  Quantum data locking is a quantum phenomenon that allows us to encrypt a long
message with a small secret key with information-theoretic security. This is in
sharp contrast with classical information theory where, according to Shannon,
the secret key needs to be at least as long as the message. Here we explore
photonic architectures for quantum data locking, where information is encoded
in multi-photon states and processed using multi-mode linear optics and
photo-detection, with the goal of extending an initial secret key into a longer
one. % The secret key consumption depends on the number of modes and photons
employed. In the no-collision limit, where the likelihood of photon bunching is
suppressed, the key consumption is shown to be logarithmic in the dimensions of
the system. Our protocol can be viewed as an application of the physics of
Boson Sampling to quantum cryptography. Experimental realisations are
challenging but feasible with state-of-the-art technology, as techniques
recently used to demonstrate Boson Sampling can be adapted to our scheme (e.g.,
Phys. Rev. Lett. 123, 250503, 2019).
