security is significantly enhanced for all persons in uncontrolled mobile conditions. Moreover, with our strategy, the concept of user categories even disappears because all persons become very robust to attacks.

Another interesting outcome is that the complexity criterion is not sufficient to enhance the security of a signature. This is clearly observed on persons with the most complex signatures (low PE category): although the name-surname type is more complex than the usual signature, it is not more reliable in terms of resistance to attacks. This is because the usual signature conveys specific ballistic information about identity; this information can be completed by other handwritten information but cannot be removed and replaced for robust identity verification.

The finding of combining signature, date and place for enhancing identity security is in total accordance with public and legal usages in which identity information is requested. This may facilitate the implementation of the proposed enrollment strategy at a large scale.

In future work, we envisage implementing our strategy by developing an application on different mobile devices to study the practical usage of the proposed enrollment strategy, in terms of acquisition time during enrollment, user HMM training when acquiring signature followed by date and place in one shot, accuracy in mobility, and user acceptability and comfort. This will be conducted considering challenging mobile scenarios in terms of interoperability and time variability. Also, since our study demonstrates that augmenting the usual signature with alphanumeric and handwritten personal information enhances significantly verification performance, it would be interesting to study the impact of reducing the number of enrollment inputs. Furthermore, we will investigate the effectiveness of our strategy in terms of relative performance improvement when confronted to other classifiers.

**Author Contributions:** Formal analysis, M.A., N.H. and S.G.-S.; Investigation, M.A., N.H. and S.G.-S.; Methodology, N.H. and S.G.-S.; Project administration, N.H. and S.G.-S.; Software, M.A. and N.H.; Supervision, N.H. and S.G.-S.; Validation, N.H. and S.G.-S.; Visualization, M.A. and N.H.; Writing—original draft, N.H. and S.G.-S. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **Appendix A**


**Table A1.** The 19 dynamic features extracted point-wise on all signature types.

For computing the derivatives of a parameter *x*(*t*)*,* we used the regression equation as follows:

$$\mathbf{x}'(t) = \text{reg}(\mathbf{x}(t), \mathbf{Z}) = \frac{\sum\_{z=1}^{Z} z \ast (\mathbf{x}(t+z) - \mathbf{x}(t-z))}{2\sum\_{z=1}^{Z} z^2}$$

where z = 2, in order to obtain soft derivative curves.

Accordingly,

• Speed in *x* and *y* (N◦ 3–4 in Table A1):

$$v\_{\mathbf{x}}(t) = \text{reg}(\mathbf{x}(t), \mathbf{2}) \qquad \qquad v\_{\mathbf{y}}(t) = \text{reg}(y(t), \mathbf{2})$$

• The absolute speed (N◦ 5 in Table A1):

$$v(t) = \sqrt{v\_x^2\left(t\right) + v\_y^2\left(t\right)}$$

• Acceleration in x and y (N◦ 7–8 in Table A1):

$$a\_{\mathbf{x}}(t) = \operatorname{reg}(v\_{\mathbf{x}}(t), \mathbf{2}) \qquad \quad a\_{\mathbf{y}}(t) = \operatorname{reg}(v\_{\mathbf{y}}(t), \mathbf{2})$$

• The absolute acceleration (N◦ 9 in Table A1):

$$a(t) = \sqrt{a\_x^2 \left(t\right) + a\_y^2 \left(t\right)}$$

• The tangential acceleration (N◦ 10 in Table A1):

$$a\_t(t) = r e\_{\mathbb{S}}(v(t), \mathbf{2}),$$

• Angle α between the absolute speed vector and the x axis (N◦ 11 in Table A1):

$$a(t) = \arcsin\left(\frac{v\_y(t)}{v(t)}\right)$$

• Sine and cosine of angle α (N◦ 12–13 in Table A1):

$$\operatorname{Sim}(\alpha(t)) = \left(\frac{v\_y(t)}{v(t)}\right) \qquad \operatorname{Cov}(\alpha(t)) = \left(\frac{v\_x(t)}{v(t)}\right)$$

• Variation φ of the angle α angle (N◦ 14 in Table A1):

$$\phi(t) = r \text{eg}(a(t), \mathbf{2})$$

• Sine and cosine of angle φ (N◦ 15–16 in Table A1):

$$\sin(\phi(t)) \qquad \qquad \cos(\phi(t))$$

• log(1 + *r*(*t*)) (N◦ 17 in Table A1), where r is the curvature radius of the signature at the present point *t*:

$$lr(t) = \log(1 + r(t)) = \log\left(1 + \frac{v\_l(t)}{\phi(t)}\right)$$

