Existential Unforgeability in Quantum Authentication From Quantum Physical Unclonable Functions Based on Random von Neumann Measurement

Physical Unclonable Functions (PUFs) are hardware devices with the assumption of possessing inherent, non-clonable physical randomness which leads to unique pairs of inputs and outputs that provide a secure fingerprint for cryptographic protocols like Authentication. In the case of quantum PUFs (QPUFs), the input-output pairs consists of quantum states instead of classical bitstrings, offering advantages over classical PUFs (CPUFs) such as challenge reusability via public channels and non-reliance over any trusted party due to the no-cloning theorem. In recent literature, a generalized mathematical frame-work for studying QPUFs was developed, which paved the way for having QPUF models with provable security. It was proved that existential unforgeability against Quantum Polynomial Time (QPT) adversaries cannot be achieved by any random unitary QPUF. Since measurements are non-unitary quantum processes, we define a QPUF based on random von Neumann measurements. We prove that such a QPUF is existentially unforgeable. Thus, we introduce the first model in existing literature that depicts such a high level of provable security. We also prove that the Quantum Phase Estimation (QPE) protocol applied on a Haar random unitary serves as an approximate implementation for this kind of QPUF as it approximates a von Neumann measurement on the eigenbasis of the unitary.