Quantum data locking is a unique quantum phenomenon that allows a relatively
short key to (un)lock an arbitrarily long message encoded in a quantum state,
in such a way that an eavesdropper who measures the state but does not know the
key has essentially no information about the encrypted message. The application
of quantum data locking in cryptography would allow one to overcome the
limitations of the one-time pad encryption, which requires the key to have the
same length as the message. However, it is known that the strength of quantum
data locking is also its Achilles heel, as the leakage of a few bits of the key
or the message may in principle allow the eavesdropper to unlock a
disproportionate amount of information. In this paper we show that there exist
quantum data locking schemes that can be made robust against information
leakage by increasing the length of the shared key by a proportionate amount.
This implies that a constant size key can still encrypt an arbitrarily long
message as long as a fraction of it remains secret to the eavesdropper.
Moreover, we greatly simplify the structure of the protocol by proving that
phase modulation suffices to generate strong locking schemes, paving the way to
optical experimental realizations. Also, we show that successful data locking
protocols can be constructed using random codewords, which very well could be
helpful in discovering random codes for data locking over noisy quantum
channels.Comment: A new result on the robustness of quantum data locking has been adde
