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In recent years, physically unclonable functions (PUFs) have gained significant attraction in IoT security applications, such as cryptographic key generation and entity authentication. PUFs extract the uncontrollable production characteristics of different devices to generate unique fingerprints for security applications. When generating PUF-based secret keys, the reliability and entropy of the keys are vital factors. This study proposes a novel method for generating PUF-based keys from a set of measurements. Firstly, it formulates the group-based key generation problem as an optimization problem and solves it using integer linear programming (ILP), which guarantees finding the optimum solution. Then, a novel scheme for the extraction of keys from groups is proposed, which we call positioning syndrome coding (PSC). The use of ILP as well as the introduction of PSC facilitates the generation of high-entropy keys with low error correction costs. These new methods have been tested by applying them on the output of a capacitor network PUF. The results confirm the application of ILP and PSC in generating high-quality keys.
Physical unclonable functions (PUFs) are increasingly generating attention in the field of hardware-based security for the Internet of Things (IoT). A PUF, as its name implies, is a physical element with a special and unique inherent characteristic and can act as the security anchor for authentication and cryptographic applications. Keeping in mind that the PUF outputs are prone to change in the presence of noise and environmental variations, it is critical to derive reliable keys from the PUF and to use the maximum entropy at the same time. In this work, the PUF output positioning (POP) method is proposed, which is a novel method for grouping the PUF outputs in order to maximize the extracted entropy. To achieve this, an offset data is introduced as helper data, which is used to relax the constraints considered for the grouping of PUF outputs, and deriving more entropy, while reducing the secret key error bits. To implement the method, the key enrollment and key generation algorithms are presented. Based on a theoretical analysis of the achieved entropy, it is proven that POP can maximize the achieved entropy, while respecting the constraints induced to guarantee the reliability of the secret key. Moreover, a detailed security analysis is presented, which shows the resilience of the method against cyber-security attacks. The findings of this work are evaluated by applying the method on a hybrid printed PUF, where it can be practically shown that the proposed method outperforms other existing group-based PUF key generation methods.