A PIN pad is a common way to authenticate, in particular for mobile applications. To strengthen PIN authentication we utilize behavioural biometrics in the form of keystroke dynamics. For authentication we require new PIN entries from the actual user to be accepted, while entries from an adversary to be rejected. Hence we strive to capture a user profile as compact as possible, such that false acceptance rates (FAR) are low, while the true acceptance rate (TAR) remains high. We estimate a user profile P by training one-class classification methods on user data U. We compare three one-class classification methods, namely Multivariate Gaussian Estimation (MGE), Support Vector Data Description (SVDD) and k-Minimal Enclosing Ball (k-MEB). We collected PIN data and analysed nine users which entered their PIN correctly at least 50 times. We find all methods outperform dummy classifiers. In most cases, a TAR score of over 0.8 combined with a maximum FAR score of at most 0.1 is achieved after tuning. Therefore, we conclude adding a behavioural biometric check does increase security of PIN authentication substantially.

A graph G=(V,E) is a mathematical model for a network with vertex set V and edge set E. A Random Graph model is a probabilistic graph. A Random Geometric Graph is a Random Graph were each vertex has a location in a space χ. We compare the Erdos-Rényi random graph, G(n,p), to the Random Geometric Graph model, RGG(n,r) where, in general we use r=c / (n^(-1/d)), with dimension d. It is known that for p = λ*/n the k-core has a first-order phase transition in G(n,p) where λ* is the critical value for the k-core. The k-core is a global property of a graph. The k-core is the largest induced subgraph where each vertex has at least degree k. We suggest by simulations and a supportive proof that for the RGG-model a first-order phase transition not plausible. A inhomogeneous extension of the RGG-model with a vertex weight distribution T is a Geometric Inhomogeneous Random Graph model (GIRG). We also prove why some heavy-tailed (i.e. power-law) distributions almost surely have a k-core, when the amount of vertices v, which have weights greater than the square root of n, is greater than k. Furthermore, we rephrase from known literature how using a fixed equation for a branching process is a useful tool for analysing the existence of a k-core. In particular, the critical value for the 3-core is recovered using the probability of a binary tree embedding in branching processes, with the root having at least 3 children.