A new Definition and Classification of Physical Unclonable Functions

A new definition of “Physical Unclonable Functions” (PUFs), the first one that fully captures its intuitive idea among experts, is presented. A PUF is an information-storage system with a security mechanism that is 1. meant to impede the duplication of a precisely described storage-functionality in another, separate system and 2. remains effective against an attacker with temporary access to the whole original system. A novel classification scheme of the security objectives and mechanisms of PUFs is proposed and its usefulness to aid future research and security evaluation is demonstrated. One class of PUF security mechanisms that prevents an attacker to apply all addresses at which secrets are stored in the information-storage system, is shown to be closely analogous to cryptographic encryption. Its development marks the dawn of a new fundamental primitive of hardware-security engineering: cryptostorage. These results firmly establish PUFs as a fundamental concept of hardware security.

💡 Research Summary

The paper presents a rigorously formulated definition of Physical Unclonable Functions (PUFs) and a comprehensive classification scheme for their security objectives and mechanisms. The authors begin by reviewing prior definitions, which often rely on auxiliary properties such as “hard to characterize,” “hard to predict,” or “physically unclonable.” These definitions suffer from circularity—once a PUF is broken, it ceases to be a PUF—making them unsuitable for certification and comparative analysis.

To resolve these issues, the authors first define a “physical information‑storage system” as a pair of modules: a storage module that maps a physical state H to a challenge C (typically an address) and an encoder module that reproducibly measures H to produce a response R. The set of all (C,R) pairs constitutes the stored information. Building on this, a PUF is defined as such a storage system equipped with a security mechanism that satisfies two conditions: (1) the mechanism’s security objective is to make it more difficult to duplicate the precisely described storage functionality in a separate system; and (2) the mechanism must remain effective even when an attacker gains temporary full physical access to the original device. This definition deliberately separates the objective from the actual effectiveness, avoiding the circularity of earlier work, and introduces the notion of “security‑memory boundedness,” i.e., the security mechanism cannot be detached from the storage mechanism.

The paper then classifies PUFs along two orthogonal dimensions. The first dimension concerns security objectives, distinguishing between preventing physical duplication (D1) and preventing mathematical duplication (D2). Physical duplication means an adversary cannot construct a device that reproduces the exact physical behavior of the original; mathematical duplication means the adversary cannot produce a device that yields identical responses to all challenges, even if the underlying physical structure differs. The authors also identify storage‑functionality classes: S1 (simple trigger or address‑based retrieval) and S2 (time‑constrained release of secrets).

The second dimension addresses the underlying security mechanisms, grouped into three families: (i) Complex Structure (CS) – the traditional approach where manufacturing creates a random, hard‑to‑analyze physical structure; (ii) No Cloning (NC) – mechanisms that rely on fundamental physical laws (e.g., quantum no‑cloning) to forbid duplication; and (iii) Cryptostorage – a novel concept where a subset of challenges (s‑challenges) is kept secret, and the system prevents an attacker from applying all s‑challenges. Cryptostorage is further divided into Minimum Readout Time (MRT) and Erase‑upon‑Readout (EUR). MRT relies on a very large challenge‑response space and a non‑negligible readout latency, making exhaustive probing infeasible. EUR erases the secret response if a non‑authorized challenge is presented, thereby destroying the secret before it can be harvested. The authors argue that cryptostorage is conceptually analogous to cryptographic encryption: both protect information by requiring a secret key (or secret challenge) for successful retrieval.

To illustrate the applicability of their framework, the authors analyze several well‑known PUF instances. The Arbiter PUF is shown to satisfy both the CS mechanism and the D1 objective, while also fitting the S1 storage class. Ring‑Oscillator and SRAM PUFs are mapped to CS with potential MRT extensions, thereby strengthening their resistance to mathematical cloning (D2). Quantum‑based PUFs fall under the NC mechanism, leveraging the no‑cloning theorem. The paper also discusses why conventional tamper‑resistant memories, despite having access control, do not qualify as PUFs because their security is not inseparable from the storage mechanism.

Finally, the authors highlight the broader impact of their work. By providing a minimal yet complete definition, they lay a solid foundation for standardization, certification, and comparative security evaluation of PUFs. The classification clarifies design trade‑offs: designers can select a security objective (physical vs. mathematical duplication) and a mechanism (CS, NC, or cryptostorage) that best matches application requirements. The introduction of cryptostorage as a hardware‑level primitive opens a new research direction, bridging hardware security and cryptography, and suggesting that future PUFs may serve not only as unique identifiers but also as secure, hardware‑bound key storage mechanisms.

Overall, the paper establishes PUFs as a fundamental concept in hardware security, equipped with a clear definition and a versatile taxonomy that can guide both academic research and practical engineering.