Hybrid Boolean Networks as Physically Unclonable Functions

Abstract

We introduce a Physically Unclonable Function (PUF) based on an ultra-fast chaotic network known as a Hybrid Boolean Network (HBN) implemented on a field programmable gate array. The network, consisting of $N$ coupled asynchronous logic gates displaying dynamics on the sub-nanosecond time scale, acts as a ‘digital fingerprint’ by amplifying small manufacturing variations during a period of transient chaos. In contrast to other PUF designs, we use both $N$ -bits per challenge and obtain $N$ -bits per response by considering challenges to be initial states of the $N$ -node network and responses to be states captured during the subsequent chaotic transient. We find that the presence of chaos amplifies the frozen-in randomness due to manufacturing differences and that the extractable entropy is approximately 50% of the maximum of $N2^{N}$ bits. We obtain PUF uniqueness and reliability metrics $\mu _{inter} = 0.40\pm 0.01$ and $\mu _{intra} = 0.05\pm 0.00$ , respectively, for an $N=256$ network. These metrics correspond to an expected Hamming distance of 102.4 bits per response. Moreover, a simple cherry-picking scheme that discards noisy bits yields $\mu _{intra} < 0.01$ while still retaining $\sim 200$ bits/response (corresponding to a Hamming distance of $\sim 80$ bits/response). In addition to characterizing the uniqueness and reliability, we demonstrate super-exponential scaling in the entropy up to $N=512$ and demonstrate that PUFmeter, a recent PUF analysis tool, is unable to model our PUF. Finally, we characterize the temperature variation of the HBN-PUF and propose future improvements.

Keywords

• Chaos
• physically unclonable function (PUF)
• field programmable gate array (FPGA)
• autonomous Boolean network (ABN)
• hybrid Boolean network (HBN)