Biometric systems are widely used for authentication and identification. The False Match Rate (FMR) quantifies the probability of matching a biometric template to a non-corresponding template and serves as an indicator of the system robustness against security threats. We analyze biometric systems through two main contributions. First, we study untargeted attacks, where an adversary aims to impersonate any user in the database. We compute the number of trials needed for a successful impersonation and derive the critical population size ( i.e., the maximum database size) and critical (FMR) required to maintain security against untargeted attacks as the database grows. Second, we address the biometric birthday problem, which quantifies the probability that there exists two distinct users that collide ( i.e., can impersonate each other). We compute approximate and exact probabilities of collision and derive the associated critical population size and critical (FMR) to bound the risk of biometric collisions, particularly in large-scale databases. These thresholds provide actionable insights for designing biometric systems that mitigate the risks of impersonation and biometric collisions, particularly in large-scale databases. Nevertheless, our findings show that current systems fail to meet the required security level against untargeted attacks, even in small databases, and face significant challenges with the biometric birthday problem as databases grow.

Cancelable biometric schemes aim at generating secure biometric templates by combining user specific tokens, such as password, stored secret or salt, along with biometric data. This type of transformation is constructed as a composition of a biometric transformation with a feature extraction algorithm. The security requirements of cancelable biometric schemes concern the irreversibility, unlinkability and revocability of templates, without losing in accuracy of comparison. While several schemes were recently attacked regarding these requirements, full reversibility of such a composition in order to produce colliding biometric characteristics, and specifically presentation attacks, were never demonstrated to the best of our knowledge. In this paper, we formalize these attacks for a traditional cancelable scheme with the help of integer linear programming (ILP) and quadratically constrained quadratic programming (QCQP). Solving these optimization problems allows an adversary to slightly alter its fingerprint image in order to impersonate any individual. Moreover, in an even more severe scenario, it is possible to simultaneously impersonate several individuals.

Biometric recognition encompasses two operating modes. The first one is biometric identification which consists in determining the identity of an individual based on her biometrics and requires browsing the entire database (i.e., a 1:N search). The other one is biometric authentication which corresponds to verifying claimed biometrics of an individual (i.e., a 1:1 search) to authenticate her, or grant her access to some services. The matching process is based on the similarities between a fresh and an enrolled biometric template. Considering the case of binary templates, we investigate how a highly populated database yields near-collisions, impacting the security of both the operating modes. Insight into the security of binary templates is given by establishing a lower bound on the size of templates and an upper bound on the size of a template database depending on security parameters. We provide efficient algorithms for partitioning a leaked template database in order to improve the generation of a master-template-set that can impersonates any enrolled user and possibly some future users. Practical impacts of proposed algorithms are finally emphasized with experimental studies.