  Quantum physical unclonable functions, or QPUFs, are rapidly emerging as
theoretical hardware solutions to provide secure cryptographic functionalities
such as key-exchange, message authentication, entity identification among
others. Recent works have shown that in order to provide provable security of
these solutions against any quantum polynomial time adversary, QPUFs are
required to be a unitary sampled uniformly randomly from the Haar measure. This
however is known to require an exponential amount of resources. In this work,
we propose an efficient construction of these devices using unitary t-designs,
called QPUF_t. Along the way, we modify the existing security definitions of
QPUFs to include efficient constructions and showcase that QPUF_t still retains
the provable security guarantees against a bounded quantum polynomial adversary
with t-query access to the device. This also provides the first use case of
unitary t-design construction for arbitrary t, as opposed to previous
applications of t-designs where usually a few (relatively low) values of t are
known to be useful for performing some task. We study the noise-resilience of
QPUF_t against specific types of noise, unitary noise, and show that some
resilience can be achieved particularly when the error rates affecting
individual qubits become smaller as the system size increases. To make the
noise-resilience more realistic and meaningful, we conclude that some notion of
error mitigation or correction should be introduced.
