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
$sim200$ bits/response (corresponding to a Hamming distance of $sim80$
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.

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