Behavioral and Physical Unclonable Functions (BPUFs): SRAM Example

Physical Unclonable Functions (PUFs) have gained a great interest for their capability to identify devices uniquely and to be a lightweight primitive in cryptographic protocols. However, several reported attacks have shown that virtual copies (mathematical clones) as well as physical clones of PUFs are possible, so that they cannot be considered as tamper-resistant or tamper-evident, as claimed. The solution presented in this article is to extend the PUFs reported until now, which are only physical, to make them Behavioral and Physical Unclonable Functions (BPUFs). Given a challenge, BPUFs provide not only a physical but also a behavioral distinctive response caused by manufacturing process variations. Hence, BPUFs are more difficult to attack than PUFs since physical and behavioral responses associated to challenges have to be predicted or cloned. Behavioral responses that are obtained from several measurements of the physical responses taken at several sample times are proposed. In this way, the behavioral responses can detect if the physical responses are manipulated. The analysis done for current PUFs is extended to allow for more versatility in the responses that can be considered in BPUFs. Particularly, Jaccard instead of Hamming distances are proposed to evaluate the similarity of behavioral responses. As example to validate the proposed solution, BPUFs based on Static Random-Access Memories (SRAM BPUFs), with one physical and one behavioral responses to given challenges, were analyzed experimentally using integrated circuits fabricated in a 90-nm CMOS technology. If an attacker succeeds in cloning the physical responses as reported, but does not attack the way to obtain the behavioral responses, the attacker fails on SRAM BPUFs. The highest probability to succeed in cloning the behavioral responses with a brute-force attack was estimated from experimental results as $1.5 \cdot 10^{-34}$ , considering the influence of changes in the operating conditions (power supply voltage, temperature, and aging).